From 4ee2b3b6ff57ebf36a8e21e040b6232c6f87cdee Mon Sep 17 00:00:00 2001 From: Brenda Praggastis Date: Wed, 9 Jun 2021 12:12:12 -0700 Subject: [PATCH] updated init to add toys --- docs/build/.buildinfo | 2 +- .../.doctrees/algorithms/algorithms.doctree | Bin 186847 -> 3515 bytes docs/build/.doctrees/classes/classes.doctree | Bin 709526 -> 3610 bytes docs/build/.doctrees/drawing/drawing.doctree | Bin 141915 -> 3657 bytes docs/build/.doctrees/environment.pickle | Bin 329167 -> 54507 bytes docs/build/.doctrees/reports/reports.doctree | Bin 69652 -> 3118 bytes .../_modules/algorithms/homology_mod2.html | 1135 ------- .../algorithms/s_centrality_measures.html | 586 ---- docs/build/_modules/classes/entity.html | 1259 -------- docs/build/_modules/classes/hypergraph.html | 2798 ----------------- docs/build/_modules/classes/staticentity.html | 1294 -------- docs/build/_modules/drawing/rubber_band.html | 715 ----- docs/build/_modules/drawing/two_column.html | 426 --- docs/build/_modules/drawing/util.html | 353 --- docs/build/_modules/index.html | 224 -- .../_modules/reports/descriptive_stats.html | 629 ---- docs/build/_static/documentation_options.js | 2 +- docs/build/algorithms/algorithms.html | 674 +--- docs/build/algorithms/modules.html | 17 +- docs/build/classes/classes.html | 2701 +--------------- docs/build/classes/modules.html | 10 +- docs/build/core.html | 37 +- docs/build/drawing/drawing.html | 443 +-- docs/build/drawing/modules.html | 10 +- docs/build/genindex.html | 656 +--- docs/build/glossary.html | 4 +- docs/build/home.html | 2 +- docs/build/index.html | 2 +- docs/build/install.html | 2 +- docs/build/license.html | 2 +- docs/build/nwhy.html | 2 +- docs/build/objects.inv | Bin 2278 -> 877 bytes docs/build/overview/index.html | 2 +- docs/build/publications.html | 2 +- docs/build/py-modindex.html | 310 -- docs/build/reports/modules.html | 6 +- docs/build/reports/reports.html | 285 +- docs/build/search.html | 2 +- docs/build/searchindex.js | 2 +- docs/build/widget.html | 2 +- docs/source/conf.py | 2 +- setup.py | 2 +- 42 files changed, 96 insertions(+), 14504 deletions(-) delete mode 100644 docs/build/_modules/algorithms/homology_mod2.html delete mode 100644 docs/build/_modules/algorithms/s_centrality_measures.html delete mode 100644 docs/build/_modules/classes/entity.html delete mode 100644 docs/build/_modules/classes/hypergraph.html delete mode 100644 docs/build/_modules/classes/staticentity.html delete mode 100644 docs/build/_modules/drawing/rubber_band.html delete mode 100644 docs/build/_modules/drawing/two_column.html delete mode 100644 docs/build/_modules/drawing/util.html delete mode 100644 docs/build/_modules/index.html delete mode 100644 docs/build/_modules/reports/descriptive_stats.html delete mode 100644 docs/build/py-modindex.html diff --git a/docs/build/.buildinfo b/docs/build/.buildinfo index d47e0bb6..15de628c 100644 --- a/docs/build/.buildinfo +++ b/docs/build/.buildinfo @@ -1,4 +1,4 @@ # Sphinx build info version 1 # This file hashes the configuration used when building these files. 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zsU%ITai0c@aRdT`Mz|J$STDvlYxgSp^8`+?yPu&yKco}3KcPQQZNQ)J(4W&M@n;|X z*@btSyC>5hdV`)zZ`gC`B3YL%nsw=v7dr*!(*8Y{_V>B80N~OB0h28A71;dlJ_8OD z92AxzlYExzZ)grvf3ELu(MKm!m@U-?y*>vT2PNW9$b!mzTr>42JRfWn#^~Z)yQu~| z%X(tup~^iGs&PWL$_nia)sM-r+oRd{q-b3tU diff --git a/docs/build/_modules/algorithms/homology_mod2.html b/docs/build/_modules/algorithms/homology_mod2.html deleted file mode 100644 index ffc33828..00000000 --- a/docs/build/_modules/algorithms/homology_mod2.html +++ /dev/null @@ -1,1135 +0,0 @@ - - - - - - - - - - algorithms.homology_mod2 — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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Source code for algorithms.homology_mod2

-"""
-Homology and Smith Normal Form
-==============================
-The purpose of computing the Homology groups for data generated
-hypergraphs is to identify data sources that correspond to interesting
-features in the topology of the hypergraph.
-
-The elements of one of these Homology groups are generated by $k$
-dimensional cycles of relationships in the original data that are not
-bound together by higher order relationships. Ideally, we want the
-briefest description of these cycles; we want a minimal set of
-relationships exhibiting interesting cyclic behavior. This minimal set
-will be a bases for the Homology group.
-
-The cyclic relationships in the data are discovered using a **boundary
-map** represented as a matrix. To discover the bases we compute the
-**Smith Normal Form** of the boundary map.
-
-Homology Mod2
--------------
-This module computes the homology groups for data represented as an
-abstract simplicial complex with chain groups $\{C_k\}$ and $Z_2$ additions.
-The boundary matrices are represented as rectangular matrices over $Z_2$.
-These matrices are diagonalized and represented in Smith
-Normal Form. The kernel and image bases are computed and the Betti
-numbers and homology bases are returned.
-
-Methods for obtaining SNF for Z/2Z are based on Ferrario's work:
-http://www.dlfer.xyz/post/2016-10-27-smith-normal-form/
-
-"""
-
-import numpy as np
-import hypernetx as hnx
-import warnings
-import copy
-from hypernetx import HyperNetXError
-from collections import defaultdict
-import itertools as it
-import pickle
-from scipy.sparse import csr_matrix
-
-__all__ = [
-    "kchainbasis",
-    "bkMatrix",
-    "swap_rows",
-    "swap_columns",
-    "add_to_row",
-    "add_to_column",
-    "logical_dot",
-    "logical_matmul",
-    "matmulreduce",
-    "logical_matadd",
-    "smith_normal_form_mod2",
-    "reduced_row_echelon_form_mod2",
-    "boundary_group",
-    "chain_complex",
-    "betti",
-    "betti_numbers",
-    "homology_basis",
-    "hypergraph_homology_basis",
-    "interpret",
-]
-
-
-
[docs]def kchainbasis(h, k):
-    """
-    Compute the set of k dimensional cells in the abstract simplicial
-    complex associated with the hypergraph.
-
-    Parameters
-    ----------
-    h : hnx.Hypergraph
-    k : int
-        dimension of cell
-
-    Returns
-    -------
-     : list
-        an ordered list of kchains represented as tuples of length k+1
-
-    See also
-    --------
-    hnx.hypergraph.toplexes
-
-    Notes
-    -----
-    - Method works best if h is simple [Berge], i.e. no edge contains another and there are no duplicate edges (toplexes).
-    - Hypergraph node uids must be sortable.
-
-    """
-
-    import itertools as it
-
-    kchains = set()
-    for e in h.edges():
-        en = sorted(h.edges[e])
-        if len(en) == k + 1:
-            kchains.add(tuple(en))
-        elif len(en) > k + 1:
-            kchains.update(set(it.combinations(en, k + 1)))
-    return sorted(list(kchains))

-
-
-
[docs]def bkMatrix(km1basis, kbasis):
-    """
-    Compute the boundary map from $C_{k-1}$-basis to $C_k$ basis with
-    respect to $Z_2$
-
-    Parameters
-    ----------
-    km1basis : indexable iterable
-        Ordered list of $k-1$ dimensional cell
-    kbasis : indexable iterable
-        Ordered list of $k$ dimensional cells
-
-    Returns
-    -------
-    bk : np.array
-        boundary matrix in $Z_2$ stored as boolean
-
-    """
-    bk = np.zeros((len(km1basis), len(kbasis)), dtype=int)
-    for cell in kbasis:
-        for idx in range(len(cell)):
-            face = cell[:idx] + cell[idx + 1 :]
-            row = km1basis.index(face)
-            col = kbasis.index(cell)
-            bk[row, col] = 1
-    return bk

-
-
-def _rswap(i, j, S):
-    """
-    Swaps ith and jth row of copy of S
-
-    Parameters
-    ----------
-    i : int
-    j : int
-    S : np.array
-
-    Returns
-    -------
-    N : np.array
-    """
-    N = copy.deepcopy(S)
-    row = copy.deepcopy(N[i])
-    N[i] = copy.deepcopy(N[j])
-    N[j] = row
-    return N
-
-
-def _cswap(i, j, S):
-    """
-    Swaps ith and jth column of copy of S
-
-    Parameters
-    ----------
-    i : int
-    j : int
-    S : np.array
-        matrix
-
-    Returns
-    -------
-    N : np.array
-    """
-    N = _rswap(i, j, S.transpose()).transpose()
-    return N
-
-
-
[docs]def swap_rows(i, j, *args):
-    """
-    Swaps ith and jth row of each matrix in args
-    Returns a list of new matrices
-
-    Parameters
-    ----------
-    i : int
-    j : int
-    args : np.arrays
-
-    Returns
-    -------
-    list
-        list of copies of args with ith and jth row swapped
-    """
-    output = list()
-    for M in args:
-        output.append(_rswap(i, j, M))
-    return output

-
-
-
[docs]def swap_columns(i, j, *args):
-    """
-    Swaps ith and jth column of each matrix in args
-    Returns a list of new matrices
-
-    Parameters
-    ----------
-    i : int
-    j : int
-    args : np.arrays
-
-    Returns
-    -------
-    list
-        list of copies of args with ith and jth row swapped
-    """
-    output = list()
-    for M in args:
-        output.append(_cswap(i, j, M))
-    return output

-
-
-
[docs]def add_to_row(M, i, j):
-    """
-    Replaces row i with logical xor between row i and j
-
-    Parameters
-    ----------
-    M : np.array
-    i : int
-        index of row being altered
-    j : int
-        index of row being added to altered
-
-    Returns
-    -------
-    N : np.array
-    """
-    N = copy.deepcopy(M)
-    N[i] = 1 * np.logical_xor(N[i], N[j])
-    return N

-
-
-
[docs]def add_to_column(M, i, j):
-    """
-    Replaces column i (of M) with logical xor between column i and j
-
-    Parameters
-    ----------
-    M : np.array
-        matrix
-    i : int
-        index of column being altered
-    j : int
-        index of column being added to altered
-
-    Returns
-    -------
-    N : np.array
-    """
-    N = M.transpose()
-    return add_to_row(N, i, j).transpose()

-
-
-
[docs]def logical_dot(ar1, ar2):
-    """
-    Returns the boolean equivalent of the dot product mod 2 on two 1-d arrays of
-    the same length.
-
-    Parameters
-    ----------
-    ar1 : numpy.ndarray
-        1-d array
-    ar2 : numpy.ndarray
-        1-d array
-
-    Returns
-    -------
-    : bool
-        boolean value associated with dot product mod 2
-
-    Raises
-    ------
-    HyperNetXError
-        If arrays are not of the same length an error will be raised.
-    """
-    if len(ar1) != len(ar2):
-        raise HyperNetXError("logical_dot requires two 1-d arrays of the same length")
-    else:
-        return 1 * np.logical_xor.reduce(np.logical_and(ar1, ar2))

-
-
-
[docs]def logical_matmul(mat1, mat2):
-    """
-    Returns the boolean equivalent of matrix multiplication mod 2 on two
-    binary arrays stored as type boolean
-
-    Parameters
-    ----------
-    mat1 : np.ndarray
-        2-d array of boolean values
-    mat2 : np.ndarray
-        2-d array of boolean values
-
-    Returns
-    -------
-    mat : np.ndarray
-        boolean matrix equivalent to the mod 2 matrix multiplication of the
-        matrices as matrices over Z/2Z
-
-    Raises
-    ------
-    HyperNetXError
-        If inner dimensions are not equal an error will be raised.
-
-    """
-    L1, R1 = mat1.shape
-    L2, R2 = mat2.shape
-    if R1 != L2:
-        raise HyperNetXError(
-            "logical_matmul called for matrices with inner dimensions mismatched"
-        )
-
-    mat = np.zeros((L1, R2), dtype=int)
-    mat2T = mat2.transpose()
-    for i in range(L1):
-        if np.any(mat1[i]):
-            for j in range(R2):
-                mat[i, j] = logical_dot(mat1[i], mat2T[j])
-        else:
-            mat[i] = np.zeros((1, R2), dtype=int)
-    return mat

-
-
-
[docs]def matmulreduce(arr, reverse=False):
-    """
-    Recursively applies a 'logical multiplication' to a list of boolean arrays.
-
-    For arr = [arr[0],arr[1],arr[2]...arr[n]] returns product arr[0]arr[1]...arr[n]
-    If reverse = True, returns product arr[n]arr[n-1]...arr[0]
-
-    Parameters
-    ----------
-    arr : list of np.array
-        list of nxm matrices represented as np.array
-    reverse : bool, optional
-        order to multiply the matrices
-
-    Returns
-    -------
-    P : np.array
-        Product of matrices in the list
-    """
-    if reverse:
-        items = range(len(arr) - 1, -1, -1)
-    else:
-        items = range(len(arr))
-    P = arr[items[0]]
-    for i in items[1:]:
-        P = logical_matmul(P, arr[i]) * 1
-    return P

-
-
-
[docs]def logical_matadd(mat1, mat2):
-    """
-    Returns the boolean equivalent of matrix addition mod 2 on two
-    binary arrays stored as type boolean
-
-    Parameters
-    ----------
-    mat1 : np.ndarray
-        2-d array of boolean values
-    mat2 : np.ndarray
-        2-d array of boolean values
-
-    Returns
-    -------
-    mat : np.ndarray
-        boolean matrix equivalent to the mod 2 matrix addition of the
-        matrices as matrices over Z/2Z
-
-    Raises
-    ------
-    HyperNetXError
-        If dimensions are not equal an error will be raised.
-
-    """
-    S1 = mat1.shape
-    S2 = mat2.shape
-    mat = np.zeros(S1, dtype=int)
-    if S1 != S2:
-        raise HyperNetXError(
-            "logical_matadd called for matrices with different dimensions"
-        )
-    if len(S1) == 1:
-        for idx in range(S1[0]):
-            mat[idx] = 1 * np.logical_xor(mat1[idx], mat2[idx])
-    else:
-        for idx in range(S1[0]):
-            for jdx in range(S1[1]):
-                mat[idx, jdx] = 1 * np.logical_xor(mat1[idx, jdx], mat2[idx, jdx])
-    return mat

-
-
-# Convenience methods for computing Smith Normal Form
-# All of these operations have themselves as inverses
-
-
-def _sr(i, j, M, L):
-    return swap_rows(i, j, M, L)
-
-
-def _sc(i, j, M, R):
-    return swap_columns(i, j, M, R)
-
-
-def _ar(i, j, M, L):
-    return add_to_row(M, i, j), add_to_row(L, i, j)
-
-
-def _ac(i, j, M, R):
-    return add_to_column(M, i, j), add_to_column(R, i, j)
-
-
-def _get_next_pivot(M, s1, s2=None):
-    """
-    Determines the first r,c indices in the submatrix of M starting
-    with row s1 and column s2 index (row,col) that is nonzero,
-    if it exists.
-
-    Search starts with the s2th column and looks for the first nonzero
-    s1 row. If none is found, search continues to the next column and so
-    on.
-
-    Parameters
-    ----------
-    M : np.array
-        matrix represented as np.array
-    s1 : int
-        index of row position to start submatrix of M
-    s2 : int, optional, default = s1
-        index of column position to start submatrix of M
-
-    Returns
-    -------
-    (r,c) : tuple of int or None
-
-    """
-    # find the next nonzero pivot to put in s,s spot for Smith Normal Form
-    m, n = M.shape
-    if not s2:
-        s2 = s1
-    for c in range(s2, n):
-        for r in range(s1, m):
-            if M[r, c]:
-                return (r, c)
-    return None
-
-
-
[docs]def smith_normal_form_mod2(M):
-    """
-    Computes the invertible transformation matrices needed to compute the
-    Smith Normal Form of M modulo 2
-
-    Parameters
-    ----------
-    M : np.array
-        a rectangular matrix with data type bool
-    track : bool
-        if track=True will print out the transformation as Z/2Z matrix as it
-        discovers L[i] and R[j]
-
-    Returns
-    -------
-    L, R, S, Linv : np.arrays
-        LMR = S is the Smith Normal Form of the matrix M.
-
-    Note
-    ----
-    Given a mxn matrix $M$ with
-    entries in $Z_2$ we start with the equation: $L M R = S$, where
-    $L = I_m$, and $R=I_n$ are identity matrices and $S = M$. We
-    repeatedly apply actions to the left and right side of the equation
-    to transform S into a diagonal matrix.
-    For each action applied to the left side we apply its inverse
-    action to the right side of I_m to generate $L^{-1}$.
-    Finally we verify:
-    $L M R = S$ and  $LLinv = I_m$.
-    """
-
-    S = copy.copy(M)
-    dimL, dimR = M.shape
-
-    # initialize left and right transformations with identity matrices
-    L = np.eye(dimL, dtype=int)
-    R = np.eye(dimR, dtype=int)
-    Linv = np.eye(dimL, dtype=int)
-    for s in range(min(dimL, dimR)):
-        # Find index pair (rdx,cdx) with value 1 in submatrix M[s:,s:]
-        pivot = _get_next_pivot(S, s)
-        if not pivot:
-            break
-        else:
-            rdx, cdx = pivot
-        # Swap rows and columns as needed so that 1 is in the s,s position
-        if rdx > s:
-            S, L = _sr(s, rdx, S, L)
-            Linv = swap_columns(rdx, s, Linv)[0]
-        if cdx > s:
-            S, R = _sc(s, cdx, S, R)
-        # add sth row to every row with 1 in sth column & sth column to every column with 1 in sth row
-        row_indices = [idx for idx in range(s + 1, dimL) if S[idx, s] == 1]
-        for rdx in row_indices:
-            S, L = _ar(rdx, s, S, L)
-            Linv = add_to_column(Linv, s, rdx)
-        column_indices = [jdx for jdx in range(s + 1, dimR) if S[s, jdx] == 1]
-        for cdx in column_indices:
-            S, R = _ac(cdx, s, S, R)
-    return L, R, S, Linv

-
-
-
[docs]def reduced_row_echelon_form_mod2(M):
-    """
-    Computes the invertible transformation matrices needed to compute
-    the reduced row echelon form of M modulo 2
-
-    Parameters
-    ----------
-    M : np.array
-        a rectangular matrix with elements in $Z_2$
-
-    Returns
-    -------
-    L, S, Linv : np.arrays
-        LM = S where S is the reduced echelon form of M
-        and M = LinvS
-    """
-    S = copy.deepcopy(M)
-    dimL, dimR = M.shape
-
-    # method with numpy
-    Linv = np.eye(dimL, dtype=int)
-    L = np.eye(dimL, dtype=int)
-
-    s2 = 0
-    s1 = 0
-    while s2 <= dimR and s1 <= dimL:
-        # Find index pair (rdx,cdx) with value 1 in submatrix M[s1:,s2:]
-        # look for the first 1 in the s2 column
-        pivot = _get_next_pivot(S, s1, s2)
-
-        if not pivot:
-            return L, S, Linv
-        else:
-            rdx, cdx = pivot
-            if rdx > s1:
-                # Swap rows as needed so that 1 leads the row
-                S, L = _sr(s1, rdx, S, L)
-                Linv = swap_columns(rdx, s1, Linv)[0]
-            # add s1th row to every nonzero row
-            row_indices = [
-                idx for idx in range(0, dimL) if idx != s1 and S[idx, cdx] == 1
-            ]
-            for idx in row_indices:
-                S, L = _ar(idx, s1, S, L)
-                Linv = add_to_column(Linv, s1, idx)
-            s1, s2 = s1 + 1, cdx + 1
-
-    return L, S, Linv

-
-
-
[docs]def boundary_group(image_basis):
-    """
-    Returns a csr_matrix with rows corresponding to the elements of the
-    group  generated by image basis over $\mathbb{Z}_2$
-
-    Parameters
-    ----------
-    image_basis : numpy.ndarray or scipy.sparse.csr_matrix
-        2d-array of basis elements
-
-    Returns
-    -------
-     : scipy.sparse.csr_matrix
-    """
-    if len(image_basis) > 10:
-        msg = """
-        This method is inefficient for large image bases.
-        """
-        warnings.warn(msg, stacklevel=2)
-    if np.sum(image_basis) == 0:
-        return None
-    dim = image_basis.shape[0]
-    itm = csr_matrix(list(it.product([0, 1], repeat=dim)))
-    return csr_matrix(np.mod(itm * image_basis, 2))

-
-
-def _compute_matrices_for_snf(bd):
-    """
-    Helper method for smith normal form decomposition for boundary maps
-    associated to chain complex
-
-    Parameters
-    ----------
-    bd : dict
-        dict of k-boundary matrices keyed on dimension of domain
-
-    Returns
-    -------
-    L,R,S,Linv : dict
-        dict of matrices ranging over krange
-
-    """
-    L, R, S, Linv = [dict() for i in range(4)]
-
-    for kdx in bd:
-        L[kdx], R[kdx], S[kdx], Linv[kdx] = smith_normal_form_mod2(bd[kdx])
-    return L, R, S, Linv
-
-
-def _get_krange(max_dim, k=None):
-    """
-    Helper method to compute range of appropriate k dimensions for homology
-    computations given k and the max dimension of a simplicial complex
-    """
-    if k is None:
-        krange = [1, max_dim]
-    elif isinstance(k, int):
-        if k == 0:
-            msg = (
-                "Only kth simplicial homology groups for k>0 may be computed."
-                "If you are interested in k=0, compute the number connected components."
-            )
-            print(msg)
-            return
-        if k > max_dim:
-            msg = f"No simplices of dim {k} exist. k adjusted to max dim."
-            print(msg)
-        krange = [min([k, max_dim])] * 2
-    elif not len(k) == 2:
-        msg = f"Please enter krange as a positive integer or list of integers: [<min k>,<max k>] inclusive."
-        print(msg)
-        return None
-    elif not k[0] <= k[1]:
-        msg = f"k must be an integer or a list of two integers [min,max] with min <=max"
-        print(msg)
-        return None
-    else:
-        krange = k
-
-    if krange[1] > max_dim:
-        msg = f"No simplices of dim {krange[1]} exist. Range adjusted to max dim."
-        print(msg)
-        krange[1] = max_dim
-    if krange[0] < 1:
-        msg = (
-            "Only kth simplicial homology groups for k>0 may be computed."
-            "If you are interested in k=0, compute the number of connected components."
-        )
-        print(msg)
-        krange[0] = 1
-    return krange
-
-
-
[docs]def chain_complex(h, k=None):
-    """
-    Compute the k-chains and k-boundary maps required to compute homology
-    for all values in k
-
-    Parameters
-    ----------
-    h : hnx.Hypergraph
-    k : int or list of length 2, optional, default=None
-        k must be an integer greater than 0 or a list of
-        length 2 indicating min and max dimensions to be
-        computed. eg. if k = [1,2] then 0,1,2,3-chains
-        and boundary maps for k=1,2,3 will be returned,
-        if None than k = [1,max dimension of edge in h]
-
-    Returns
-    -------
-    C, bd : dict
-        C is a dictionary of lists
-        bd is a dictionary of numpy arrays
-    """
-    max_dim = np.max([len(h.edges[e]) for e in h.edges()]) - 1
-    krange = _get_krange(max_dim, k)
-    if not krange:
-        return
-    # Compute chain complex
-
-    C = defaultdict(list)
-    C[krange[0] - 1] = kchainbasis(h, krange[0] - 1)
-    bd = dict()
-    for kdx in range(krange[0], krange[1] + 2):
-        C[kdx] = kchainbasis(h, kdx)
-        bd[kdx] = bkMatrix(C[kdx - 1], C[kdx])
-    return C, bd

-
-
-
[docs]def betti(bd, k=None):
-    """
-    Generate the kth-betti numbers for a chain complex with boundary
-    matrices given by bd
-
-    Parameters
-    ----------
-    bd: dict of k-boundary matrices keyed on dimension of domain
-    k : int, list or tuple, optional, default=None
-        list must be min value and max value of k values inclusive
-        if None, then all betti numbers for dimensions of existing cells will be
-        computed.
-
-    Returns
-    -------
-    betti : dict
-        Description
-    """
-    rank = defaultdict(int)
-    if k:
-        max_dim = max(bd.keys())
-        krange = _get_krange(max_dim, k)
-        if not krange:
-            return
-        kvals = sorted(set(range(krange[0], krange[1] + 2)).intersection(bd.keys()))
-    else:
-        kvals = bd.keys()
-    for kdx in kvals:
-        _, S, _ = hnx.reduced_row_echelon_form_mod2(bd[kdx])
-        rank[kdx] = np.sum(np.sum(S, axis=1).astype(bool))
-
-    betti = dict()
-    for kdx in kvals:
-        if kdx + 1 in kvals:
-            betti[kdx] = bd[kdx].shape[1] - rank[kdx] - rank[kdx + 1]
-        else:
-            continue
-
-    return betti

-
-
-
[docs]def betti_numbers(h, k=None):
-    """
-    Return the kth betti numbers for the simplicial homology of the ASC
-    associated to h
-
-    Parameters
-    ----------
-    h : hnx.Hypergraph
-        Hypergraph to compute the betti numbers from
-    k : int or list, optional, default=None
-        list must be min value and max value of k values inclusive
-        if None, then all betti numbers for dimensions of existing cells will be
-        computed.
-
-    Returns
-    -------
-    betti : dict
-        A dictionary of betti numbers keyed by dimension
-    """
-    _, bd = chain_complex(h, k)
-    return betti(bd)

-
-
-
[docs]def homology_basis(bd, k=None, boundary=False, **kwargs):
-    """
-    Compute a basis for the kth-simplicial homology group, $H_k$, defined by a
-    chain complex $C$ with boundary maps given by bd $= \{k:\partial_k$\}$
-
-    Parameters
-    ----------
-    bd : dict
-        dict of boundary matrices on k-chains to k-1 chains keyed on k
-        if krange is a tuple then all boundary matrices k \in [krange[0],..,krange[1]]
-        inclusive must be in the dictionary
-    k : int or list of ints, optional, default=None
-        k must be a positive integer or a list of
-        2 integers indicating min and max dimensions to be
-        computed, if none given all homology groups will be computed from
-        available boundary matrices in bd
-    boundary : bool
-        option to return a basis for the boundary group from each dimension.
-        Needed to compute the shortest generators in the homology group.
-
-    Returns
-    -------
-    basis : dict
-        dict of generators as 0-1 tuples keyed by dim
-        basis for dimension k will be returned only if bd[k] and bd[k+1] have
-        been provided.
-    im : dict
-        dict of boundary group generators keyed by dim
-    """
-    max_dim = max(bd.keys())
-    if k:
-        krange = _get_krange(max_dim, k)
-        kvals = sorted(
-            set(bd.keys()).intersection(range(krange[0], krange[1] + 2))
-        )  # to get kth dim need k+1 bdry matrix
-    else:
-        kvals = bd.keys()
-
-    L, R, S, Linv = _compute_matrices_for_snf(
-        {k: v for k, v in bd.items() if k in kvals}
-    )
-
-    rank = dict()
-    for kdx in kvals:
-        rank[kdx] = np.sum(S[kdx])
-
-    basis = dict()
-    im = dict()
-    for kdx in kvals:
-        if kdx + 1 not in kvals:
-            continue
-        rank1 = rank[kdx]
-        rank2 = rank[kdx + 1]
-        ker1 = R[kdx][:, rank1:]
-        im2 = Linv[kdx + 1][:, :rank2]
-        cokernel2 = Linv[kdx + 1][:, rank2:]
-        cokproj2 = L[kdx + 1][rank2:, :]
-
-        proj = matmulreduce([cokernel2, cokproj2, ker1]).transpose()
-        _, proj, _ = reduced_row_echelon_form_mod2(proj)
-        # proj = np.array(proj)
-        basis[kdx] = np.array([row for row in proj if np.any(row)])
-        if boundary:
-            im[kdx] = im2.transpose()
-    if boundary:
-        return basis, im
-    else:
-        return basis

-
-
-
[docs]def hypergraph_homology_basis(h, k=None, shortest=False, interpreted=True):
-    """
-    Computes the kth-homology groups mod 2 for the ASC
-    associated with the hypergraph h for k in krange inclusive
-
-    Parameters
-    ----------
-    h : hnx.Hypergraph
-    k : int or list of length 2, optional, default = None
-        k must be an integer greater than 0 or a list of
-        length 2 indicating min and max dimensions to be
-        computed
-    shortest : bool, optional, default=False
-        option to look for shortest representative for each coset in the
-        homology group, only good for relatively small examples
-    interpreted : bool, optional, default = True
-        if True will return an explicit basis in terms of the k-chains
-
-    Returns
-    -------
-    basis : list
-        list of generators as k-chains as boolean vectors
-    interpreted_basis :
-        lists of kchains in basis
-
-    """
-    C, bd = chain_complex(h, k)
-    if shortest:
-        basis = defaultdict(list)
-        tbasis, im = homology_basis(bd, boundary=True)
-        for kdx in tbasis:
-            imgrp = boundary_group(im[kdx])
-            if imgrp is None:
-                basis[kdx] = tbasis[kdx]
-            else:
-                for b in tbasis[kdx]:
-                    coset = np.array(
-                        np.mod(imgrp + b, 2)
-                    )  # dimensions appear to be wrong. See tests2 cell 5
-                    idx = np.argmin(np.sum(coset, axis=1))
-                    basis[kdx].append(coset[idx])
-        basis = dict(basis)
-
-    else:
-        basis = homology_basis(bd)
-
-    if interpreted:
-        interpreted_basis = dict()
-        for kdx in basis:
-            interpreted_basis[kdx] = interpret(C[kdx], basis[kdx], labels=None)
-        return basis, interpreted_basis
-    else:
-        return basis

-
-
-
[docs]def interpret(Ck, arr, labels=None):
-    """
-    Returns the data as represented in Ck associated with the arr
-
-    Parameters
-    ----------
-    Ck : list
-        a list of k-cells being referenced by arr
-    arr : np.array
-        array of 0-1 vectors
-    labels : dict, optional
-        dictionary of labels to associate to the nodes in the cells
-
-    Returns
-    ----
-    : list
-        list of k-cells referenced by data in Ck
-
-    """
-
-    def translate(cell, labels=labels):
-        if not labels:
-            return cell
-        else:
-            temp = list()
-            for node in cell:
-                temp.append(labels[node])
-            return tuple(temp)
-
-    output = list()
-    for vec in arr:
-        if len(Ck) != len(vec):
-            raise HyperNetXError("elements of arr must have the same length as Ck")
-        output.append([translate(Ck[idx]) for idx in range(len(vec)) if vec[idx] == 1])
-    return output

-
- -
- -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_modules/algorithms/s_centrality_measures.html b/docs/build/_modules/algorithms/s_centrality_measures.html deleted file mode 100644 index b3b67d10..00000000 --- a/docs/build/_modules/algorithms/s_centrality_measures.html +++ /dev/null @@ -1,586 +0,0 @@ - - - - - - - - - - algorithms.s_centrality_measures — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Source code for algorithms.s_centrality_measures

-# Copyright © 2018 Battelle Memorial Institute
-# All rights reserved.
-
-"""
-
-S-Centrality Measures
-=====================
-We generalize graph metrics to s-metrics for a hypergraph by using its s-connected
-components. This is accomplished by computing the s edge-adjacency matrix and
-constructing the corresponding graph of the matrix. We then use existing graph metrics
-on this representation of the hypergraph. In essence we construct an *s*-line graph
-corresponding to the hypergraph on which to apply our methods.
-
-S-Metrics for hypergraphs are discussed in depth in:        
-*Aksoy, S.G., Joslyn, C., Ortiz Marrero, C. et al. Hypernetwork science via high-order hypergraph walks.
-EPJ Data Sci. 9, 16 (2020). https://doi.org/10.1140/epjds/s13688-020-00231-0*
-
-"""
-
-import numpy as np
-from collections import defaultdict
-import networkx as nx
-import warnings
-import sys
-from functools import partial
-
-try:
-    import nwhy
-
-    nwhy_available = True
-except:
-    nwhy_available = False
-
-sys.setrecursionlimit(10000)
-
-__all__ = [
-    "s_betweenness_centrality",
-    "s_harmonic_closeness_centrality",
-    "s_harmonic_centrality",
-    "s_closeness_centrality",
-    "s_eccentricity",
-]
-
-
-def _s_centrality(
-    func, H, s=1, edges=True, f=None, return_singletons=True, use_nwhy=True, **kwargs
-):
-    """
-    Wrapper for computing s-centrality either in NetworkX or in NWHy
-
-    Parameters
-    ----------
-    func : function
-        Function or partial function from NetworkX or NWHy
-    H : hnx.Hypergraph
-
-    s : int, optional
-        s-width for computation
-    edges : bool, optional
-        If True, an edge linegraph will be used, otherwise a node linegraph will be used
-    f : str, optional
-        Identifier of node or edge of interest for computing centrality
-    return_singletons : bool, optional
-        If True will return 0 value for each singleton in the s-linegraph
-    use_nwhy : bool, optional
-        If True will attempt to use nwhy centrality methods if availaable
-    **kwargs
-        Centrality metric specific keyword arguments to be passed to func
-
-    Returns
-    : dict
-        dictionary of centrality scores keyed by names
-    """
-    comps = H.s_component_subgraphs(
-        s=s, edges=edges, return_singletons=return_singletons
-    )
-    if f is not None:
-        for cps in comps:
-            if (edges and f in cps.edges) or (not edges and f in cps.nodes):
-                comps = [cps]
-                break
-        else:
-            return {f: 0}
-
-    stats = dict()
-    if H.isstatic:
-        for h in comps:
-            if edges:
-                vertices = h.edges
-            else:
-                vertices = h.nodes
-
-            if h.shape[edges * 1] == 1:
-                stats.update({v: 0 for v in vertices})
-            elif use_nwhy and nwhy_available and h.nwhy:
-                g = h.get_linegraph(s=s, edges=edges, use_nwhy=True)
-                stats.update(dict(zip(vertices, func(g, **kwargs))))
-            else:
-                g = h.get_linegraph(s=s, edges=edges, use_nwhy=False)
-                stats.update(
-                    {
-                        h.get_name(k, edges=edges): v
-                        for k, v in func(g, **kwargs).items()
-                    }
-                )
-            if f:
-                return {f: stats[f]}
-    else:
-        for h in comps:
-            if edges:
-                A, Adict = h.edge_adjacency_matrix(s=s, index=True)
-            else:
-                A, Adict = h.adjacency_matrix(s=s, index=True)
-            A = (A >= s) * 1
-            g = nx.from_scipy_sparse_matrix(A)
-            stats.update({Adict[k]: v for k, v in func(g, **kwargs).items()})
-            if f:
-                return {f: stats[f]}
-
-    return stats
-
-
-
[docs]def s_betweenness_centrality(
-    H, s=1, edges=True, normalized=True, return_singletons=True, use_nwhy=True
-):
-    """
-    A centrality measure for an s-edge(node) subgraph of H based on shortest paths.
-    Equals the betweenness centrality of vertices in the edge(node) s-linegraph.
-
-    In a graph (2-uniform hypergraph) the betweenness centrality of a vertex $v$ 
-    is the ratio of the number of non-trivial shortest paths between any pair of 
-    vertices in the graph that pass through $v$ divided by the total number of 
-    non-trivial shortest paths in the graph.
-
-    The centrality of edge to all shortest s-edge paths
-    $V$ = the set of vertices in the linegraph.  
-    $\sigma(s,t)$ = the number of shortest paths between vertices $s$ and $t$.  
-    $\sigma(s, t|v)$ = the number of those paths that pass through vertex $v$
-    $$c_B(v) =\sum_{s \neq t \in V} \frac{\sigma(s, t|v)}{\sigma(s, t)}$$
-
-    Parameters
-    ----------
-    H : hnx.Hypergraph
-    s : int
-        s connectedness requirement
-    edges : bool, optional
-        determines if edge or node linegraph
-    normalized
-        bool, default=False,
-        If true the betweenness values are normalized by `2/((n-1)(n-2))`,
-        where n is the number of edges in H
-    return_singletons : bool, optional
-        if False will ignore singleton components of linegraph
-
-
-    Returns
-    -------
-     : dict
-        A dictionary of s-betweenness centrality value of the edges.
-
-    """
-    if use_nwhy and nwhy_available and H.nwhy:
-        func = partial(nwhy.Slinegraph.s_betweenness_centrality, normalized=False)
-    else:
-        use_nwhy = False
-        func = partial(nx.betweenness_centrality, normalized=False)
-    result = _s_centrality(
-        func,
-        H,
-        s=s,
-        edges=edges,
-        return_singletons=return_singletons,
-        use_nwhy=use_nwhy,
-    )
-
-    if normalized and H.shape[edges * 1] > 2:
-        n = H.shape[edges * 1]
-        return {k: v * 2 / ((n - 1) * (n - 2)) for k, v in result.items()}
-    else:
-        return result

-
-
-
[docs]def s_closeness_centrality(
-    H, s=1, edges=True, return_singletons=True, source=None, use_nwhy=True
-):
-    """
-    In a connected component the reciprocal of the sum of the distance between an
-    edge(node) and all other edges(nodes) in the component times the number of edges(nodes)
-    in the component minus 1.
-
-    $V$ = the set of vertices in the linegraph.  
-    $n = |V|$
-    $d$ = shortest path distance
-    $$C(u) = \frac{n - 1}{\sum_{v \neq u \in V} d(v, u)}$$
-
-    
-    Parameters
-    ----------
-    H : hnx.Hypergraph
-        
-    s : int, optional
-        
-    edges : bool, optional
-        Indicates if method should compute edge linegraph (default) or node linegraph.
-    return_singletons : bool, optional
-        Indicates if method should return values for singleton components.
-    source : str, optional
-        Identifier of node or edge of interest for computing centrality
-    use_nwhy : bool, optional
-        If true will use the :ref:`NWHy library <nwhy>` if available.
-
-    Returns
-    -------
-     : dict or float
-        returns the s-closeness centrality value of the edges(nodes).
-        If source=None a dictionary of values for each s-edge in H is returned.
-        If source then a single value is returned.
-    """
-    if use_nwhy and nwhy_available and H.nwhy:
-        func = partial(nwhy.Slinegraph.s_closeness_centrality)
-    else:
-        use_nwhy = False
-        func = partial(nx.closeness_centrality)
-    return _s_centrality(
-        func,
-        H,
-        s=s,
-        edges=edges,
-        return_singletons=return_singletons,
-        f=source,
-        use_nwhy=use_nwhy,
-    )

-
-
-
[docs]def s_harmonic_closeness_centrality(H, s=1, edge=None, use_nwhy=True):
-    msg = """
-    s_harmonic_closeness_centrality is being replaced with s_harmonic_centrality 
-    and will not be available in future releases. 
-    """
-    warnings.warn(msg)
-    return s_harmonic_centrality(H, s=s, edges=True, normalized=True, source=edge)

-
-
-
[docs]def s_harmonic_centrality(
-    H,
-    s=1,
-    edges=True,
-    source=None,
-    normalized=False,
-    return_singletons=True,
-    use_nwhy=True,
-):
-    """
-    A centrality measure for an s-edge subgraph of H. A value equal to 1 means the s-edge
-    intersects every other s-edge in H. All values range between 0 and 1.
-    Edges of size less than s return 0. If H contains only one s-edge a 0 is returned.
-
-    The denormalized reciprocal of the harmonic mean of all distances from $u$ to all other vertices.  
-    $V$ = the set of vertices in the linegraph.
-    $d$ = shortest path distance
-    $$C(u) = \sum_{v \neq u \in V} \frac{1}{d(v, u)}$$
-
-    Normalized this becomes:
-    $$C(u) = \sum_{v \neq u \in V} \frac{1}{d(v, u)}\cdot\frac{2}{(n-1)(n-2)}$$
-    where $n$ is the number vertices.
-
-    Parameters
-    ----------
-    H : hnx.Hypergraph
-        
-    s : int, optional
-        
-    edges : bool, optional
-        Indicates if method should compute edge linegraph (default) or node linegraph.
-    return_singletons : bool, optional
-        Indicates if method should return values for singleton components.
-    source : str, optional
-        Identifier of node or edge of interest for computing centrality
-    use_nwhy : bool, optional
-        If true will use the :ref:`NWHy library <nwhy>` if available.
-
-    Returns
-    -------
-     : dict or float
-        returns the s-harmonic closeness centrality value of the edges, a number between 0 and 1 inclusive.
-        If source=None a dictionary of values for each s-edge in H is returned.
-        If source then a single value is returned.
-
-    """
-
-    if use_nwhy and nwhy_available and H.nwhy:
-        func = partial(nwhy.Slinegraph.s_harmonic_closeness_centrality)
-    else:
-        use_nwhy = False
-        func = partial(nx.harmonic_centrality)
-    result = _s_centrality(
-        func,
-        H,
-        s=s,
-        edges=edges,
-        return_singletons=return_singletons,
-        f=source,
-        use_nwhy=use_nwhy,
-    )
-
-    if normalized and H.shape[edges * 1] > 2:
-        n = H.shape[edges * 1]
-        return {k: v * 2 / ((n - 1) * (n - 2)) for k, v in result.items()}
-    else:
-        return result

-
-
-
[docs]def s_eccentricity(
-    H, s=1, edges=True, source=None, return_singletons=True, use_nwhy=True
-):
-    """
-    The length of the longest shortest path from a vertex $u$ to every other vertex in the linegraph.  
-    $V$ = set of vertices in the linegraph
-    $d$ = shortest path distance
-    $$ \text{s-ecc}(u) = \text{max}\{d(u,v): v \in V\} $$
-
-    Parameters
-    ----------
-    H : hnx.Hypergraph
-        
-    s : int, optional
-        
-    edges : bool, optional
-        Indicates if method should compute edge linegraph (default) or node linegraph.
-    return_singletons : bool, optional
-        Indicates if method should return values for singleton components.
-    source : str, optional
-        Identifier of node or edge of interest for computing centrality
-    use_nwhy : bool, optional
-        If true will use the :ref:`NWHy library <nwhy>` if available.
-
-    Returns
-    -------
-     : dict or float
-        returns the s-eccentricity value of the edges(nodes).
-        If source=None a dictionary of values for each s-edge in H is returned.
-        If source then a single value is returned.
-
-    """
-    if use_nwhy and nwhy_available and H.nwhy:
-        func = nwhy.Slinegraph.s_eccentricity
-    else:
-        use_nwhy = False
-        func = nx.eccentricity
-
-    if source is not None:
-        return _s_centrality(
-            func,
-            H,
-            s=s,
-            edges=edges,
-            f=source,
-            return_singletons=return_singletons,
-            use_nwhy=use_nwhy,
-        )
-    else:
-        return _s_centrality(
-            func,
-            H,
-            s=s,
-            edges=edges,
-            return_singletons=return_singletons,
-            use_nwhy=use_nwhy,
-        )

-
- -
- -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_modules/classes/entity.html b/docs/build/_modules/classes/entity.html deleted file mode 100644 index c240bd16..00000000 --- a/docs/build/_modules/classes/entity.html +++ /dev/null @@ -1,1259 +0,0 @@ - - - - - - - - - - classes.entity — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Source code for classes.entity

-# Copyright © 2018 Battelle Memorial Institute
-# All rights reserved.
-
-from collections import defaultdict
-import warnings
-from copy import copy
-import numpy as np
-import networkx as nx
-from hypernetx import HyperNetXError
-
-__all__ = ["Entity", "EntitySet"]
-
-
-
[docs]class Entity(object):
-    """
-    Base class for objects used in building network-like objects including
-    Hypergraphs, Posets, Cell Complexes.
-
-    Parameters
-    ----------
-    uid : hashable
-        a unique identifier
-
-    elements : list or dict, optional, default: None
-        a list of entities with identifiers different than uid and/or
-        hashables different than uid, see `Honor System`_
-
-    entity : Entity
-        an Entity object to be cloned into a new Entity with uid. If the uid is the same as
-        Entity.uid then the entities will not be distinguishable and error will be raised.
-        The `elements` in the signature will be added to the cloned entity.
-
-    props : keyword arguments, optional, default: {}
-        properties belonging to the entity added as key=value pairs.
-        Both key and value must be hashable.
-
-    Notes
-    -----
-
-    An Entity is a container-like object, which has a unique identifier and
-    may contain elements and have properties.
-    The Entity class was created as a generic object providing structure for
-    Hypergraph nodes and edges.
-
-    - An Entity is distinguished by its identifier (sortable,hashable) :func:`Entity.uid`
-    - An Entity is a container for other entities but may not contain itself, :func:`Entity.elements`
-    - An Entity has properties :func:`Entity.properties`
-    - An Entity has memberships to other entities, :func:`Entity.memberships`.
-    - An Entity has children, :func:`Entity.children`, which are the elements of its elements.
-    - :func:`Entity.children` are registered in the :func:`Entity.registry`.
-    - All descendents of Entity are registered in :func:`Entity.fullregistry()`.
-
-    .. _Honor System:
-
-    **Honor System**
-
-    HyperNetX has an Honor System that applies to Entity uid values.
-    Two entities are equal if their __dict__ objects match.
-    For performance reasons many methods distinguish entities by their uids.
-    It is, therefore, up to the user to ensure entities with the same uids are indeed the same.
-    Not doing so may cause undesirable side effects.
-    In particular, the methods in the Hypergraph class assume distinct nodes and edges
-    have distinct uids.
-
-    Examples
-    --------
-
-        >>> x = Entity('x')
-        >>> y = Entity('y',[x])
-        >>> z = Entity('z',[x,y],weight=1)
-        >>> z
-        Entity(z,['y', 'x'],{'weight': 1})
-        >>> z.uid
-        'z'
-        >>> z.elements
-        {'x': Entity(x,[],{}), 'y': Entity(y,['x'],{})}
-        >>> z.properties
-        {'weight': 1}
-        >>> z.children
-        {'x'}
-        >>> x.memberships
-        {'y': Entity(y,['x'],{}), 'z': Entity(z,['y', 'x'],{'weight': 1})}
-        >>> z.fullregistry()
-        {'x': Entity(x,[],{}), 'y': Entity(y,['x'],{})}
-
-
-    See Also
-    --------
-    EntitySet
-
-    """
-
-    def __init__(self, uid, elements=[], entity=None, **props):
-        super().__init__()
-
-        self._uid = uid
-
-        if entity is not None:
-            if isinstance(entity, Entity):
-                if uid == entity.uid:
-                    raise HyperNetXError(
-                        "The new entity will be indistinguishable from the original with the same uid. Use a differen uid."
-                    )
-                self._elements = entity.elements
-                self._memberships = entity.memberships
-                self.__dict__.update(entity.properties)
-        else:
-            self._elements = dict()
-            self._memberships = dict()
-            self._registry = dict()
-
-        self.__dict__.update(props)
-        self._registry = self.registry
-
-        if isinstance(elements, dict):
-            for k, v in elements.items():
-                if isinstance(v, Entity):
-                    self.add_element(v)
-                else:
-                    self.add_element(Entity(k, v))
-        elif elements is not None:
-            self.add(*elements)
-
-    @property
-    def properties(self):
-        """Dictionary of properties of entity"""
-        temp = self.__dict__.copy()
-        del temp["_elements"]
-        del temp["_memberships"]
-        del temp["_registry"]
-        del temp["_uid"]
-        return temp
-
-    @property
-    def uid(self):
-        """String identifier for entity"""
-        return self._uid
-
-    @property
-    def elements(self):
-        """
-        Dictionary of elements belonging to entity.
-        """
-        return dict(self._elements)
-
-    @property
-    def memberships(self):
-        """
-        Dictionary of elements to which entity belongs.
-
-        This assignment is done on construction and controlled by
-        :func:`Entity.add_element()`
-        and :func:`Entity.remove_element()` methods.
-        """
-
-        return {
-            k: self._memberships[k]
-            for k in self._memberships
-            if not isinstance(self._memberships[k], EntitySet)
-        }
-
-    @property
-    def children(self):
-        """
-        Set of uids of the elements of elements of entity.
-
-        To return set of ids for deeper level use:
-        :code:`Entity.levelset(level).keys()`
-        see: :func:`Entity.levelset`
-        """
-        return set(self.levelset(2).keys())
-
-    @property
-    def registry(self):
-        """
-        Dictionary of uid:Entity pairs for children entity.
-
-        To return a dictionary of all entities at all depths
-        :func:`Entity.complete_registry()`
-        """
-        return self.levelset(2)
-
-    @property
-    def uidset(self):
-        """
-        Set of uids of elements of entity.
-        """
-        return frozenset(self._elements.keys())
-
-    @property
-    def incidence_dict(self):
-        """
-        Dictionary of element.uid:element.uidset for each element in entity
-
-        To return an incidence dictionary of all nested entities in entity
-        use nested_incidence_dict
-        """
-        temp = dict()
-        for ent in self.elements.values():
-            temp[ent.uid] = {item for item in ent.elements}
-        return temp
-
-    @property
-    def is_empty(self):
-        """Boolean indicating if entity.elements is empty"""
-        return len(self) == 0
-
-    @property
-    def is_bipartite(self):
-        """
-        Returns boolean indicating if the entity satisfies the `Bipartite Condition`_
-        """
-        if self.uidset.isdisjoint(self.children):
-            return True
-        else:
-            return False
-
-    def __eq__(self, other):
-        """
-        Defines equality for Entities based on equivalence of their __dict__ objects.
-
-        Checks all levels of self and other to verify they are
-        referencing the same uids and that they have the same set of properties.
-        If at any point we get duplicate addresses we stop checking that branch
-        because we are guaranteed equality from there on.
-
-        May cause a recursion error if depth is too great.
-        """
-        seen = set()
-        # Define a compare method to call recursively on each level of self and other
-
-        def _comp(a, b, seen):
-            # Compare top level properties: same class? same ids? same children? same parents? same attributes?
-            if (
-                (a.__class__ != b.__class__)
-                or (a.uid != b.uid)
-                or (a.uidset != b.uidset)
-                or (a.properties != b.properties)
-                or (a.memberships != b.memberships)
-            ):
-                return False
-            # If all agree then look at the next level down since a and b share uidsets.
-            for uid, elt in a.elements.items():
-                if isinstance(elt, Entity):
-                    if uid in seen:
-                        continue
-                    seen.add(uid)
-                    if not _comp(elt, b[uid], seen):
-                        return False
-                # if not an Entity then elt is hashable so we usual equality
-                elif elt != b[uid]:
-                    return False
-            return True
-
-        return _comp(self, other, seen)
-
-    def __len__(self):
-        """Returns the number of elements in entity"""
-        return len(self._elements)
-
-    def __str__(self):
-        """Return the entity uid."""
-        return f"{self.uid}"
-
-    def __repr__(self):
-        """Returns a string resembling the constructor for entity without any
-        children"""
-        return f"Entity({self._uid},{list(self.uidset)},{self.properties})"
-
-    def __contains__(self, item):
-        """
-        Defines containment for Entities.
-
-        Parameters
-        ----------
-        item : hashable or Entity
-
-        Returns
-        -------
-        Boolean
-
-        Depends on the `Honor System`_ . Allows for uids to be used as shorthand for their entity.
-        This is done for performance reasons, but will fail if uids are
-        not unique to their entities.
-        Is not transitive.
-        """
-        if isinstance(item, Entity):
-            return item.uid in self._elements
-        else:
-            return item in self._elements
-
-    def __getitem__(self, item):
-        """
-        Returns Entity element by uid. Use :func:`E[uid]`.
-
-        Parameters
-        ----------
-        item : hashable or Entity
-
-        Returns
-        -------
-        Entity or None
-
-        If item not in entity, returns None.
-        """
-        if isinstance(item, Entity):
-            return self._elements.get(item.uid, "")
-        else:
-            return self._elements.get(item)
-
-    def __iter__(self):
-        """Returns iterator on element ids."""
-        return iter(self.elements)
-
-    def __call__(self):
-        """Returns an iterator on elements"""
-        for e in self.elements.values():
-            yield e
-
-    def __setattr__(self, k, v):
-        """Sets entity property.
-
-        Parameters
-        ----------
-        k : hashable, property key
-        v : hashable, property value
-            Will not set uid or change elements or memberships.
-
-        Returns
-        -------
-        None
-
-        """
-        if k == "uid":
-            raise HyperNetXError(
-                "Cannot reassign uid to Entity once it"
-                " has been created. Create a clone instead."
-            )
-        elif k == "elements":
-            raise HyperNetXError("To add elements to Entity use self.add().")
-        elif k == "memberships":
-            raise HyperNetXError(
-                "Can't choose your own memberships, " "they are like parents!"
-            )
-        else:
-            self.__dict__[k] = v
-
-    def _depth_finder(self, entset=None):
-        """
-        Helper method when working with levels.
-
-        Parameters
-        ----------
-        entset : dict, optional
-            a dictionary of entities keyed by uid
-
-        Returns
-        -------
-        Dictionary extending entset
-        """
-        temp = dict()
-        for uid, item in entset.items():
-            temp.update(item.elements)
-        return temp
-
-
[docs]    def level(self, item, max_depth=10):
-        """
-        The first level where item appears in self.
-
-        Parameters
-        ----------
-        item : hashable
-            uid for an entity
-
-        max_depth : int, default: 10
-            last level to check for entity
-
-        Returns
-        -------
-        level : int
-
-        Note
-        ----
-        Item must be the uid of an entity listed
-        in :func:`fullregistry()`
-        """
-        d = 1
-        currentlevel = self.levelset(1)
-        while d <= max_depth + 1:
-            if item in currentlevel:
-                return d
-            else:
-                d += 1
-                currentlevel = self._depth_finder(currentlevel)
-        return None

-
-
[docs]    def levelset(self, k=1):
-        """
-        A dictionary of level k of self.
-
-        Parameters
-        ----------
-        k : int, optional, default: 1
-
-        Returns
-        -------
-        levelset : dict
-
-        Note
-        ----
-        An Entity contains other entities, hence the relationships between entities
-        and their elements may be represented in a directed graph with entity as root.
-        The levelsets are sets of entities which make up the elements appearing at
-        a certain level.
-        """
-        if k <= 0:
-            return None
-        currentlevel = self.elements
-        if k > 1:
-            for idx in range(k - 1):
-                currentlevel = self._depth_finder(currentlevel)
-        return currentlevel

-
-
[docs]    def depth(self, max_depth=10):
-        """
-        Returns the number of nonempty level sets of level <= max_depth
-
-        Parameters
-        ----------
-        max_depth : int, optional, default: 10
-            If full depth is desired set max_depth to number of entities in
-            system + 1.
-
-        Returns
-        -------
-        depth : int
-            If max_depth is exceeded output will be numpy infinity.
-            If there is a cycle output will be numpy infinity.
-
-        """
-        if max_depth < 0:
-            return 0
-        currentlevel = self.elements
-        if not currentlevel:
-            return 0
-        else:
-            depth = 1
-        while depth < max_depth + 1:
-            currentlevel = self._depth_finder(currentlevel)
-            if not currentlevel:
-                return depth
-            depth += 1
-        return np.inf

-
-
[docs]    def fullregistry(self, lastlevel=10, firstlevel=1):
-        """
-        A dictionary of all entities appearing in levels firstlevel
-        to lastlevel.
-
-        Parameters
-        ----------
-        lastlevel : int, optional, default: 10
-
-        firstlevel : int, optional, default: 1
-
-        Returns
-        -------
-        fullregistry : dict
-
-        """
-        currentlevel = self.levelset(firstlevel)
-        accumulater = dict(currentlevel)
-        for idx in range(firstlevel, lastlevel):
-            currentlevel = self._depth_finder(currentlevel)
-            accumulater.update(currentlevel)
-        return accumulater

-
-
[docs]    def complete_registry(self):
-        """
-        A dictionary of all entities appearing in any level of
-        entity
-
-        Returns
-        -------
-        complete_registry : dict
-        """
-        results = dict()
-        Entity._complete_registry(self, results)
-        return results

-
-    @staticmethod
-    def _complete_registry(entity, results):
-        """
-        Helper method for complete_registry
-        """
-        for uid, e in entity.elements.items():
-            if uid not in results:
-                results[uid] = e
-                Entity._complete_registry(e, results)
-
-
[docs]    def nested_incidence_dict(self, level=10):
-        """
-        Returns a nested dictionary with keys up to level
-
-        Parameters
-        ----------
-        level : int, optional, default: 10
-            If level<=1, returns the incidence_dict.
-
-        Returns
-        -------
-        nested_incidence_dict : dict
-
-        """
-        if level > 1:
-            return {ent.uid: ent.nested_incidence_dict(level - 1) for ent in self()}
-        else:
-            return self.incidence_dict

-
-
[docs]    def size(self):
-        """
-        Returns the number of elements in entity
-        """
-        return len(self)

-
-
[docs]    def clone(self, newuid):
-        """
-        Returns shallow copy of entity with newuid. Entity's elements will
-        belong to two distinct Entities.
-
-        Parameters
-        ----------
-        newuid : hashable
-            Name of the new entity
-
-        Returns
-        -------
-        clone : Entity
-
-        """
-        return Entity(newuid, entity=self)

-
-
[docs]    def intersection(self, other):
-        """
-        A dictionary of elements belonging to entity and other.
-
-        Parameters
-        ----------
-        other : Entity
-
-        Returns
-        -------
-        Dictionary of elements : dict
-
-        """
-        return {e: self[e] for e in self if e in other}

-
-
[docs]    def restrict_to(self, element_subset, name=None):
-        """
-        Shallow copy of entity removing elements not in element_subset.
-
-        Parameters
-        ----------
-        element_subset : iterable
-            A subset of entities elements
-
-        name: hashable, optional
-            If not given, a name is generated to reflect entity uid
-
-        Returns
-        -------
-        New Entity : Entity
-            Could be empty.
-
-        """
-        newelements = [self[e] for e in element_subset if e in self]
-        name = name or f"{self.uid}_r"
-        return Entity(name, newelements, **self.properties)

-
-
[docs]    def add(self, *args):
-        """
-        Adds unpacked args to entity elements. Depends on add_element()
-
-        Parameters
-        ----------
-        args : One or more entities or hashables
-
-        Returns
-        -------
-        self : Entity
-
-        Note
-        ----
-        Adding an element to an object in a hypergraph will not add the
-        element to the hypergraph and will cause an error. Use :func:`Hypergraph.add_edge <classes.hypergraph.Hypergraph.add_edge>`
-        or :func:`Hypergraph.add_node_to_edge <classes.hypergraph.Hypergraph.add_node_to_edge>` instead.
-
-        """
-        for item in args:
-            self.add_element(item)
-
-        return self

-
-
[docs]    def add_elements_from(self, arg_set):
-        """
-        Similar to :func:`add()` it allows for adding from an interable.
-
-        Parameters
-        ----------
-        arg_set : Iterable of hashables or entities
-
-        Returns
-        -------
-        self : Entity
-
-        """
-        for item in arg_set:
-            self.add_element(item)
-
-        return self

-
-
[docs]    def add_element(self, item):
-        """
-        Adds item to entity elements and adds entity to item.memberships.
-
-        Parameters
-        ----------
-        item : hashable or Entity
-            If hashable, will be replaced with empty Entity using hashable as uid
-
-        Returns
-        -------
-        self : Entity
-
-        Notes
-        -----
-        If item is in entity elements, no new element is added but properties
-        will be updated.
-        If item is in complete_registry(), only the item already known to self will be added.
-        This method employs the `Honor System`_ since membership in complete_registry is checked
-        using the item's uid. It is assumed that the user will only use the same uid
-        for identical instances within the entities registry.
-
-        """
-        checkelts = self.complete_registry()
-        if isinstance(item, Entity):
-            # if item is an Entity, descendents will be compared to avoid collisions
-            if item.uid == self.uid:
-                raise HyperNetXError(
-                    f"Error: Self reference in submitted elements."
-                    f" Entity {self.uid} may not contain itself. "
-                )
-            elif item in self:
-                # item is already an element so only the properties will be updated
-                checkelts[item.uid].__dict__.update(item.properties)
-            elif item.uid in checkelts:
-                # if item belongs to an element or a descendent of an element
-                # then the existing descendent becomes an element
-                # and properties are updated.
-                checkelts[item.uid]._memberships[self.uid] = self
-                checkelts[item.uid].__dict__.update(item.properties)
-                self._elements[item.uid] = checkelts[item.uid]
-            else:
-                # if item's uid doesn't appear in complete_registry
-                # then it is added as something new
-                item._memberships[self.uid] = self
-                self._elements[item.uid] = item
-        else:
-            # item must be a hashable.
-            # if it appears as a uid in checkelts then
-            # the corresponding Entity will become an element of entity.
-            # Otherwise, at most it will be added as an empty Entity.
-            if self.uid == item:
-                raise HyperNetXError(
-                    f"Error: Self reference in submitted elements."
-                    f" Entity {self.uid} may not contain itself."
-                )
-            elif item not in self._elements:
-                if item in checkelts:
-                    self._elements[item] = checkelts[item]
-                    checkelts[item]._memberships[self.uid] = self
-                else:
-                    self._elements[item] = Entity(item, _memberships={self.uid: self})
-
-        return self

-
-
[docs]    def remove(self, *args):
-        """
-        Removes args from entitie's elements if they belong.
-        Does nothing with args not in entity.
-
-        Parameters
-        ----------
-        args : One or more hashables or entities
-
-        Returns
-        -------
-        self : Entity
-
-
-        """
-        for item in args:
-            Entity.remove_element(self, item)
-        return self

-
-
[docs]    def remove_elements_from(self, arg_set):
-        """
-        Similar to :func:`remove()`. Removes elements in arg_set.
-
-        Parameters
-        ----------
-        arg_set : Iterable of hashables or entities
-
-        Returns
-        -------
-        self : Entity
-
-        """
-        for item in arg_set:
-            Entity.remove_element(self, item)
-        return self

-
-
[docs]    def remove_element(self, item):
-        """
-        Removes item from entity and reference to entity from
-        item.memberships
-
-        Parameters
-        ----------
-        item : Hashable or Entity
-
-        Returns
-        -------
-        self : Entity
-
-
-        """
-        if isinstance(item, Entity):
-            del item._memberships[self.uid]
-            del self._elements[item.uid]
-        else:
-            del self[item]._memberships[self.uid]
-            del self._elements[item]
-
-        return self

-
-
[docs]    @staticmethod
-    def merge_entities(name, ent1, ent2):
-        """
-        Merge two entities making sure they do not conflict.
-
-        Parameters
-        ----------
-        name : hashable
-
-        ent1 : Entity
-            First entity to have elements and properties added to new
-            entity
-
-        ent2 : Entity
-            elements of ent2 will be checked against ent1.complete_registry()
-            and only nonexisting elements will be added using add() method.
-            Properties of ent2 will update properties of ent1 in new entity.
-
-        Returns
-        -------
-        a new entity : Entity
-
-        """
-        newent = ent1.clone(name)
-        newent.add_elements_from(ent2.elements.values())
-        for k, v in ent2.properties.items():
-            newent.__setattr__(k, v)
-        return newent

-
-
-
[docs]class EntitySet(Entity):
-    """
-    .. _entityset:
-
-    Parameters
-    ----------
-    uid : hashable
-        a unique identifier
-
-    elements : list or dict, optional, default: None
-        a list of entities with identifiers different than uid and/or
-        hashables different than uid, see `Honor System`_
-
-    props : keyword arguments, optional, default: {}
-        properties belonging to the entity added as key=value pairs.
-        Both key and value must be hashable.
-
-    Notes
-    -----
-    The EntitySet class was created to distinguish Entities satifying the Bipartite Condition.
-
-    .. _Bipartite Condition:
-
-    **Bipartite Condition**
-
-    *Entities that are elements of the same EntitySet, may not contain each other as elements.*
-    The elements and children of an EntitySet generate a specific partition for a bipartite graph.
-    The partition is isomorphic to a Hypergraph where the elements correspond to hyperedges and
-    the children correspond to the nodes. EntitySets are the basic objects used to construct hypergraphs
-    in HNX.
-
-    Example: ::
-
-        >>> y = Entity('y')
-        >>> x = Entity('x')
-        >>> x.add(y)
-        >>> y.add(x)
-        >>> w = EntitySet('w',[x,y])
-        HyperNetXError: Error: Fails the Bipartite Condition for EntitySet.
-        y references a child of an existing Entity in the EntitySet.
-
-    """
-
-    def __init__(self, uid, elements=[], **props):
-        super().__init__(uid, elements, **props)
-        if not self.is_bipartite:
-            raise HyperNetXError(
-                "Entity does not satisfy the Bipartite Condition, elements and children are not disjoint."
-            )
-
-    def __str__(self):
-        """Return the entityset uid."""
-        return f"{self.uid}"
-
-    def __repr__(self):
-        """Returns a string resembling the constructor for entityset without any
-        children"""
-        return f"EntitySet({self._uid},{list(self.uidset)},{self.properties})"
-
-
[docs]    def add(self, *args):
-        """
-        Adds args to entityset's elements, checking to make sure no self references are
-        made to element ids.
-        Ensures Bipartite Condition of EntitySet.
-
-        Parameters
-        ----------
-        args : One or more entities or hashables
-
-        Returns
-        -------
-        self : EntitySet
-
-        """
-        for item in args:
-            if isinstance(item, Entity):
-                if item.uid in self.children:
-                    raise HyperNetXError(
-                        f"Error: Fails the Bipartite Condition for EntitySet. {item.uid} references a child of an existing Entity in the EntitySet."
-                    )
-                elif not self.uidset.isdisjoint(item.uidset):
-                    raise HyperNetXError(
-                        f"Error: Fails the bipartite condition for EntitySet."
-                    )
-                else:
-                    Entity.add_element(self, item)
-            else:
-                if not item in self.children:
-                    Entity.add_element(self, item)
-                else:
-                    raise HyperNetXError(
-                        f"Error: {item} references a child of an existing Entity in the EntitySet."
-                    )
-        return self

-
-
[docs]    def clone(self, newuid):
-        """
-        Returns shallow copy of entityset with newuid. Entityset's
-        elements will belong to two distinct entitysets.
-
-
-        Parameters
-        ----------
-        newuid : hashable
-            Name of the new entityset
-
-        Returns
-        -------
-        clone : EntitySet
-
-        """
-        return EntitySet(newuid, elements=self.elements.values(), **self.properties)

-
-
[docs]    def collapse_identical_elements(self, newuid, return_equivalence_classes=False):
-        """
-        Returns a deduped copy of the entityset, using representatives of equivalence classes as element keys.
-        Two elements of an EntitySet are collapsed if they share the same children.
-
-        Parameters
-        ----------
-        newuid : hashable
-
-        return_equivalence_classes : boolean, default=False
-            If True, return a dictionary of equivalence classes keyed by new edge names
-
-        Returns
-        -------
-         : EntitySet
-        eq_classes : dict
-            if return_equivalence_classes = True
-
-        Notes
-        -----
-        Treats elements of the entityset as equal if they have the same uidsets. Using this
-        as an equivalence relation, the entityset's uidset is partitioned into equivalence classes.
-        The equivalent elements are identified using a single entity by using the
-        frozenset of uids associated to these elements as the uid for the new element
-        and dropping the properties.
-        If use_reps is set to True a representative element of the equivalence class is
-        used as identifier instead of the frozenset.
-
-        Example: ::
-
-            >>> E = EntitySet('E',elements=[Entity('E1', ['a','b']),Entity('E2',['a','b'])])
-            >>> E.incidence_dict
-            {'E1': {'a', 'b'}, 'E2': {'a', 'b'}}
-            >>> E.collapse_identical_elements('_',).incidence_dict
-            {'E2': {'a', 'b'}}
-
-        """
-
-        shared_children = defaultdict(set)
-        for e in self.__call__():
-            shared_children[frozenset(e.uidset)].add(e.uid)
-        new_entity_dict = {
-            f"{next(iter(v))}:{len(v)}": set(k) for k, v in shared_children.items()
-        }
-        if return_equivalence_classes:
-            eq_classes = {
-                f"{next(iter(v))}:{len(v)}": v for k, v in shared_children.items()
-            }
-            return EntitySet(newuid, new_entity_dict), dict(eq_classes)
-        else:
-            return EntitySet(newuid, new_entity_dict)

-
-
[docs]    def incidence_matrix(self, sparse=True, index=False):
-        """
-        An incidence matrix for the EntitySet indexed by children x uidset.
-
-        Parameters
-        ----------
-        sparse : boolean, optional, default: True
-
-        index : boolean, optional, default False
-            If True return will include a dictionary of children uid : row number
-            and element uid : column number
-
-        Returns
-        -------
-        incidence_matrix : scipy.sparse.csr.csr_matrix or np.ndarray
-
-        row dictionary : dict
-            Dictionary identifying row with item in entityset's children
-
-        column dictionary : dict
-            Dictionary identifying column with item in entityset's uidset
-
-        Notes
-        -----
-
-        Example: ::
-
-            >>> E = EntitySet('E',{'a':{1,2,3},'b':{2,3},'c':{1,4}})
-            >>> E.incidence_matrix(sparse=False, index=True)
-            (array([[0, 1, 1],
-                    [1, 1, 0],
-                    [1, 1, 0],
-                    [0, 0, 1]]), {0: 1, 1: 2, 2: 3, 3: 4}, {0: 'b', 1: 'a', 2: 'c'})
-        """
-        if sparse:
-            from scipy.sparse import csr_matrix
-
-        nchildren = len(self.children)
-        nuidset = len(self.uidset)
-
-        ndict = dict(zip(self.children, range(nchildren)))
-        edict = dict(zip(self.uidset, range(nuidset)))
-
-        if len(ndict) != 0:
-
-            if index:
-                rowdict = {v: k for k, v in ndict.items()}
-                coldict = {v: k for k, v in edict.items()}
-
-            if sparse:
-                # Create csr sparse matrix
-                rows = list()
-                cols = list()
-                data = list()
-                for e in self:
-                    for n in self[e].elements:
-                        data.append(1)
-                        rows.append(ndict[n])
-                        cols.append(edict[e])
-                MP = csr_matrix((data, (rows, cols)))
-            else:
-                # Create an np.matrix
-                MP = np.zeros((nchildren, nuidset), dtype=int)
-                for e in self:
-                    for n in self[e].elements:
-                        MP[ndict[n], edict[e]] = 1
-            if index:
-                return MP, rowdict, coldict
-            else:
-                return MP
-        else:
-            if index:
-                return np.zeros(1), {}, {}
-            else:
-                return np.zeros(1)

-
-
[docs]    def restrict_to(self, element_subset, name=None):
-        """
-        Shallow copy of entityset removing elements not in element_subset.
-
-        Parameters
-        ----------
-        element_subset : iterable
-            A subset of the entityset's elements
-
-        name: hashable, optional
-            If not given, a name is generated to reflect entity uid
-
-        Returns
-        -------
-        new entityset : EntitySet
-            Could be empty.
-
-        See also
-        --------
-        Entity.restrict_to
-
-        """
-        newelements = [self[e] for e in element_subset if e in self]
-        name = name or f"{self.uid}_r"
-        return EntitySet(name, newelements, **self.properties)

-
- -
- -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_modules/classes/hypergraph.html b/docs/build/_modules/classes/hypergraph.html deleted file mode 100644 index 29e149a6..00000000 --- a/docs/build/_modules/classes/hypergraph.html +++ /dev/null @@ -1,2798 +0,0 @@ - - - - - - - - - - classes.hypergraph — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Source code for classes.hypergraph

-# Copyright © 2018 Battelle Memorial Institute
-# All rights reserved.
-
-import warnings
-import pickle
-import networkx as nx
-from networkx.algorithms import bipartite
-import numpy as np
-import pandas as pd
-from scipy.sparse import issparse, coo_matrix, dok_matrix, csr_matrix
-from collections import OrderedDict, defaultdict
-from hypernetx.classes.entity import Entity, EntitySet
-from hypernetx.classes.staticentity import StaticEntity, StaticEntitySet
-from hypernetx.exception import HyperNetXError
-from hypernetx.utils.decorators import not_implemented_for
-
-
-__all__ = ["Hypergraph"]
-
-
-
[docs]class Hypergraph:
-    """
-    Hypergraph H = (V,E) references a pair of disjoint sets:
-    V = nodes (vertices) and E = (hyper)edges.
-
-    An HNX Hypergraph is either dynamic or static.
-    Dynamic hypergraphs can change by adding or subtracting objects
-    from them. Static hypergraphs require that all of the nodes and edges
-    be known at creation. A hypergraph is dynamic by default.
-
-    *Dynamic hypergraphs* require the user to keep track of its objects,
-    by using a unique names for each node and edge. This allows for multi-edge graphs and
-    inseperable nodes.
-
-    For example: Let V = {1,2,3} and E = {e1,e2,e3},
-    where e1 = {1,2}, e2 = {1,2}, and e3 = {1,2,3}.
-    The edges e1 and e2 contain the same set of nodes and yet
-    are distinct and must be distinguishable within H.
-
-    In a dynamic hypergraph each node and edge is
-    instantiated as an Entity and given an identifier or uid. Entities
-    keep track of inclusion relationships and can be nested. Since
-    hypergraphs can be quite large, only the entity identifiers will be used
-    for computation intensive methods, this means the user must take care
-    to keep a one to one correspondence between their set of uids and
-    the objects in their hypergraph. See `Honor System`_
-    Dynamic hypergraphs are most practical for small to modestly sized
-    hypergraphs (<1000 objects).
-
-    *Static hypergraphs* store node and edge information in numpy arrays and
-    are immutable. Each node and edge receives a class generated internal
-    identifier used for computations so do not require the user to create
-    different ids for nodes and edges. To create a static hypergraph set
-    `static = True` in the signature.
-
-    We will create hypergraphs in multiple ways:
-
-    1. As an empty instance: ::
-
-        >>> H = hnx.Hypergraph()
-        >>> H.nodes, H.edges
-        ({}, {})
-
-    2. From a dictionary of iterables (elements of iterables must be of type hypernetx.Entity or hashable): ::
-
-        >>> H = Hypergraph({'a':[1,2,3],'b':[4,5,6]})
-        >>> H.nodes, H.edges
-        # output: (EntitySet(_:Nodes,[1, 2, 3, 4, 5, 6],{}), EntitySet(_:Edges,['b', 'a'],{}))
-
-    3. From an iterable of iterables: (elements of iterables must be of type hypernetx.Entity or hashable): ::
-
-        >>> H = Hypergraph([{'a','b'},{'b','c'},{'a','c','d'}])
-        >>> H.nodes, H.edges
-        # output: (EntitySet(_:Nodes,['d', 'b', 'c', 'a'],{}), EntitySet(_:Edges,['_1', '_2', '_0'],{}))
-
-    4. From a hypernetx.EntitySet or StaticEntitySet: ::
-
-        >>> a = Entity('a',{1,2}); b = Entity('b',{2,3})
-        >>> E = EntitySet('sample',elements=[a,b])
-        >>> H = Hypergraph(E)
-        >>> H.nodes, H.edges.
-        # output: (EntitySet(_:Nodes,[1, 2, 3],{}), EntitySet(_:Edges,['b', 'a'],{}))
-
-    All of these constructions apply for both dynamic and static hypergraphs. To
-    create a static hypergraph set the parameter `static=True`. In addition a static
-    hypergraph is automatically created if a StaticEntity, StaticEntitySet, or pandas.DataFrame object
-    is passed to the Hypergraph constructor.
-
-    5. | From a pandas.DataFrame. The dataframe must have at least two columns with headers and there can be no nans. 
-       | By default the first column corresponds to the edge names and the second column to the node names.
-       | You can specify the columns by restricting the dataframe to the columns of interest in the order:
-       | :code:`hnx.Hypergraph(df[[edge_column_name,node_column_name]])`
-       | See :ref:`Colab Tutorials <colab>`  Tutorial 6 - Static Hypergraphs and Entities for additional information.
-
-
-    Parameters
-    ----------
-    setsystem : (optional) EntitySet, StaticEntitySet, dict, iterable, pandas.dataframe, default: None
-        See notes above for setsystem requirements.
-
-    name : hashable, optional, default: None
-        If None then a placeholder '_'  will be inserted as name
-
-    static : boolean, optional, default: False
-        If True the hypergraph will be immutable, edges and nodes may not be changed.
-
-    use_nwhy : boolean, optional, default = False
-        If True hypergraph will be static and computations will be done using
-        C++ backend offered by NWHypergraph. This requires installation of the
-        NWHypergraph C++ library. Please see the :ref:`NWHy documentation <nwhy>` for more information.
-
-
-    """
-
-    # TODO: remove lambda functions from constructor in H and E.
-
-    def __init__(
-        self, setsystem=None, name=None, static=False, use_nwhy=False, filepath=None
-    ):
-        self.filepath = filepath
-        if use_nwhy:
-            static = True
-            try:
-                import nwhy
-
-                self.nwhy = True
-
-            except:
-                self.nwhy = False
-                print("NWHypergraph is not available. Will continue with static=True.")
-                use_nwhy = False
-        else:
-            self.nwhy = False
-        if not name:
-            self.name = ""
-        else:
-            self.name = name
-
-        if static == True or (
-            isinstance(setsystem, StaticEntitySet) or
-            isinstance(setsystem, StaticEntity) or
-            isinstance(setsystem, pd.DataFrame) ) :
-            self._static=True
-            if setsystem is None:
-                self._edges=StaticEntitySet()
-                self._nodes=StaticEntitySet()
-            else:
-                E=StaticEntitySet(entity = setsystem)
-                self._edges=E
-                self._nodes=E.restrict_to_levels([1])
-        else:
-            self._static=False
-            if setsystem is None:
-                setsystem=EntitySet("_", elements = [])
-            elif isinstance(setsystem, Entity):
-                setsystem=EntitySet("_", setsystem.incidence_dict)
-            elif isinstance(setsystem, dict):
-                # Must be a dictionary with values equal to iterables of Entities and hashables.
-                # Keys will be uids for new edges and values of the dictionary will generate the nodes.
-                setsystem=EntitySet("_", setsystem)
-            elif not isinstance(setsystem, EntitySet):
-                # If no ids are given, return default ids indexed by position in iterator
-                # This should be an iterable of sets
-                edge_labels=[self.name + str(x) for x in range(len(setsystem))]
-                setsystem=EntitySet("_", dict(zip(edge_labels, setsystem)))
-
-            _reg=setsystem.registry
-            _nodes={k: Entity(k, **_reg[k].properties) for k in _reg}
-            _elements={j: {k: _nodes[k] for k in setsystem[j]} for j in setsystem}
-            _edges={
-                j: Entity(j, elements=_elements[j].values(), **setsystem[j].properties)
-                for j in setsystem
-            }
-
-            self._edges = EntitySet(
-                f"{self.name}:Edges", elements=_edges.values(), **setsystem.properties
-            )
-            self._nodes = EntitySet(f"{self.name}:Nodes", elements=_nodes.values())
-        if self._static:
-            temprows, tempcols = self.edges.data.T
-            tempdata = np.ones(len(temprows), dtype=int)
-            self.state_dict = {
-                "data": (temprows, tempcols, tempdata)
-            }  # how can we incorporate the counts into the nwhy hypergraph?
-            if self.nwhy:
-                self.g = nwhy.NWHypergraph(*self.state_dict["data"])
-                self.nwhy_dict = {"snodelg": dict(), "sedgelg": dict()}
-            self.state_dict["snodelg"] = dict()
-            self.state_dict["sedgelg"] = dict()
-            if self.filepath is not None:
-                self.save_state(fpath=self.filepath)
-
-    @property
-    def edges(self):
-        """
-        Object associated with self._edges.
-        
-        Returns
-        -------
-        StaticEntitySet or EntitySet
-            If self.isstatic the StaticEntitySet, otherwise EntitySet.
-        """
-        return self._edges
-
-    @property
-    def nodes(self):
-        """
-        Object associated with self._nodes.
-        
-        Returns
-        -------
-        StaticEntitySet or EntitySet
-            If self.isstatic the StaticEntitySet, otherwise EntitySet.
-
-        """
-        return self._nodes
-
-    @property
-    def isstatic(self):
-        """
-        Checks whether nodes and edges are immutable
-        
-        Returns
-        -------
-        Boolean
-    
-        """
-        return self._static
-
-    @property
-    def incidence_dict(self):
-        """
-        Dictionary keyed by edge uids with values the uids of nodes in each edge
-        
-        Returns
-        -------
-        dict
-        
-        """
-        return self._edges.incidence_dict
-
-    @property
-    def shape(self):
-        """
-        (number of nodes, number of edges)
-        
-        Returns
-        -------
-        tuple
-            
-        """
-        if self.nwhy:
-            return (self.g.number_of_nodes(), self.g.number_of_edges())
-        else:
-            return (len(self._nodes.elements), len(self._edges.elements))
-
-    def __str__(self):
-        """
-        String representation of hypergraph
-        
-        Returns
-        -------
-        str
-            
-        """
-        return f"Hypergraph({self.edges.elements},name={self.name})"
-
-    def __repr__(self):
-        """
-        String representation of hypergraph
-        
-        Returns
-        -------
-        str
-            
-        """
-        return f"Hypergraph({self.edges.elements},name={self.name})"
-
-    def __len__(self):
-        """
-        Number of nodes
-        
-        Returns
-        -------
-        int
-            
-        """
-        if self.nwhy:
-            return self.g.number_of_nodes()
-        else:
-            return len(self._nodes)
-
-    def __iter__(self):
-        """
-        Iterate over the nodes of the hypergraph
-        
-        Returns
-        -------
-        dict_keyiterator
-            
-        """
-        return iter(self.nodes)
-
-    def __contains__(self, item):
-        """
-        Returns boolean indicating if item is in self.nodes
-
-        Parameters
-        ----------
-        item : hashable or Entity
-
-        """
-        if isinstance(item, Entity):
-            return item.uid in self.nodes
-        else:
-            return item in self.nodes
-
-    def __getitem__(self, node):
-        """
-        Returns the neighbors of node
-
-        Parameters
-        ----------
-        node : Entity or hashable
-            If hashable, then must be uid of node in hypergraph
-
-        Returns
-        -------
-        neighbors(node) : iterator
-
-        """
-        return self.neighbors(node)
-
-
[docs]    @not_implemented_for("dynamic")
-    def get_id(self, uid, edges=False):
-        """
-        Return the internally assigned id associated with a label.
-
-        Parameters
-        ----------
-        uid : string
-            User provided name/id/label for hypergraph object
-        edges : bool, optional
-            Determines if uid is an edge or node name
-        
-        Returns
-        -------
-        : int
-            internal id assigned at construction
-        """
-        kdx = (edges + 1) % 2
-        return int(np.argwhere(self.edges.labs(kdx) == uid)[0])

-
-
[docs]    @not_implemented_for("dynamic")
-    def get_name(self, id, edges=False):
-        """
-        Return the user defined name/id/label associated to an
-        internally assigned id.
-
-        Parameters
-        ----------
-        id : int
-            Internally assigned id
-        edges : bool, optional
-            Determines if id references an edge or node
-        
-        Returns
-        -------
-        str
-            User provided name/id/label for hypergraph object
-        """
-        kdx = (edges + 1) % 2
-        return self.edges.labs(kdx)[id]

-
-
[docs]    @not_implemented_for("dynamic")
-    def get_linegraph(self, s, edges=True, use_nwhy=True):
-        """
-        Creates an ::term::s-linegraph for the Hypergraph.
-        If edges=True (default)then the edges will be the vertices of the line graph.
-        Two vertices are connected by an s-line-graph edge if the corresponding
-        hypergraphedges intersect in at least s hypergraph nodes.
-        If edges=False, the hypergraph nodes will be the vertices of the line graph.
-        Two vertices are connected if the nodes they correspond to share at least s
-        incident hyper edges.
-
-        Parameters
-        ----------
-        s : int
-            The width of the connections.
-        edges : bool, optional
-            Determine if edges or nodes will be the vertices in the linegraph.
-        use_nwhy : bool, optional
-            Requests that nwhy be used to construct the linegraph. If NWHy is not available this is ignored.
-
-        Returns
-        -------
-        nx.Graph
-            A NetworkX graph.
-        """
-        if use_nwhy and self.nwhy:
-            d = self.nwhy_dict
-        else:
-            d = self.state_dict
-        key = "sedgelg" if edges else "snodelg"
-        if s in d[key]:
-            return d[key][s]
-        else:
-            if use_nwhy and self.nwhy:
-                d[key][s] = self.g.s_linegraph(s=s, edges=edges)
-            else:
-                if edges:
-                    A = self.edge_adjacency_matrix(s=s)
-                else:
-                    A = self.adjacency_matrix(s=s)
-                d[key][s] = nx.from_scipy_sparse_matrix(A)
-                if self.filepath is not None:
-                    self.save_state(fpath=self.filepath)
-            return d[key][s]

-
-
[docs]    @not_implemented_for("dynamic")
-    def set_state(self, **kwargs):
-        """
-        Allow state_dict updates from outside of class. Use with caution.
-
-        Parameters
-        ----------
-        **kwargs
-            key=value pairs to save in state dictionary
-        """
-        self.state_dict.update(kwargs)
-        if self.filepath is not None:
-            self.save_state(fpath=self.filepath)

-
-
[docs]    @not_implemented_for("dynamic")
-    def save_state(self, fpath=None):
-        """
-        Save the hypergraph as an ordered pair: [state_dict,labels]
-        The hypergraph can be recovered using the command:
-
-            >>> H = hnx.Hypergraph.recover_from_state(fpath)
-
-        Parameters
-        ----------
-        fpath : str, optional
-        """
-        if fpath is None:
-            fpath = self.filepath or "current_state.p"
-        pickle.dump([self.state_dict, self.edges.labels], open(fpath, "wb"))

-
-
[docs]    @classmethod
-    def recover_from_state(cls, fpath="current_state.p", newfpath=None, use_nwhy=True):
-        """
-        Recover a static hypergraph pickled using save_state.
-
-        Parameters
-        ----------
-        fpath : str
-            Full path to pickle file containing state_dict and labels
-            of hypergraph
-
-        Returns
-        -------
-        H : Hypergraph
-            static hypergraph with state dictionary prefilled
-        """
-        temp, labels = pickle.load(open(fpath, "rb"))
-        recovered_data = np.array(temp["data"])[[0, 1]].T  # need to save counts as well
-        recovered_counts = np.array(temp["data"])[
-            [2]
-        ]  # ammend this to store cell weights
-        E = StaticEntitySet(data=recovered_data, labels=labels)
-        E.properties["counts"] = recovered_counts
-        H = Hypergraph(E, use_nwhy=use_nwhy)
-        H.state_dict.update(temp)
-        if newfpath == "same":
-            newfpath = fpath
-        if newfpath is not None:
-            H.filepath = newfpath
-            H.save_state()
-        return H

-
-
[docs]    @classmethod
-    def add_nwhy(cls, h, fpath=None):
-        """
-        Add nwhy functionality to a hypergraph.
-
-        Parameters
-        ----------
-        h : hnx.Hypergraph
-        fpath : file path for storage of hypergraph state dictionary
-
-        Returns
-        -------
-        hnx.Hypergraph
-            Returns a copy of h with static set to true and nwhy set to True
-            if it is available.
-
-        """
-
-        if h.isstatic:
-            sd = h.state_dict
-            H = Hypergraph(h.edges, use_nwhy=True, filepath=fpath)
-            H.state_dict.update(sd)
-            return H
-        else:
-            return Hypergraph(StaticEntitySet(h.edges), use_nwhy=True, filepath=fpath)

-
-
[docs]    def edge_size_dist(self):
-        """
-        Returns the size for each edge
-        
-        Returns
-        -------
-        np.array
-            
-        """
-        if self.isstatic:
-            dist = self.state_dict.get("edge_size_dist", None)
-            if dist:
-                return dist
-            else:
-                if self.nwhy:
-                    dist = self.g.edge_size_dist()
-                else:
-                    dist = list(np.array(np.sum(self.incidence_matrix(), axis=0))[0])
-
-                self.set_state(edge_size_dist=dist)
-                return dist
-        else:
-            return list(np.array(np.sum(self.incidence_matrix(), axis=0))[0])

-
-
[docs]    def convert_to_static(
-        self,
-        name=None,
-        nodes_name="nodes",
-        edges_name="edges",
-        use_nwhy=False,
-        filepath=None,
-    ):
-        """
-        Returns new static hypergraph with the same dictionary as original hypergraph
-
-        Parameters
-        ----------
-        name : None, optional
-            Name
-        nodes_name : str, optional
-            name for list of node labels
-        edges_name : str, optional
-            name for list of edge labels
-
-        Returns
-        -------
-        hnx.Hypergraph
-            Will have attribute static = True
-
-        Note
-        ----
-        Static hypergraphs store the user defined node and edge names in
-        a dictionary of labeled lists. The order of the lists provides an
-        index, which the hypergraph uses in place of the node and edge names
-        for fast processing.
-        """
-        arr, cdict, rdict = self.edges.incidence_matrix(index=True)
-        labels = OrderedDict(
-            [
-                (edges_name, [cdict[k] for k in range(len(cdict))]),
-                (nodes_name, [rdict[k] for k in range(len(rdict))]),
-            ]
-        )
-        E = StaticEntity(arr=arr.T, labels=labels)
-        return Hypergraph(setsystem=E, name=name)

-
-
[docs]    def remove_static(self, name=None):
-        """
-        Returns dynamic hypergraph
-
-        Parameters
-        ----------
-        name : None, optional
-            User defined namae of hypergraph
-
-        Returns
-        -------
-        hnx.Hypergraph
-            A new hypergraph with the same dictionary as self but allowing dynamic
-            changes to nodes and edges.
-            If hypergraph is not static, returns self.
-        """
-        if not self.isstatic:
-            return self
-        else:
-            return Hypergraph(self.edges.incidence_dict, name=name)

-
-
[docs]    def translate(self, idx, edges=False):
-        """
-        Returns the translation of numeric values associated with hypergraph.
-        Only needed if exposing the static identifiers assigned by the class.
-        If not static then the idx is returned.
-
-        Parameters
-        ----------
-        idx : int
-            class assigned integer for internal manipulation of Hypergraph data
-        edges : bool, optional, default: True
-            If True then translates from edge index. Otherwise will translate from
-            node index, default=False
-
-        Returns
-        -------
-         : int or string
-            User assigned identifier corresponding to idx
-        """
-        if self.isstatic:
-            return self.get_name(idx, edges=edges)
-        else:
-            return idx

-
-
[docs]    def s_degree(self, node, s=1):  # deprecate this to degree
-        """
-        Same as `degree`
-
-        Parameters
-        ----------
-        node : Entity or hashable
-            If hashable, then must be uid of node in hypergraph
-
-        s : positive integer, optional, default: 1
-
-        Returns
-        -------
-        s_degree : int
-            The degree of a node in the subgraph induced by edges
-            of size s
-
-        Note
-        ----
-        The :term:`s-degree` of a node is the number of edges of size
-        at least s that contain the node.
-
-        """
-        msg = (
-            "s-degree is deprecated and will be removed in"
-            " release 1.0.0. Use degree(node,s=int) instead."
-        )
-
-        warnings.warn(msg, DeprecationWarning)
-        return self.degree(node, s)

-
-
[docs]    def degree(self, node, s=1, max_size=None):
-        """
-        The number of edges of size s that contain node.
-
-        Parameters
-        ----------
-        node : hashable
-            identifier for the node.
-        s : positive integer, optional, default: 1
-            smallest size of edge to consider in degree
-        max_size : positive integer or None, optional, default: None
-            largest size of edge to consider in degree
-
-        Returns
-        -------
-         : int
-
-        """
-        if self.isstatic:
-            ndx = self.get_id(node)
-            #             if s == 1:
-            #                 return np.sum(self.edges.data.T[1] == ndx)
-            if self.nwhy:
-                return self.g.degree(ndx, min_size=s, max_size=None)
-
-            else:
-                if max_size is not None:
-                    ids = np.where(
-                        np.array(self.edge_size_dist()) in range(s, max_size + 1)
-                    )[0]
-                else:
-                    ids = np.where(np.array(self.edge_size_dist()) >= s)[0]
-                imat = self.incidence_matrix()
-                return np.sum(imat[ndx, ids])
-        else:
-            memberships = set(self.nodes[node].memberships)
-            if max_size is not None:
-                return len(
-                    set(
-                        e
-                        for e in memberships
-                        if len(self.edges[e]) in range(s, max_size + 1)
-                    )
-                )
-            elif s > 1:
-                return len(set(e for e in memberships if len(self.edges[e]) >= s))
-            else:
-                return len(memberships)

-
-
[docs]    def size(self, edge):
-        """
-        The number of nodes that belong to edge.
-
-        Parameters
-        ----------
-        edge : hashable
-            The uid of an edge in the hypergraph
-
-        Returns
-        -------
-        size : int
-
-        """
-        if self.isstatic:
-            edx = self.get_id(edge, edges=True)
-            esd = self.state_dict.get("edge_size_dist", None)
-            if esd is not None:
-                return esd[edx]
-            else:
-                if self.nwhy:
-                    return self.g.size(edx)
-                else:
-                    return np.sum(self.edges.data.T[0] == edx)
-        else:
-            return len(self.edges[edge])

-
-
[docs]    def number_of_nodes(self, nodeset=None):
-        """
-        The number of nodes in nodeset belonging to hypergraph.
-
-        Parameters
-        ----------
-        nodeset : an interable of Entities, optional, default: None
-            If None, then return the number of nodes in hypergraph.
-
-        Returns
-        -------
-        number_of_nodes : int
-
-        """
-        if nodeset:
-            return len([n for n in self.nodes if n in nodeset])
-        else:
-            if self.nwhy == True:
-                return self.g.number_of_nodes()
-            else:
-                return len(self.nodes)

-
-
[docs]    def number_of_edges(self, edgeset=None):
-        """
-        The number of edges in edgeset belonging to hypergraph.
-
-        Parameters
-        ----------
-        edgeset : an interable of Entities, optional, default: None
-            If None, then return the number of edges in hypergraph.
-
-        Returns
-        -------
-        number_of_edges : int
-        """
-        if edgeset:
-            return len([e for e in self.edges if e in edgeset])
-        else:
-            if self.nwhy == True:
-                return self.g.number_of_edges()
-            else:
-                return len(self.edges)

-
-
[docs]    def order(self):
-        """
-        The number of nodes in hypergraph.
-
-        Returns
-        -------
-        order : int
-        """
-        if self.nwhy:
-            return self.g.number_of_nodes()
-        else:
-            return len(self.nodes)

-
-
[docs]    def dim(self, edge):
-        """
-        Same as size(edge)-1.
-        """
-        return self.size(edge) - 1

-
-
[docs]    def neighbors(self, node, s=1):
-        """
-        The nodes in hypergraph which share s edge(s) with node.
-
-        Parameters
-        ----------
-        node : hashable or Entity
-            uid for a node in hypergraph or the node Entity
-
-        s : int, list, optional, default : 1
-            Minimum number of edges shared by neighbors with node.
-
-        Returns
-        -------
-         : list
-            List of neighbors
-
-        """
-        if not node in self.nodes:
-            print(f"Node is not in hypergraph {self.name}.")
-            return
-
-        if self.isstatic:
-            g = self.get_linegraph(s=s, edges=False)
-            ndx = self.get_id(node)
-            if self.nwhy == True:
-                nbrs = g.s_neighbors(ndx)
-            else:
-                nbrs = list(g.neighbors(ndx))
-            return [self.translate(nb, edges=False) for nb in nbrs]
-
-        else:
-            node = self.nodes[
-                node
-            ].uid  # this allows node to be an Entity instead of a string
-            memberships = set(self.nodes[node].memberships).intersection(
-                self.edges.uidset
-            )
-            edgeset = {e for e in memberships if len(self.edges[e]) >= s}
-
-            neighborlist = set()
-            for e in edgeset:
-                neighborlist.update(self.edges[e].uidset)
-            neighborlist.discard(node)
-            return list(neighborlist)

-
-
[docs]    def edge_neighbors(self, edge, s=1):
-        """
-        The edges in hypergraph which share s nodes(s) with edge.
-
-        Parameters
-        ----------
-        edge : hashable or Entity
-            uid for a edge in hypergraph or the edge Entity
-
-        s : int, list, optional, default : 1
-            Minimum number of nodes shared by neighbors edge node.
-
-        Returns
-        -------
-         : list
-            List of edge neighbors
-
-        """
-        if not edge in self.edges:
-            print(f"Edge is not in hypergraph {self.name}.")
-            return
-
-        if self.isstatic:
-            g = self.get_linegraph(s=s, edges=True)
-            edx = self.get_id(edge, edges=True)
-            if self.nwhy == True:
-                nbrs = g.s_neighbors(edx)
-            else:
-                nbrs = list(g.neighbors(edx))
-            return [self.translate(nb, edges=True) for nb in nbrs]
-
-        else:
-            node = self.edges[edge].uid
-            return self.dual().neighbors(node, s=s)

-
-
[docs]    @not_implemented_for("static")
-    def remove_node(self, node):
-        """
-        Removes node from edges and deletes reference in hypergraph nodes
-
-        Parameters
-        ----------
-        node : hashable or Entity
-            a node in hypergraph
-
-        Returns
-        -------
-        hypergraph : Hypergraph
-
-        """
-        if not node in self._nodes:
-            return self
-        else:
-            if not isinstance(node, Entity):
-                node = self._nodes[node]
-            for edge in node.memberships:
-                self._edges[edge].remove(node)
-            self._nodes.remove(node)
-        return self

-
-
[docs]    @not_implemented_for("static")
-    def remove_nodes(self, node_set):
-        """
-        Removes nodes from edges and deletes references in hypergraph nodes
-
-        Parameters
-        ----------
-        node_set : an iterable of hashables or Entities
-            Nodes in hypergraph
-
-        Returns
-        -------
-        hypergraph : Hypergraph
-
-        """
-        for node in node_set:
-            self.remove_node(node)
-        return self

-
-    @not_implemented_for("static")
-    def _add_nodes_from(self, nodes):
-        """
-        Private helper method instantiates new nodes when edges added to hypergraph.
-
-        Parameters
-        ----------
-        nodes : iterable of hashables or Entities
-
-        """
-        for node in nodes:
-            if node in self._edges:
-                raise HyperNetXError("Node already an edge.")
-            elif node in self._nodes and isinstance(node, Entity):
-                self._nodes[node].__dict__.update(node.properties)
-            elif node not in self._nodes:
-                if isinstance(node, Entity):
-                    self._nodes.add(Entity(node.uid, **node.properties))
-                else:
-                    self._nodes.add(Entity(node))
-
-
[docs]    @not_implemented_for("static")
-    def add_edge(self, edge):
-        """
-
-        Adds a single edge to hypergraph.
-
-        Parameters
-        ----------
-        edge : hashable or Entity
-            If hashable the edge returned will be empty.
-
-        Returns
-        -------
-        hypergraph : Hypergraph
-
-        Notes
-        -----
-        When adding an edge to a hypergraph children must be removed
-        so that nodes do not have elements.
-        Each node (element of edge) must be instantiated as a node,
-        making sure its uid isn't already present in the self.
-        If an added edge contains nodes that cannot be added to hypergraph
-        then an error will be raised.
-
-        """
-        if edge in self._edges:
-            warnings.warn("Cannot add edge. Edge already in hypergraph")
-        elif edge in self._nodes:
-            warnings.warn("Cannot add edge. Edge is already a Node")
-        elif isinstance(edge, Entity):
-            if len(edge) > 0:
-                self._add_nodes_from(edge.elements.values())
-                self._edges.add(
-                    Entity(
-                        edge.uid,
-                        elements=[self._nodes[k] for k in edge],
-                        **edge.properties,
-                    )
-                )
-                for n in edge.elements:
-                    self._nodes[n].memberships[edge.uid] = self._edges[edge.uid]
-            else:
-                self._edges.add(Entity(edge.uid, **edge.properties))
-        else:
-            self._edges.add(Entity(edge))  # this generates an empty edge
-        return self

-
-
[docs]    @not_implemented_for("static")
-    def add_edges_from(self, edge_set):
-        """
-        Add edges to hypergraph.
-
-        Parameters
-        ----------
-        edge_set : iterable of hashables or Entities
-            For hashables the edges returned will be empty.
-
-        Returns
-        -------
-        hypergraph : Hypergraph
-
-        """
-        for edge in edge_set:
-            self.add_edge(edge)
-        return self

-
-
[docs]    @not_implemented_for("static")
-    def add_node_to_edge(self, node, edge):
-        """
-
-        Adds node to an edge in hypergraph edges
-
-        Parameters
-        ----------
-        node: hashable or Entity
-            If Entity, only uid and properties will be used.
-            If uid is already in nodes then the known node will
-            be used
-
-        edge: uid of edge or edge, must belong to self.edges
-
-        Returns
-        -------
-        hypergraph : Hypergraph
-
-        """
-        if edge in self._edges:
-            if not isinstance(edge, Entity):
-                edge = self._edges[edge]
-            if node in self._nodes:
-                self._edges[edge].add(self._nodes[node])
-            else:
-                if not isinstance(node, Entity):
-                    node = Entity(node)
-                else:
-                    node = Entity(node.uid, **node.properties)
-                self._edges[edge].add(node)
-                self._nodes.add(node)
-
-        return self

-
-
[docs]    @not_implemented_for("static")
-    def remove_edge(self, edge):
-        """
-        Removes a single edge from hypergraph.
-
-        Parameters
-        ----------
-        edge : hashable or Entity
-
-        Returns
-        -------
-        hypergraph : Hypergraph
-
-        Notes
-        -----
-
-        Deletes reference to edge from all of its nodes.
-        If any of its nodes do not belong to any other edges
-        the node is dropped from self.
-
-        """
-        if edge in self._edges:
-            if not isinstance(edge, Entity):
-                edge = self._edges[edge]
-            for node in edge.uidset:
-                edge.remove(node)
-                if len(self._nodes[node]._memberships) == 1:
-                    self._nodes.remove(node)
-            self._edges.remove(edge)
-        return self

-
-
[docs]    @not_implemented_for("static")
-    def remove_edges(self, edge_set):
-        """
-        Removes edges from hypergraph.
-
-        Parameters
-        ----------
-        edge_set : iterable of hashables or Entities
-
-        Returns
-        -------
-        hypergraph : Hypergraph
-
-        """
-        for edge in edge_set:
-            self.remove_edge(edge)
-        return self

-
-
[docs]    def incidence_matrix(self, index=False):
-        """
-        An incidence matrix for the hypergraph indexed by nodes x edges.
-
-        Parameters
-        ----------
-        index : boolean, optional, default False
-            If True return will include a dictionary of node uid : row number
-            and edge uid : column number
-
-        Returns
-        -------
-        incidence_matrix : scipy.sparse.csr.csr_matrix or np.ndarray
-
-        row dictionary : dict
-            Dictionary identifying rows with nodes
-
-        column dictionary : dict
-            Dictionary identifying columns with edges
-
-        """
-        if self.isstatic:
-            mat = self.state_dict.get("incidence_matrix", None)
-            if mat is None:
-                mat = self.edges.incidence_matrix()
-                self.state_dict["incidence_matrix"] = mat
-            if index:
-                rdict = dict(enumerate(self.edges.labs(1)))
-                cdict = dict(enumerate(self.edges.labs(0)))
-                return mat, rdict, cdict
-            else:
-                return mat
-
-        else:
-            return self.edges.incidence_matrix(index=index)

-
-
[docs]    @staticmethod
-    def incidence_to_adjacency(M, s=1, weighted=True):
-        """
-        Helper method to obtain adjacency matrix from incidence matrix.
-
-        Parameters
-        ----------
-        M : scipy.sparse.csr.csr_matrix
-
-        s : int, optional, default: 1
-
-        weighted : boolean, optional, default: True
-
-        Returns
-        -------
-        a matrix : scipy.sparse.csr.csr_matrix
-
-        """
-        A = M.dot(M.transpose())
-        if issparse(A):
-            A.setdiag(0)
-            B = (A >= s) * 1
-            A = A.multiply(B)
-        else:
-            np.fill_diagonal(A, 0)
-            B = (A >= s) * 1
-            A = np.multiply(A, B)
-
-        if not weighted:
-            A = (A > 0) * 1
-        return csr_matrix(A)

-
-
[docs]    def adjacency_matrix(self, index=False, s=1, weighted=True):
-        """
-        The sparse weighted :term:`s-adjacency matrix`
-
-        Parameters
-        ----------
-        s : int, optional, default: 1
-
-        index: boolean, optional, default: False
-            if True, will return a rowdict of row to node uid
-
-        weighted: boolean, optional, default: True
-
-
-        Returns
-        -------
-        adjacency_matrix : scipy.sparse.csr.csr_matrix
-
-        row dictionary : dict
-
-        Notes
-        -----
-        If weighted is True each off diagonal cell will equal the number
-        of edges shared by the nodes indexing the row and column if that number is
-        greater than s, otherwise the cell will equal 0. If weighted is False, the off
-        diagonal cell will equal 1 if the nodes indexed by the row and column share at
-        least s edges and 0 otherwise.
-
-        """
-        M = self.incidence_matrix(index=index)
-        if index:
-            return Hypergraph.incidence_to_adjacency(M[0], s=s, weighted=weighted), M[1]
-        else:
-            return Hypergraph.incidence_to_adjacency(M, s=s, weighted=weighted)

-
-
[docs]    def edge_adjacency_matrix(self, index=False, s=1, weighted=True):
-        """
-        The weighted :term:`s-adjacency matrix` for the dual hypergraph.
-
-        Parameters
-        ----------
-        s : int, optional, default: 1
-
-        index: boolean, optional, default: False
-            if True, will return a coldict of column to edge uid
-
-        sparse: boolean, optional, default: True
-
-        weighted: boolean, optional, default: True
-
-        Returns
-        -------
-        edge_adjacency_matrix : scipy.sparse.csr.csr_matrix or numpy.ndarray
-
-        column dictionary : dict
-
-        Notes
-        -----
-        This is also the adjacency matrix for the line graph.
-        Two edges are s-adjacent if they share at least s nodes.
-        If index=True, returns a dictionary column_index:edge_uid
-
-        """
-        M = self.incidence_matrix(index=index)
-        if index:
-            return (
-                Hypergraph.incidence_to_adjacency(
-                    M[0].transpose(), s=s, weighted=weighted
-                ),
-                M[2],
-            )
-        else:
-            return Hypergraph.incidence_to_adjacency(
-                M.transpose(), s=s, weighted=weighted
-            )

-
-
[docs]    def auxiliary_matrix(self, s=1, index=False):
-        """
-        The unweighted :term:`s-auxiliary matrix` for hypergraph
-
-        Parameters
-        ----------
-        s : int
-        index : bool, optional, default: False
-            return a dictionary of labels for the rows of the matrix
-
-
-        Returns
-        -------
-        auxiliary_matrix : scipy.sparse.csr.csr_matrix or numpy.ndarray
-            Will return the same type of matrix as self.arr
-
-        Notes
-        -----
-        Creates subgraph by restricting to edges of cardinality at least s.
-        Returns the unweighted s-edge adjacency matrix for the subgraph.
-
-        """
-
-        edges = [e for e in self.edges if len(self.edges[e]) >= s]
-        H = self.restrict_to_edges(edges)
-        return H.edge_adjacency_matrix(s=s, index=index, weighted=False)

-
-
[docs]    def bipartite(self):
-        """
-        Constructs the networkX bipartite graph associated to hypergraph.
-
-        Returns
-        -------
-        bipartite : nx.Graph()
-
-        Notes
-        -----
-        Creates a bipartite networkx graph from hypergraph.
-        The nodes and (hyper)edges of hypergraph become the nodes of bipartite graph.
-        For every (hyper)edge e in the hypergraph and node n in e there is an edge (n,e)
-        in the graph.
-
-        """
-        B = nx.Graph()
-        E = self.edges
-        V = self.nodes
-        B.add_nodes_from(E, bipartite=1)
-        B.add_nodes_from(V, bipartite=0)
-        B.add_edges_from([(v, e) for e in E for v in self.edges[e]])
-        return B

-
-
[docs]    def dual(self, name=None):
-        """
-        Constructs a new hypergraph with roles of edges and nodes of hypergraph reversed.
-
-        Parameters
-        ----------
-        name : hashable
-
-        Returns
-        -------
-        dual : hypergraph
-        """
-        if self.isstatic:
-            E = self.edges.restrict_to_levels((1, 0))
-            return Hypergraph(E, name=name, use_nwhy=self.nwhy)
-        else:
-            E = defaultdict(list)
-            for k, v in self.edges.incidence_dict.items():
-                for n in v:
-                    E[n].append(k)
-            return Hypergraph(E, name=name)

-
-    def _collapse_nwhy(self, edges, rec):
-        """
-        Helper method for collapsing nodes and edges when hypergraph
-        is static and using nwhy
-
-        Parameters
-        ----------
-        edges : bool
-            Collapse the edges if True, otherwise the nodes
-        rec : bool
-            return the equivalence classes
-        """
-
-        if edges:
-            d = self.g.collapse_edges(return_equivalence_class=rec)
-        else:
-            d = self.g.collapse_nodes(return_equivalence_class=rec)
-
-        if rec:
-            en = {
-                self.get_name(
-                    k, edges=edges
-                ): f"{self.get_name(k,edges=edges)}:{len(v)}"
-                for k, v in d.items()
-            }
-            ec = {
-                f"{self.get_name(k,edges=edges)}:{len(v)}": {
-                    self.get_name(vd, edges=edges) for vd in v
-                }
-                for k, v in d.items()
-            }
-        else:
-            en = {
-                self.get_name(
-                    k, edges=edges
-                ): f"{self.get_name(k,edges=edges)}:{v.pop()}"
-                for k, v in d.items()
-            }
-            ec = {}
-        lev = self.edges.keys[1-1*edges]
-        E = self.edges.restrict_to_indices(sorted(d.keys()), level=1-1*edges)
-        E.labels[str(lev)] = np.array([en[k] for k in E.labels[lev]])
-        if rec:
-            return E, ec
-        else:
-            return E
-
-
[docs]    def collapse_edges(
-        self,
-        name=None,
-        use_reps=None,
-        return_counts=None,
-        return_equivalence_classes=False,
-    ):
-        """
-        Constructs a new hypergraph gotten by identifying edges containing the same nodes
-
-        Parameters
-        ----------
-        name : hashable, optional, default: None
-
-        return_equivalence_classes: boolean, optional, default: False
-            Returns a dictionary of edge equivalence classes keyed by frozen sets of nodes
-
-        Returns
-        -------
-        new hypergraph : Hypergraph
-            Equivalent edges are collapsed to a single edge named by a representative of the equivalent
-            edges followed by a colon and the number of edges it represents.
-
-        equivalence_classes : dict
-            A dictionary keyed by representative edge names with values equal to the edges in
-            its equivalence class
-
-        Notes
-        -----
-        Two edges are identified if their respective elements are the same.
-        Using this as an equivalence relation, the uids of the edges are partitioned into
-        equivalence classes.
-
-        A single edge from the collapsed edges followed by a colon and the number of elements
-        in its equivalence class as uid for the new edge
-
-
-        """
-        if use_reps is not None or return_counts is not None:
-            msg = """
-            use_reps ane return_counts are no longer supported keyword arguments and will throw
-            an error in the next release.
-            collapsed hypergraph automatically names collapsed objects by a string "rep:count"
-            """
-            warnings.warn(msg, DeprecationWarning)
-
-        if self.nwhy:
-            temp = self._collapse_nwhy(True, return_equivalence_classes)
-        else:
-            temp = self.edges.collapse_identical_elements(
-                "_", return_equivalence_classes=return_equivalence_classes
-            )
-        if return_equivalence_classes:
-            return Hypergraph(temp[0], name, use_nwhy=self.nwhy), temp[1]
-        else:
-            return Hypergraph(temp, name, use_nwhy=self.nwhy)

-
-
[docs]    def collapse_nodes(
-        self,
-        name=None,
-        use_reps=True,
-        return_counts=True,
-        return_equivalence_classes=False,
-    ):
-        """
-        Constructs a new hypergraph gotten by identifying nodes contained by the same edges
-
-        Parameters
-        ----------
-        name: str, optional, default: None
-
-        return_equivalence_classes: boolean, optional, default: False
-            Returns a dictionary of node equivalence classes keyed by frozen sets of edges
-
-        use_reps : boolean, optional, default: False - Deprecated, this no longer works and will be removed
-            Choose a single element from the collapsed nodes as uid for the new node, otherwise uses
-            a frozen set of the uids of nodes in the equivalence class
-
-        return_counts: boolean, - Deprecated, this no longer works and will be removed
-            if use_reps is True the new nodes have uids given by a tuple of the rep
-            and the count
-
-        Returns
-        -------
-        new hypergraph : Hypergraph
-
-        Notes
-        -----
-        Two nodes are identified if their respective memberships are the same.
-        Using this as an equivalence relation, the uids of the nodes are partitioned into
-        equivalence classes. A single member of the equivalence class is chosen to represent
-        the class followed by the number of members of the class.
-
-        Example
-        -------
-
-            >>> h = Hypergraph(EntitySet('example',elements=[Entity('E1', ['a','b']),Entity('E2',['a','b'])]))
-            >>> h.incidence_dict
-            {'E1': {'a', 'b'}, 'E2': {'a', 'b'}}
-            >>> h.collapse_nodes().incidence_dict
-            {'E1': {frozenset({'a', 'b'})}, 'E2': {frozenset({'a', 'b'})}} ### Fix this
-            >>> h.collapse_nodes(use_reps=True).incidence_dict
-            {'E1': {('a', 2)}, 'E2': {('a', 2)}}
-
-        """
-        if use_reps is not None or return_counts is not None:
-            msg = """
-            use_reps ane return_counts are no longer supported keyword arguments and will throw
-            an error in the next release.
-            collapsed hypergraph automatically names collapsed objects by a string "rep:count"
-            """
-            warnings.warn(msg, DeprecationWarning)
-
-        if self.nwhy:
-            temp = self._collapse_nwhy(False, return_equivalence_classes)
-            if return_equivalence_classes:
-                return Hypergraph(temp[0], name, use_nwhy=self.nwhy), temp[1]
-            else:
-                return Hypergraph(temp, name, use_nwhy=self.nwhy)
-        else:
-            temp = self.dual().edges.collapse_identical_elements(
-                "_", return_equivalence_classes=return_equivalence_classes
-            )
-
-            if return_equivalence_classes:
-                return Hypergraph(temp[0], name, use_nwhy=self.nwhy).dual(), temp[1]
-            else:
-                return Hypergraph(temp, name, use_nwhy=self.nwhy).dual()

-
-
[docs]    def collapse_nodes_and_edges(
-        self,
-        name=None,
-        use_reps=True,
-        return_counts=True,
-        return_equivalence_classes=False,
-    ):
-        """
-        Returns a new hypergraph by collapsing nodes and edges.
-
-        Parameters
-        ----------
-
-        name: str, optional, default: None
-
-        use_reps: boolean, optional, default: False
-            Choose a single element from the collapsed elements as a representative
-
-        return_counts: boolean, optional, default: True
-            if use_reps is True the new elements are keyed by a tuple of the rep
-            and the count
-
-        return_equivalence_classes: boolean, optional, default: False
-            Returns a dictionary of edge equivalence classes keyed by frozen sets of nodes
-
-        Returns
-        -------
-        new hypergraph : Hypergraph
-
-        Notes
-        -----
-        Collapses the Nodes and Edges EntitySets. Two nodes(edges) are duplicates
-        if their respective memberships(elements) are the same. Using this as an
-        equivalence relation, the uids of the nodes(edges) are partitioned into
-        equivalence classes. A single member of the equivalence class is chosen to represent
-        the class followed by the number of members of the class.
-
-        Example
-        -------
-
-            >>> h = Hypergraph(EntitySet('example',elements=[Entity('E1', ['a','b']),Entity('E2',['a','b'])]))
-            >>> h.incidence_dict
-            {'E1': {'a', 'b'}, 'E2': {'a', 'b'}}
-            >>> h.collapse_nodes_and_edges().incidence_dict   ### Fix this
-            {('E1', 2): {('a', 2)}}
-
-        """
-        if use_reps is not None or return_counts is not None:
-            msg = """
-            use_reps ane return_counts are no longer supported keyword arguments and will throw
-            an error in the next release.
-            collapsed hypergraph automatically names collapsed objects by a string "rep:count"
-            """
-            warnings.warn(msg, DeprecationWarning)
-
-        if return_equivalence_classes:
-            temp, neq = self.collapse_nodes(
-                name="temp", return_equivalence_classes=True
-            )
-            ntemp, eeq = temp.collapse_edges(name=name, return_equivalence_classes=True)
-            return ntemp, neq, eeq
-        else:
-            temp = self.collapse_nodes(name="temp")
-            return temp.collapse_edges(name=name)

-
-
[docs]    def restrict_to_edges(self, edgeset, name=None):
-        """
-        Constructs a hypergraph using a subset of the edges in hypergraph
-
-        Parameters
-        ----------
-        edgeset: iterable of hashables or Entities
-            A subset of elements of the hypergraph edges
-
-        name: str, optional
-
-        Returns
-        -------
-        new hypergraph : Hypergraph
-        """
-        if self._static:
-            E = self._edges
-            setsystem = E.restrict_to(sorted(E.indices(E.keys[0], list(edgeset))))
-            return Hypergraph(setsystem, name=name, use_nwhy=self.nwhy)
-        else:
-            inneredges = set()
-            for e in edgeset:
-                if isinstance(e, Entity):
-                    inneredges.add(e.uid)
-                else:
-                    inneredges.add(e)
-            return Hypergraph({e: self.edges[e] for e in inneredges}, name=name)

-
-
[docs]    def restrict_to_nodes(self, nodeset, name=None):
-        """
-        Constructs a new hypergraph by restricting the edges in the hypergraph to
-        the nodes referenced by nodeset.
-
-        Parameters
-        ----------
-        nodeset: iterable of hashables
-            References a subset of elements of self.nodes
-
-        name: string, optional, default: None
-
-        Returns
-        -------
-        new hypergraph : Hypergraph
-        """
-        if self.isstatic:
-            E = self.edges.restrict_to_levels((1, 0))
-            setsystem = E.restrict_to(sorted(E.indices(E.keys[0], list(nodeset))))
-            return Hypergraph(
-                setsystem.restrict_to_levels((1, 0)), name=name, use_nwhy=self.nwhy
-            )
-        else:
-            memberships = set()
-            innernodes = set()
-            for node in nodeset:
-                innernodes.add(node)
-                if node in self.nodes:
-                    memberships.update(set(self.nodes[node].memberships))
-            newedgeset = dict()
-            for e in memberships:
-                if e in self.edges:
-                    temp = self.edges[e].uidset.intersection(innernodes)
-                    if temp:
-                        newedgeset[e] = Entity(e, temp, **self.edges[e].properties)
-            return Hypergraph(newedgeset, name=name)

-
-
[docs]    def toplexes(self, name=None, collapse=False, use_reps=False, return_counts=True):
-        """
-        Returns a :term:`simple hypergraph` corresponding to self.
-
-        Warning
-        -------
-        Collapsing is no longer supported inside the toplexes method. Instead generate a new
-        collapsed hypergraph and compute the toplexes of the new hypergraph.
-
-        Parameters
-        ----------
-        name: str, optional, default: None
-
-        # collapse: boolean, optional, default: False
-        #     Should the hypergraph be collapsed? This would preserve a link between duplicate maximal sets.
-        #     If False then only one of these sets will be used and uniqueness will be up to sets of equal size.
-
-        # use_reps: boolean, optional, default: False
-        #     If collapse=True then each toplex will be named by a representative of the set of
-        #     equivalent edges, default is False (see collapse_edges).
-
-        return_counts: boolean, optional, default: True
-            # If collapse=True then each toplex will be named by a tuple of the representative
-            # of the set of equivalent edges and their count
-
-        """
-        # TODO: There is a better way to do this....need to refactor
-        if collapse:
-            if len(self.edges) > 20:  # TODO: Determine how big is too big.
-                warnings.warn(
-                    "Collapsing a hypergraph can take a long time. It may be preferable to collapse the graph first and pickle it then apply the toplex method separately."
-                )
-            temp = self.collapse_edges()
-        else:
-            temp = self
-
-        if collapse:
-            msg = """
-            collapse, return_counts, and use_reps are no longer supported keyword arguments 
-            and will throw an error in the next release.
-            """
-            warnings.warn(msg, DeprecationWarning)
-
-        thdict = dict()
-        if self.nwhy:
-            tops = self.g.toplexes()
-            E = self.edges.restrict_to(tops)
-            return hnx.Hypergraph(E, use_nwhy=True)
-        else:
-            if self.isstatic:
-                for e in temp.edges:
-                    thdict[e] = temp.edges[e]
-            else:
-                for e in temp.edges:
-                    thdict[e] = temp.edges[e].uidset
-            tops = list()
-            for e in temp.edges:
-                flag = True
-                old_tops = list(tops)
-                for top in old_tops:
-                    if set(thdict[e]).issubset(thdict[top]):
-                        flag = False
-                        break
-                    elif set(thdict[top]).issubset(thdict[e]):
-                        tops.remove(top)
-                if flag:
-                    tops += [e]
-            return self.restrict_to_edges(tops, name=name)

-
-
[docs]    def is_connected(self, s=1, edges=False):
-        """
-        Determines if hypergraph is :term:`s-connected <s-connected, s-node-connected>`.
-
-        Parameters
-        ----------
-        s: int, optional, default: 1
-
-        edges: boolean, optional, default: False
-            If True, will determine if s-edge-connected.
-            For s=1 s-edge-connected is the same as s-connected.
-
-        Returns
-        -------
-        is_connected : boolean
-
-        Notes
-        -----
-
-        A hypergraph is s node connected if for any two nodes v0,vn
-        there exists a sequence of nodes v0,v1,v2,...,v(n-1),vn
-        such that every consecutive pair of nodes v(i),v(i+1)
-        share at least s edges.
-
-        A hypergraph is s edge connected if for any two edges e0,en
-        there exists a sequence of edges e0,e1,e2,...,e(n-1),en
-        such that every consecutive pair of edges e(i),e(i+1)
-        share at least s nodes.
-
-        """
-
-        if self.isstatic:
-            g = self.get_linegraph(s=s, edges=edges)
-            if self.nwhy:
-                return g.is_s_connected()
-            else:
-                return g.is_connected()
-            return result
-        else:
-            if edges:
-                A = self.edge_adjacency_matrix(s=s)
-            else:
-                A = self.adjacency_matrix(s=s)
-            G = nx.from_scipy_sparse_matrix(A)
-            return nx.is_connected(G)

-
-
[docs]    def singletons(self):
-        """
-        Returns a list of singleton edges. A singleton edge is an edge of
-        size 1 with a node of degree 1.
-
-        Returns
-        -------
-        singles : list
-            A list of edge uids.
-        """
-        if self.nwhy:
-            return self.edges.translate(0, self.g.singletons())
-        else:
-            M, rdict, cdict = self.incidence_matrix(index=True)
-            idx = np.argmax(M.shape)  # which axis has fewest members? if 1 then columns
-            cols = M.sum(idx)  # we add down the row index if there are fewer columns
-            singles = list()
-            for c in range(cols.shape[(idx + 1) % 2]):  # index along opposite axis
-                if cols[idx * c, c * ((idx + 1) % 2)] == 1:
-                    # then see if the singleton entry in that column is also singleton in its row
-                    # find the entry
-                    if idx == 0:
-                        r = np.argmax(M.getcol(c))
-                        # and get its sum
-                        s = np.sum(M.getrow(r))
-                        # if this is also 1 then the entry in r,c represents a singleton
-                        # so we want to change that entry to 0 and remove the row.
-                        # this means we want to remove the edge corresponding to c
-                        if s == 1:
-                            singles.append(cdict[c])
-                    else:  # switch the role of r and c
-                        r = np.argmax(M.getrow(c))
-                        s = np.sum(M.getcol(r))
-                        if s == 1:
-                            singles.append(cdict[r])
-            return singles

-
-
[docs]    def remove_singletons(self, name=None):
-        """XX
-        Constructs clone of hypergraph with singleton edges removed.
-
-        Parameters
-        ----------
-        name: str, optional, default: None
-
-        Returns
-        -------
-        new hypergraph : Hypergraph
-
-        """
-        E = [e for e in self.edges if e not in self.singletons()]
-        return self.restrict_to_edges(E)

-
-
[docs]    def s_connected_components(self, s=1, edges=True, return_singletons=False):
-        """
-        Returns a generator for the :term:`s-edge-connected components <s-edge-connected component>`
-        or the :term:`s-node-connected components <s-connected component, s-node-connected component>`
-        of the hypergraph.
-
-        Parameters
-        ----------
-        s : int, optional, default: 1
-
-        edges : boolean, optional, default: True
-            If True will return edge components, if False will return node components
-        return_singletons : bool, optional, default : False
-
-        Notes
-        -----
-        If edges=True, this method returns the s-edge-connected components as
-        lists of lists of edge uids.
-        An s-edge-component has the property that for any two edges e1 and e2
-        there is a sequence of edges starting with e1 and ending with e2
-        such that pairwise adjacent edges in the sequence intersect in at least
-        s nodes. If s=1 these are the path components of the hypergraph.
-
-        If edges=False this method returns s-node-connected components.
-        A list of sets of uids of the nodes which are s-walk connected.
-        Two nodes v1 and v2 are s-walk-connected if there is a
-        sequence of nodes starting with v1 and ending with v2 such that pairwise
-        adjacent nodes in the sequence share s edges. If s=1 these are the
-        path components of the hypergraph.
-
-        Example
-        -------
-            >>> S = {'A':{1,2,3},'B':{2,3,4},'C':{5,6},'D':{6}}
-            >>> H = Hypergraph(S)
-
-            >>> list(H.s_components(edges=True))
-            [{'C', 'D'}, {'A', 'B'}]
-            >>> list(H.s_components(edges=False))
-            [{1, 2, 3, 4}, {5, 6}]
-
-        Yields
-        ------
-        s_connected_components : iterator
-            Iterator returns sets of uids of the edges (or nodes) in the s-edge(node)
-            components of hypergraph.
-
-        """
-        components = list()
-
-        if self.nwhy:
-            g = self.get_linegraph(s, edges=edges)
-            if return_singletons:
-                allobjects = set(self.edges) if edges == True else set(self.nodes)
-                for c in g.s_connected_components():
-                    comp = {self.get_name(nd, edges=edges) for nd in c}
-                    allobjects.difference_update(comp)
-                for c in g.s_connected_components():
-                    yield {self.get_name(nd, edges=edges) for nd in c}
-                for obj in allobjects:
-                    yield {obj}
-            else:
-                for c in g.s_connected_components():
-                    comp = {self.get_name(nd, edges=edges) for nd in c}
-                    yield comp
-
-        elif self.isstatic:
-            g = self.get_linegraph(s, edges=edges)
-            for c in nx.connected_components(g):
-                if not return_singletons and len(c) == 1:
-                    continue
-                yield {self.get_name(n, edges=edges) for n in c}
-        else:
-            if edges:
-                A, coldict = self.edge_adjacency_matrix(s=s, index=True)
-                G = nx.from_scipy_sparse_matrix(A)
-                # if not return_singletons:
-                #     temp = [c for c in nx.connected_components(G) if len(c) > 1]
-                # else:
-                #     temp = nx.connected_components(G)
-                for c in nx.connected_components(G):
-                    if not return_singletons and len(c) == 1:
-                        continue
-                    yield {coldict[n] for n in c}
-            else:
-                A, rowdict = self.adjacency_matrix(s=s, index=True)
-                G = nx.from_scipy_sparse_matrix(A)
-                for c in nx.connected_components(G):
-                    if not return_singletons:
-                        if len(c) == 1:
-                            continue
-                    yield {rowdict[n] for n in c}

-
-
[docs]    def s_component_subgraphs(self, s=1, edges=True, return_singletons=False):
-        """
-
-        Returns a generator for the induced subgraphs of s_connected components.
-        Removes singletons unless return_singletons is set to True. Computed using
-        s-linegraph generated either by the hypergraph (edges=True) or its dual
-        (edges = False)
-
-        Parameters
-        ----------
-        s : int, optional, default: 1
-
-        edges : boolean, optional, edges=False
-            Determines if edge or node components are desired. Returns
-            subgraphs equal to the hypergraph restricted to each set of nodes(edges) in the
-            s-connected components or s-edge-connected components
-        return_singletons : bool, optional
-
-        Yields
-        ------
-        s_component_subgraphs : iterator
-            Iterator returns subgraphs generated by the edges (or nodes) in the
-            s-edge(node) components of hypergraph.
-
-        """
-        for idx, c in enumerate(
-            self.s_components(s=s, edges=edges, return_singletons=return_singletons)
-        ):
-            if edges:
-                yield self.restrict_to_edges(c, name=f"{self.name}:{idx}")
-            else:
-                yield self.restrict_to_nodes(c, name=f"{self.name}:{idx}")

-
-
[docs]    def s_components(self, s=1, edges=True, return_singletons=True):
-        """
-        Same as s_connected_components
-
-        See Also
-        --------
-        s_connected_components
-        """
-        return self.s_connected_components(
-            s=s, edges=edges, return_singletons=return_singletons
-        )

-
-
[docs]    def connected_components(self, edges=False, return_singletons=True):
-        """
-        Same as :meth:`s_connected_components` with s=1, but nodes are returned
-        by default. Return iterator.
-
-        See Also
-        --------
-        s_connected_components
-        """
-        return self.s_connected_components(edges=edges, return_singletons=True)

-
-
[docs]    def connected_component_subgraphs(self, return_singletons=True):
-        """
-        Same as :meth:`s_component_subgraphs` with s=1. Returns iterator
-
-        See Also
-        --------
-        s_component_subgraphs
-        """
-        return self.s_component_subgraphs(return_singletons=return_singletons)

-
-
[docs]    def components(self, edges=False, return_singletons=True):
-        """
-        Same as :meth:`s_connected_components` with s=1, but nodes are returned
-        by default. Return iterator.
-
-        See Also
-        --------
-        s_connected_components
-        """
-        return self.s_connected_components(s=1, edges=edges)

-
-
[docs]    def component_subgraphs(self, return_singletons=False):
-        """
-        Same as :meth:`s_components_subgraphs` with s=1. Returns iterator.
-
-        See Also
-        --------
-        s_component_subgraphs
-        """
-        return self.s_component_subgraphs(return_singletons=return_singletons)

-
-
[docs]    def node_diameters(self, s=1):
-        """
-        Returns the node diameters of the connected components in hypergraph.
-
-        Parameters
-        ----------
-        list of the diameters of the s-components and
-        list of the s-component nodes
-        """
-        if self.nwhy:
-            g = self.get_linegraph(s, edges=False)
-            if g.is_s_connected():
-                return g.s_diameter()
-            else:
-                diameters = list()
-                nodelists = list()
-                for c in g.s_connected_components():
-                    tc = self.edges.labs(1)[c]
-                    nodelists.append(tc)
-                    diameters.append(self.restrict_to_nodes(tc).node_diameters(s=s))
-        else:
-            A, coldict = self.adjacency_matrix(s=s, index=True)
-            G = nx.from_scipy_sparse_matrix(A)
-            diams = []
-            comps = []
-            for c in nx.connected_components(G):
-                diamc = nx.diameter(G.subgraph(c))
-                temp = set()
-                for e in c:
-                    temp.add(coldict[e])
-                comps.append(temp)
-                diams.append(diamc)
-            loc = np.argmax(diams)
-            return diams[loc], diams, comps

-
-
[docs]    def edge_diameters(self, s=1):
-        """
-        Returns the edge diameters of the s_edge_connected component subgraphs
-        in hypergraph.
-
-        Parameters
-        ----------
-        s : int, optional, default: 1
-
-        Returns
-        -------
-        maximum diameter : int
-
-        list of diameters : list
-            List of edge_diameters for s-edge component subgraphs in hypergraph
-
-        list of component : list
-            List of the edge uids in the s-edge component subgraphs.
-
-        """
-        if self.nwhy:
-            g = self.get_linegraph(s, edges=True)
-            if g.is_s_connected():
-                return g.s_diameter()
-            else:
-                diameters = list()
-                edgelists = list()
-                for c in g.s_connected_components():
-                    tc = self.edges.labs(0)[c]
-                    edgelists.append(tc)
-                    diameters.append(self.restrict_to_edges(tc).edge_diameters(s=s))
-        else:
-            A, coldict = self.edge_adjacency_matrix(s=s, index=True)
-            G = nx.from_scipy_sparse_matrix(A)
-            diams = []
-            comps = []
-            for c in nx.connected_components(G):
-                diamc = nx.diameter(G.subgraph(c))
-                temp = set()
-                for e in c:
-                    temp.add(coldict[e])
-                comps.append(temp)
-                diams.append(diamc)
-            loc = np.argmax(diams)
-            return diams[loc], diams, comps

-
-
[docs]    def diameter(self, s=1):
-        """
-        Returns the length of the longest shortest s-walk between nodes in hypergraph
-
-        Parameters
-        ----------
-        s : int, optional, default: 1
-
-        Returns
-        -------
-        diameter : int
-
-        Raises
-        ------
-        HyperNetXError
-            If hypergraph is not s-edge-connected
-
-        Notes
-        -----
-        Two nodes are s-adjacent if they share s edges.
-        Two nodes v_start and v_end are s-walk connected if there is a sequence of
-        nodes v_start, v_1, v_2, ... v_n-1, v_end such that consecutive nodes
-        are s-adjacent. If the graph is not connected, an error will be raised.
-
-        """
-        if self.nwhy:
-            g = self.get_linegraph(s, edges=False)
-            if g.is_s_connected():
-                return g.s_diameter()
-            else:
-                raise HyperNetXError(f"Hypergraph is not s-connected. s={s}")
-        else:
-            A = self.adjacency_matrix(s=s)
-            G = nx.from_scipy_sparse_matrix(A)
-            if nx.is_connected(G):
-                return nx.diameter(G)
-            else:
-                raise HyperNetXError(f"Hypergraph is not s-connected. s={s}")

-
-
[docs]    def edge_diameter(self, s=1):
-        """
-        Returns the length of the longest shortest s-walk between edges in hypergraph
-
-        Parameters
-        ----------
-        s : int, optional, default: 1
-
-        Return
-        ------
-        edge_diameter : int
-
-        Raises
-        ------
-        HyperNetXError
-            If hypergraph is not s-edge-connected
-
-        Notes
-        -----
-        Two edges are s-adjacent if they share s nodes.
-        Two nodes e_start and e_end are s-walk connected if there is a sequence of
-        edges e_start, e_1, e_2, ... e_n-1, e_end such that consecutive edges
-        are s-adjacent. If the graph is not connected, an error will be raised.
-
-        """
-        if self.nwhy:
-            g = self.get_linegraph(s, edges=True)
-            if g.is_s_connected():
-                return g.s_diameter()
-            else:
-                raise HyperNetXError(f"Hypergraph is not s-connected. s={s}")
-        else:
-            A = self.edge_adjacency_matrix(s=s)
-            G = nx.from_scipy_sparse_matrix(A)
-            if nx.is_connected(G):
-                return nx.diameter(G)
-            else:
-                raise HyperNetXError(f"Hypergraph is not s-connected. s={s}")

-
-
[docs]    def distance(self, source, target, s=1):
-        """
-        Returns the shortest s-walk distance between two nodes in the hypergraph.
-
-        Parameters
-        ----------
-        source : node.uid or node
-            a node in the hypergraph
-
-        target : node.uid or node
-            a node in the hypergraph
-
-        s : positive integer
-            the number of edges
-
-        Returns
-        -------
-        s-walk distance : int
-
-        See Also
-        --------
-        edge_distance
-
-        Notes
-        -----
-        The s-distance is the shortest s-walk length between the nodes.
-        An s-walk between nodes is a sequence of nodes that pairwise share
-        at least s edges. The length of the shortest s-walk is 1 less than
-        the number of nodes in the path sequence.
-
-        Uses the networkx shortest_path_length method on the graph
-        generated by the s-adjacency matrix.
-
-        """
-        if self.isstatic:
-            g = self.get_linegraph(s=s, edges=False)
-            src = self.get_id(source, edges=False)
-            tgt = self.get_id(target, edges=False)
-            try:
-                if self.nwhy:
-                    d = g.s_distance(src, tgt)
-                    if d == -1:
-                        warnings.warn(f"No {s}-path between {source} and {target}")
-                        return np.inf
-                    else:
-                        return d
-                else:
-                    return nx.shortest_path(g, src, tgt)
-            except:
-                warnings.warn(f"No {s}-path between {source} and {target}")
-                return np.inf
-        else:
-            if isinstance(source, Entity):
-                source = source.uid
-            if isinstance(target, Entity):
-                target = target.uid
-            A, rowdict = self.adjacency_matrix(s=s, index=True)
-            g = nx.from_scipy_sparse_matrix(A)
-            rkey = {v: k for k, v in rowdict.items()}
-            try:
-                path = nx.shortest_path_length(g, rkey[source], rkey[target])
-                return path
-            except:
-                warnings.warn(f"No {s}-path between {source} and {target}")
-                return np.inf

-
-
[docs]    def edge_distance(self, source, target, s=1):
-        """XX TODO: still need to return path and translate into user defined nodes and edges
-        Returns the shortest s-walk distance between two edges in the hypergraph.
-
-        Parameters
-        ----------
-        source : edge.uid or edge
-            an edge in the hypergraph
-
-        target : edge.uid or edge
-            an edge in the hypergraph
-
-        s : positive integer
-            the number of intersections between pairwise consecutive edges
-
-        TODO: add edge weights
-        weight : None or string, optional, default: None
-            if None then all edges have weight 1. If string then edge attribute
-            string is used if available.
-
-
-        Returns
-        -------
-        s- walk distance : the shortest s-walk edge distance
-            A shortest s-walk is computed as a sequence of edges,
-            the s-walk distance is the number of edges in the sequence
-            minus 1. If no such path exists returns np.inf.
-
-        See Also
-        --------
-        distance
-
-        Notes
-        -----
-            The s-distance is the shortest s-walk length between the edges.
-            An s-walk between edges is a sequence of edges such that consecutive pairwise
-            edges intersect in at least s nodes. The length of the shortest s-walk is 1 less than
-            the number of edges in the path sequence.
-
-            Uses the networkx shortest_path_length method on the graph
-            generated by the s-edge_adjacency matrix.
-
-        """
-        if self.isstatic:
-            g = self.get_linegraph(s=s, edges=True)
-            src = self.get_id(source, edges=True)
-            tgt = self.get_id(target, edges=True)
-            try:
-                if self.nwhy:
-                    d = g.s_distance(src, tgt)
-                    if d == -1:
-                        warnings.warn(f"No {s}-path between {source} and {target}")
-                        return np.inf
-                    else:
-                        return d
-                else:
-                    return nx.shortest_path(g, src, tgt)
-            except:
-                warnings.warn(f"No {s}-path between {source} and {target}")
-                return np.inf
-        else:
-            if isinstance(source, Entity):
-                source = source.uid
-            if isinstance(target, Entity):
-                target = target.uid
-            A, coldict = self.edge_adjacency_matrix(s=s, index=True)
-            g = nx.from_scipy_sparse_matrix(A)
-            ckey = {v: k for k, v in coldict.items()}
-            try:
-                path = nx.shortest_path_length(g, ckey[source], ckey[target])
-                return path
-            except:
-                warnings.warn(f"No {s}-path between {source} and {target}")
-                return np.inf

-
-
[docs]    def dataframe(self, sort_rows=False, sort_columns=False):
-        """
-        Returns a pandas dataframe for hypergraph indexed by the nodes and
-        with column headers given by the edge names.
-
-        Parameters
-        ----------
-        sort_rows : bool, optional, default=True
-            sort rows based on hashable node names
-        sort_columns : bool, optional, default=True
-            sort columns based on hashable edge names
-
-        """
-
-        mat, rdx, cdx = self.edges.incidence_matrix(index=True)
-        index = [rdx[i] for i in rdx]
-        columns = [cdx[j] for j in cdx]
-        df = pd.DataFrame(mat.todense(), index=index, columns=columns)
-        if sort_rows:
-            df = df.sort_index()
-        if sort_columns:
-            df = df[sorted(columns)]
-        return df

-
-
[docs]    @classmethod
-    def from_bipartite(
-        cls, B, set_names=("nodes", "edges"), name=None, static=False, use_nwhy=False
-    ):
-        """
-        Static method creates a Hypergraph from a bipartite graph.
-
-        Parameters
-        ----------
-
-        B: nx.Graph()
-            A networkx bipartite graph. Each node in the graph has a property
-            'bipartite' taking the value of 0 or 1 indicating a 2-coloring of the graph.
-
-        set_names: iterable of length 2, optional, default = ['nodes','edges']
-            Category names assigned to the graph nodes associated to each bipartite set
-
-        name: hashable
-
-        static: bool
-
-        Returns
-        -------
-         : Hypergraph
-
-        Notes
-        -----
-        A partition for the nodes in a bipartite graph generates a hypergraph.
-
-            >>> import networkx as nx
-            >>> B = nx.Graph()
-            >>> B.add_nodes_from([1, 2, 3, 4], bipartite=0)
-            >>> B.add_nodes_from(['a', 'b', 'c'], bipartite=1)
-            >>> B.add_edges_from([(1, 'a'), (1, 'b'), (2, 'b'), (2, 'c'), (3, 'c'), (4, 'a')])
-            >>> H = Hypergraph.from_bipartite(B)
-            >>> H.nodes, H.edges
-            # output: (EntitySet(_:Nodes,[1, 2, 3, 4],{}), EntitySet(_:Edges,['b', 'c', 'a'],{}))
-
-        """
-        # TODO: Add filepath keyword to signatures here and with dataframe and numpy array
-        edges = []
-        nodes = []
-        for n, d in B.nodes(data=True):
-            if d["bipartite"] == 0:
-                nodes.append(n)
-            else:
-                edges.append(n)
-
-        if not bipartite.is_bipartite_node_set(B, nodes):
-            raise HyperNetXError(
-                "Error: Method requires a 2-coloring of a bipartite graph."
-            )
-
-        if static:
-            elist = []
-            for e in list(B.edges):
-                if e[0] in nodes:
-                    elist.append([e[0], e[1]])
-                else:
-                    elist.append([e[1], e[0]])
-            df = pd.DataFrame(elist, columns=set_names)
-            E = StaticEntitySet(entity=df)
-            name = name or "_"
-            return Hypergraph(E, name=name, use_nwhy=use_nwhy)
-        else:
-            node_entities = {
-                n: Entity(n, [], properties=B.nodes(data=True)[n]) for n in nodes
-            }
-            edge_dict = {
-                e: [node_entities[n] for n in list(B.neighbors(e))] for e in edges
-            }
-            name = name or "_"
-            return Hypergraph(setsystem=edge_dict, name=name)

-
-
[docs]    @classmethod
-    def from_numpy_array(
-        cls,
-        M,
-        node_names=None,
-        edge_names=None,
-        node_label="nodes",
-        edge_label="edges",
-        name=None,
-        key=None,
-        static=False,
-        use_nwhy=False,
-    ):
-        """
-        Create a hypergraph from a real valued matrix represented as a 2 dimensionsl numpy array.
-        The matrix is converted to a matrix of 0's and 1's so that any truthy cells are converted to 1's and
-        all others to 0's.
-
-        Parameters
-        ----------
-        M : real valued array-like object, 2 dimensions
-            representing a real valued matrix with rows corresponding to nodes and columns to edges
-
-        node_names : object, array-like, default=None
-            List of node names must be the same length as M.shape[0].
-            If None then the node names correspond to row indices with 'v' prepended.
-
-        edge_names : object, array-like, default=None
-            List of edge names must have the same length as M.shape[1].
-            If None then the edge names correspond to column indices with 'e' prepended.
-
-        name : hashable
-
-        key : (optional) function
-            boolean function to be evaluated on each cell of the array,
-            must be applicable to numpy.array
-
-        Returns
-        -------
-         : Hypergraph
-
-        Note
-        ----
-        The constructor does not generate empty edges.
-        All zero columns in M are removed and the names corresponding to these
-        edges are discarded.
-
-
-        """
-        # Create names for nodes and edges
-        # Validate the size of the node and edge arrays
-
-        M = np.array(M)
-        if len(M.shape) != (2):
-            raise HyperNetXError("Input requires a 2 dimensional numpy array")
-        # apply boolean key if available
-        if key:
-            M = key(M)
-
-        if node_names is not None:
-            nodenames = np.array(node_names)
-            if len(nodenames) != M.shape[0]:
-                raise HyperNetXError(
-                    "Number of node names does not match number of rows."
-                )
-        else:
-            nodenames = np.array([f"v{idx}" for idx in range(M.shape[0])])
-
-        if edge_names is not None:
-            edgenames = np.array(edge_names)
-            if len(edgenames) != M.shape[1]:
-                raise HyperNetXError(
-                    "Number of edge_names does not match number of columns."
-                )
-        else:
-            edgenames = np.array([f"e{jdx}" for jdx in range(M.shape[1])])
-
-        if static or use_nwhy:
-            arr = np.array(M)
-            if key:
-                arr = key(arr) * 1
-            arr = arr.transpose()
-            labels = OrderedDict([(edge_label, edgenames), (node_label, nodenames)])
-            E = StaticEntitySet(arr=arr, labels=labels)
-            return Hypergraph(E, name=name, use_nwhy=use_nwhy)
-
-        else:
-            # Remove empty column indices from M columns and edgenames
-            colidx = np.array([jdx for jdx in range(M.shape[1]) if any(M[:, jdx])])
-            colidxsum = np.sum(colidx)
-            if not colidxsum:
-                return Hypergraph()
-            else:
-                M = M[:, colidx]
-                edgenames = edgenames[colidx]
-                edict = dict()
-                # Create an EntitySet of edges from M
-                for jdx, e in enumerate(edgenames):
-                    edict[e] = nodenames[
-                        [idx for idx in range(M.shape[0]) if M[idx, jdx]]
-                    ]
-                return Hypergraph(edict, name=name)

-
-
[docs]    @classmethod
-    def from_dataframe(
-        cls,
-        df,
-        columns=None,
-        rows=None,
-        name=None,
-        fillna=0,
-        transpose=False,
-        transforms=[],
-        key=None,
-        node_label="nodes",
-        edge_label="edges",
-        static=False,
-        use_nwhy=False,
-    ):
-        """
-        Create a hypergraph from a Pandas Dataframe object using index to label vertices
-        and Columns to label edges. The values of the dataframe are transformed into an 
-        incidence matrix.  
-        Note this is different than passing a dataframe directly
-        into the Hypergraph constructor. The latter automatically generates a static hypergraph
-        with edge and node labels given by the cell values.
-
-        Parameters
-        ----------
-        df : Pandas.Dataframe
-            a real valued dataframe with a single index
-
-        columns : (optional) list, default = None
-            restricts df to the columns with headers in this list.
-
-        rows : (optional) list, default = None
-            restricts df to the rows indexed by the elements in this list.
-
-        name : (optional) string, default = None
-
-        fillna : float, default = 0
-            a real value to place in empty cell, all-zero columns will not generate
-            an edge.
-
-        transpose : (optional) bool, default = False
-            option to transpose the dataframe, in this case df.Index will label the edges
-            and df.columns will label the nodes, transpose is applied before transforms and
-            key
-
-        transforms : (optional) list, default = []
-            optional list of transformations to apply to each column,
-            of the dataframe using pd.DataFrame.apply().
-            Transformations are applied in the order they are
-            given (ex. abs). To apply transforms to rows or for additional
-            functionality, consider transforming df using pandas.DataFrame methods
-            prior to generating the hypergraph.
-
-        key : (optional) function, default = None
-            boolean function to be applied to dataframe. Must be defined on numpy
-            arrays.
-
-        See also
-        --------
-        from_numpy_array())
-
-
-        Returns
-        -------
-        : Hypergraph
-
-        Notes
-        -----
-        The `from_dataframe` constructor does not generate empty edges.
-        All-zero columns in df are removed and the names corresponding to these
-        edges are discarded.
-        Restrictions and data processing will occur in this order:
-
-            1. column and row restrictions
-            2. fillna replace NaNs in dataframe
-            3. transpose the dataframe
-            4. transforms in the order listed
-            5. boolean key
-
-        This method offers the above options for wrangling a dataframe into an incidence
-        matrix for a hypergraph. For more flexibility we recommend you use the Pandas
-        library to format the values of your dataframe before submitting it to this
-        constructor.
-
-        """
-
-        if type(df) != pd.core.frame.DataFrame:
-            raise HyperNetXError("Error: Input object must be a pandas dataframe.")
-
-        if columns:
-            df = df[columns]
-        if rows:
-            df = df.loc[rows]
-
-        df = df.fillna(fillna)
-        if transpose:
-            df = df.transpose()
-
-        # node_names = np.array(df.index)
-        # edge_names = np.array(df.columns)
-
-        for t in transforms:
-            df = df.apply(t)
-        if key:
-            mat = key(df.values) * 1
-        else:
-            mat = df.values * 1
-
-        params = {
-            "node_names": np.array(df.index),
-            "edge_names": np.array(df.columns),
-            "name": name,
-            "node_label": node_label,
-            "edge_label": edge_label,
-            "static": static,
-            "use_nwhy": use_nwhy,
-        }
-        return cls.from_numpy_array(mat, **params)

-
-
-# end of Hypergraph class
-
-
-def _make_3_arrays(mat):
-    arr = coo_matrix(mat)
-    return arr.row, arr.col, arr.data
-
- -
- -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_modules/classes/staticentity.html b/docs/build/_modules/classes/staticentity.html deleted file mode 100644 index 091c7421..00000000 --- a/docs/build/_modules/classes/staticentity.html +++ /dev/null @@ -1,1294 +0,0 @@ - - - - - - - - - - classes.staticentity — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - -
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Source code for classes.staticentity

-from collections import OrderedDict, defaultdict
-from collections.abc import Iterable
-import warnings
-from copy import copy
-import numpy as np
-import networkx as nx
-from hypernetx import *
-from hypernetx.exception import HyperNetXError
-from hypernetx.classes.entity import Entity, EntitySet
-from hypernetx.utils import HNXCount, DefaultOrderedDict, remove_row_duplicates
-from scipy.sparse import coo_matrix, csr_matrix, issparse
-import itertools as it
-import pandas as pd
-
-__all__ = ["StaticEntity", "StaticEntitySet"]
-
-
-
[docs]class StaticEntity(object):
-
-    """
-    .. _staticentity:
-
-    Parameters
-    ----------
-    entity : StaticEntity, StaticEntitySet, Entity, EntitySet, pandas.DataFrame, dict, or list of lists
-        If a pandas.DataFrame, an error will be raised if there are nans. 
-    data : array or array-like
-        Two dimensional array of integers. Provides sparse tensor indices for incidence
-        tensor. 
-    arr : numpy.ndarray or scip.sparse.matrix, optional, default=None
-        Incidence tensor of data. 
-    labels : OrderedDict of lists, optional, default=None
-        User defined labels corresponding to integers in data.  
-    uid : hashable, optional, default=None  
-
-    props : user defined keyword arguments to be added to a properties dictionary, optional
-
-    Attributes
-    ----------
-    properties : dict
-        Description
-
-    """
-
-    def __init__(
-        self, entity=None, data=None, arr=None, labels=None, uid=None, **props
-    ):
-
-        self._uid = uid
-        self.properties = {}
-        if entity is not None:
-            if isinstance(entity, StaticEntity) or isinstance(entity, StaticEntitySet):
-                self.properties.update(entity.properties)
-                self.properties.update(props)
-                self.__dict__.update(self.properties)
-                self.__dict__.update(props)
-                self._data = entity.data.copy()
-                self._dimensions = entity.dimensions
-                self._dimsize = entity.dimsize
-                self._labels = OrderedDict(
-                    (category, np.array(values))
-                    for category, values in entity.labels.items()
-                )
-                self._keys = np.array(list(self._labels.keys()))
-                self._keyindex = lambda category: int(
-                    np.where(np.array(list(self._labels.keys())) == category)[0]
-                )
-                self._index = (
-                    lambda category, value: int(
-                        np.where(self._labels[category] == value)[0]
-                    )
-                    if np.where(self._labels[category] == value)[0].size > 0
-                    else None
-                )
-                self._arr = None
-            elif isinstance(entity, pd.DataFrame):
-                self.properties.update(props)
-                data, labels, counts = _turn_dataframe_into_entity(
-                    entity, return_counts=True
-                )
-                self.properties.update({"counts": counts})
-                self.__dict__.update(self.properties)
-                self._data = data
-                self._labels = labels
-                self._arr = None
-                self._dimensions = tuple([max(x) + 1 for x in self._data.transpose()])
-                self._dimsize = len(self._dimensions)
-                self._keys = np.array(list(self._labels.keys()))
-                self._keyindex = lambda category: int(
-                    np.where(np.array(list(self._labels.keys())) == category)[0]
-                )
-                self._index = (
-                    lambda category, value: int(
-                        np.where(self._labels[category] == value)[0]
-                    )
-                    if np.where(self._labels[category] == value)[0].size > 0
-                    else None
-                )
-            else:
-                if isinstance(entity, Entity) or isinstance(entity, EntitySet):
-                    d = entity.incidence_dict
-                    self._data, self._labels = _turn_dict_to_staticentity(
-                        d
-                    )  # For now duplicate entries will be removed.
-                elif isinstance(entity, dict):  # returns only 2 levels
-                    self._data, self._labels = _turn_dict_to_staticentity(
-                        entity
-                    )  # For now duplicate entries will be removed.
-                else:  # returns only 2 levels
-                    self._data, self._labels = _turn_iterable_to_staticentity(entity)
-                self._dimensions = tuple([len(self._labels[k]) for k in self._labels])
-                self._dimsize = len(self._dimensions)
-                self._keys = np.array(list(self._labels.keys()))
-                self._keyindex = lambda category: int(
-                    np.where(np.array(list(self._labels.keys())) == category)[0]
-                )
-                self._index = (
-                    lambda category, value: int(
-                        np.where(self._labels[category] == value)[0]
-                    )
-                    if np.where(self._labels[category] == value)[0].size > 0
-                    else None
-                )
-                self.properties.update(props)
-                self.__dict__.update(
-                    self.properties
-                )  # Add function to set attributes ###########!!!!!!!!!!!!!
-                self._arr = None
-        elif data is not None:
-            self._arr = None
-            self._data, counts = remove_row_duplicates(
-                data, return_counts=True
-            )  # TODO Incorporate counts into data for distance
-            self.properties["counts"] = counts
-            self._dimensions = tuple([max(x) + 1 for x in self._data.transpose()])
-            self._dimsize = len(self._dimensions)
-            self.properties.update(props)
-            self.__dict__.update(props)
-            if (
-                labels is not None
-            ):  # determine if hashmaps might be better than lambda expressions to recover indices
-                self._labels = OrderedDict(
-                    (category, np.array(values)) for category, values in labels.items()
-                )  # OrderedDict(category,np.array([categorical values ....])) is aligned to arr
-                self._keyindex = lambda category: int(
-                    np.where(np.array(list(self._labels.keys())) == category)[0]
-                )
-                self._keys = np.array(list(labels.keys()))
-                self._index = (
-                    lambda category, value: int(
-                        np.where(self._labels[category] == value)[0]
-                    )
-                    if np.where(self._labels[category] == value)[0].size > 0
-                    else None
-                )
-            else:
-                self._labels = OrderedDict(
-                    [
-                        (int(dim), np.arange(ct))
-                        for dim, ct in enumerate(self.dimensions)
-                    ]
-                )
-                self._keyindex = lambda category: int(category)
-                self._keys = np.arange(self._dimsize)
-                self._index = (
-                    lambda category, value: value
-                    if value in self._labels[category]
-                    else None
-                )
-                # self._index = lambda category, value: int(np.where(self._labels[category] == value)[0]) if np.where(self._labels[category] == value)[0].size > 0 else None
-        elif arr is not None:
-            self._arr = arr
-            self.properties.update(props)
-            self.__dict__.update(props)
-            self._state_dict = {"arr": arr * 1}
-            self._dimensions = arr.shape
-            self._dimsize = len(arr.shape)
-            self._data = _turn_tensor_to_data(arr * 1)
-            if (
-                labels is not None
-            ):  # determine if hashmaps might be better than lambda expressions to recover indices
-                self._labels = OrderedDict(
-                    (category, np.array(values)) for category, values in labels.items()
-                )
-                self._keyindex = lambda category: int(
-                    np.where(np.array(list(self._labels.keys())) == category)[0]
-                )
-                self._keys = np.array(list(labels.keys()))
-                self._index = (
-                    lambda category, value: int(
-                        np.where(self._labels[category] == value)[0]
-                    )
-                    if np.where(self._labels[category] == value)[0].size > 0
-                    else None
-                )
-            else:
-                self._labels = OrderedDict(
-                    [
-                        (int(dim), np.arange(ct))
-                        for dim, ct in enumerate(self.dimensions)
-                    ]
-                )
-                self._keyindex = lambda category: int(category)
-                self._keys = np.arange(self._dimsize)
-                self._index = (
-                    lambda category, value: value
-                    if value in self._labels[category]
-                    else None
-                )
-        else:  # no entity, data or arr is given
-
-            if labels is not None:
-                self._labels = OrderedDict(
-                    (category, np.array(values)) for category, values in labels.items()
-                )
-                self._dimensions = tuple([len(labels[k]) for k in labels])
-                self._data = np.zeros((0, len(labels)), dtype=int)
-                self._arr = np.empty(self._dimensions, dtype=int)
-                self._state_dict = {"arr": np.empty(self.dimensions, dtype=int)}
-                self._dimsize = len(self._dimensions)
-                self._keyindex = lambda category: int(
-                    np.where(np.array(list(self._labels.keys())) == category)[0]
-                )
-                self._keys = np.array(list(labels.keys()))
-                self._index = (
-                    lambda category, value: int(
-                        np.where(self._labels[category] == value)[0]
-                    )
-                    if np.where(self._labels[category] == value)[0].size > 0
-                    else None
-                )
-            else:
-                self._data = np.zeros((0, 0), dtype=int)
-                self._arr = np.array([], dtype=int)
-                self._labels = OrderedDict([])
-                self._dimensions = tuple([])
-                self._dimsize = 0
-                self._keyindex = lambda category: None
-                self._keys = np.array([])
-                self._index = lambda category, value: None
-
-            # if labels is a list of categorical values, then change it into an
-            # ordered dictionary?
-            self.properties = props
-            self.__dict__.update(props)  # keyed by the method name and signature
-
-        if len(self._labels) > 0:
-            self._labs = lambda kdx: self._labels.get(self._keys[kdx], {})
-        else:
-            self._labs = lambda kdx: {}
-
-    @property
-    def arr(self):
-        if self._arr is not None:
-            if type(self._arr) == int and self._arr == 0:
-                print("arr cannot be computed")
-        else:
-            try:
-                imat = np.zeros(self.dimensions, dtype=int)
-                for d in self._data:
-                    imat[tuple(d)] = 1
-                self._arr = imat
-            except Exception as ex:
-                print(ex)
-                print("arr cannot be computed")
-                self._arr = 0
-        return self._arr  # Do we need to return anything here
-
-    # @property
-    # def array_with_counts(self):
-    #     """
-    #     This method will be included in future release.
-    #     It allows duplicate rows in the data table
-    #     Returns
-    #     -------
-    #     np.ndarray
-    #     """
-    #     if self._arr is not None:
-    #         if type(self._arr) == int and self._arr == 0:
-    #             print("arr cannot be computed")
-    #         else:
-    #             try:
-    #                 imat = np.zeros(self.dimensions, dtype=int)
-    #                 for d in self._data:
-    #                     imat[tuple(d)] += 1
-    #                 self._arr = imat
-    #             except Exception as ex:
-    #                 print(ex)
-    #                 print("arr cannot be computed")
-    #                 self._arr = 0
-    #     return self._arr
-
-    @property
-    def data(self):
-        """
-        Data array or tensor array of Static Entity
-
-        Returns
-        -------
-        np.ndarray
-        """
-
-        return self._data
-
-    @property
-    def labels(self):
-        """
-        Ordered dictionary of labels
-
-        Returns
-        -------
-        collections.OrderedDict
-        """
-        return self._labels
-
-    @property
-    def dimensions(self):
-        """
-        Dimension of Static Entity data
-
-        Returns
-        -------
-        tuple
-        """
-        return self._dimensions
-
-    @property
-    def dimsize(self):
-        """
-        Number of categories in the data
-
-        Returns
-        -------
-        int
-        """
-        return self._dimsize
-
-    @property
-    def keys(self):
-        """
-        Array of keys of labels
-
-        Returns
-        -------
-        np.ndarray
-        """
-        return self._keys
-
-    @property
-    def keyindex(self):
-        """
-        Returns the index of a category in keys array
-
-        Returns
-        -------
-        int
-        """
-        return self._keyindex
-
-    @property
-    def uid(self):
-        return self._uid
-
-    @property
-    def uidset(self):
-        """
-        Returns a set of the string identifiers for Static Entity
-
-        Returns
-        -------
-        frozenset
-        """
-        return self.uidset_by_level(0)
-
-    @property
-    def elements(self):
-        """
-        Keys and values in the order of insertion 
-
-        Returns
-        -------
-        collections.OrderedDict
-
-        level1 = elements, level2 = children
-        """
-        if len(self._keys) == 1:
-            return {k: {} for k in self._labels[self._keys[0]]}
-        else:
-            return self.elements_by_level(0, translate=True)
-
-    @property
-    def children(self):
-        """
-        Labels of keys of first index
-
-        Returns
-        -------
-        set
-        """
-        return set(self._labs(1))
-
-    @property
-    def incidence_dict(self):
-        """
-        Dictionary using index 0 as nodes and index 1 as edges
-
-        Returns
-        -------
-        collections.OrderedDict
-        """
-        return self.elements_by_level(0, 1, translate=True)
-
-    @property
-    def dataframe(self):
-        """
-        Returns the entity data in DataFrame format
-
-        Returns
-        -------
-        pandas.core.frame.DataFrame
-        """
-        return self.turn_entity_data_into_dataframe(self.data)
-
-    def __len__(self):
-        """
-        Returns the number of elements in Static Entity
-
-        Returns
-        -------
-        int
-        """
-        return self._dimensions[0]
-
-    def __str__(self):
-        """
-        Return the Static Entity uid
-
-        Returns
-        -------
-        string
-        """
-        return f"{self.uid}"
-
-    def __repr__(self):
-        """
-        Returns a string resembling the constructor for staticentity without any
-        children
-
-        Returns
-        -------
-        string
-        """
-        return f"StaticEntity({self._uid},{list(self.uidset)},{self.properties})"
-
-    def __contains__(self, item):
-        """
-        Defines containment for StaticEntity based on labels/categories.
-
-        Parameters
-        ----------
-        item : string
-
-        Returns
-        -------
-        bool
-        """
-        return item in np.concatenate(list(self._labels.values()))
-
-    def __getitem__(self, item):
-        """
-        Get value of key in E.elements
-
-        Parameters
-        ----------
-        item : string
-
-        Returns
-        -------
-        list
-        """
-        # return self.elements_by_level(0, 1)[item]
-        return self.elements[item]
-
-    def __iter__(self):
-        """
-        Create iterator from E.elements
-
-        Returns
-        -------
-        odict_iterator
-        """
-        return iter(self.elements)
-
-    def __call__(self, label_index=0):
-        return iter(self._labs(label_index))
-
-
[docs]    def size(self):
-        """
-        The number of elements in E, the size of dimension 0 in the E.arr
-
-        Returns
-        -------
-        int
-        """
-        return len(self)

-
-
[docs]    def labs(self, kdx):
-        """
-        Retrieve labels by index in keys
-
-        Parameters
-        ----------
-        kdx : int
-            index of key in E.keys
-
-        Returns
-        -------
-        np.ndarray
-        """
-        return self._labs(kdx)

-
-
[docs]    def is_empty(self, level=0):
-        """
-        Boolean indicating if entity.elements is empty
-
-        Parameters
-        ----------
-        level : int, optional
-
-        Returns
-        -------
-        bool
-        """
-        return len(self._labs(level)) == 0

-
-
[docs]    def uidset_by_level(self, level=0):
-        """
-        The labels found in columns = level
-
-        Parameters
-        ----------
-        level : int, optional
-
-        Returns
-        -------
-        frozenset
-        """
-        return frozenset(self._labs(level))  # should be update this to tuples?

-
-
[docs]    def elements_by_level(self, level1=0, level2=None, translate=False):
-        """
-        Elements of staticentity by specified column
-
-        Parameters
-        ----------
-        level1 : int, optional
-            edges
-        level2 : int, optional
-            nodes
-        translate : bool, optional
-            whether to replace indices with labels
-
-        Returns
-        -------
-        collections.defaultdict
-
-        think: level1 = edges, level2 = nodes
-        """
-        # Is there a better way to view a slice of self._arr?
-        if level1 > self.dimsize - 1 or level1 < 0:
-            print(f"This StaticEntity has no level {level1}.")
-            return
-        if level2 is None:
-            level2 = level1 + 1
-
-        if level2 > self.dimsize - 1 or level2 < 0:
-            print(f"This StaticEntity has no level {level2}.")
-            elts = OrderedDict([[k, np.array([])] for k in self._labs(level1)])
-        elif level1 == level2:
-            print(f"level1 equals level2")
-            elts = OrderedDict([[k, np.array([])] for k in self._labs(level1)])
-
-        temp = remove_row_duplicates(self.data[:, [level1, level2]])
-        elts = defaultdict(list)
-        for row in temp:
-            elts[row[0]].append(row[1])
-
-        if translate:
-            telts = OrderedDict()
-            for kdx, vec in elts.items():
-                k = self._labs(level1)[kdx]
-                telts[k] = list()
-                for vdx in vec:
-                    telts[k].append(self._labs(level2)[vdx])
-            return telts
-        else:
-            return elts

-
-
[docs]    def incidence_matrix(self, level1=0, level2=1, weighted=False, index=False):
-        """
-        Convenience method to navigate large tensor
-
-        Parameters
-        ----------
-        level1 : int, optional
-            indexes columns
-        level2 : int, optional
-            indexes rows
-        weighted : bool, optional
-        index : bool, optional
-
-        Returns
-        -------
-        scipy.sparse.csr.csr_matrix
-
-        think level1 = edges, level2 = nodes
-        """
-        if not weighted:
-            temp = remove_row_duplicates(self.data[:, [level2, level1]])
-        else:
-            temp = self.data[:, [level2, level1]]
-        result = csr_matrix((np.ones(len(temp)), temp.transpose()), dtype=int)
-
-        if index:  # give index of rows then columns
-            return (
-                result,
-                {k: v for k, v in enumerate(self._labs(level2))},
-                {k: v for k, v in enumerate(self._labs(level1))},
-            )
-        else:
-            return result

-
-
[docs]    def restrict_to_levels(self, levels, uid=None):
-        """
-        Limit Static Entity data to specific labels
-
-        Parameters
-        ----------
-        levels : array
-            index of labels in data
-        uid : None, optional
-
-        Returns
-        -------
-        Static Entity class
-            hnx.classes.staticentity.StaticEntity
-        """
-
-        if len(levels) == 1:
-            if levels[0] >= self.dimsize:
-                return self.__class__()
-            else:
-                newlabels = OrderedDict(
-                    [(self.keys[lev], self._labs(lev)) for lev in levels]
-                )
-                return self.__class__(labels=newlabels)
-        temp = remove_row_duplicates(self.data[:, levels])
-        newlabels = OrderedDict([(self.keys[lev], self._labs(lev)) for lev in levels])
-        return self.__class__(data=temp, labels=newlabels, uid=uid)

-
-
[docs]    def turn_entity_data_into_dataframe(
-        self, data_subset
-    ):  # add option to include multiplicities stored in properties
-        """
-        Convert rows of original data in StaticEntity to dataframe
-
-        Parameters
-        ----------
-        data : numpy.ndarray
-            Subset of the rows in the original data held in the StaticEntity
-
-        Returns
-        -------
-        pandas.core.frame.DataFrame
-            Columns and cell entries are derived from data and self.labels
-        """
-        df = pd.DataFrame(data=data_subset, columns=self.keys)
-        width = data_subset.shape[1]
-        for ddx, row in enumerate(data_subset):
-            nrow = [self.labs(idx)[row[idx]] for idx in range(width)]
-            df.iloc[ddx] = nrow
-        return df

-
-
[docs]    def restrict_to_indices(
-        self, indices, level=0, uid=None
-    ):  # restricting to indices requires renumbering the labels.
-        """
-        Limit Static Entity data to specific indices of keys
-
-        Parameters
-        ----------
-        indices : array
-            array of category indices
-        level : int, optional
-            index of label
-        uid : None, optional
-
-        Returns
-        -------
-        Static Entity class
-            hnx.classes.staticentity.StaticEntity
-        """
-        indices = list(indices)
-        idx = np.concatenate(
-            [np.argwhere(self.data[:, level] == k) for k in indices], axis=0
-        ).transpose()[0]
-        temp = self.data[idx]
-        df = self.turn_entity_data_into_dataframe(temp)
-        return self.__class__(entity=df, uid=uid)

-
-
[docs]    def translate(self, level, index):
-        """
-        Replaces a category index and value index with label
-
-        Parameters
-        ----------
-        level : int
-            category index of label
-        index : int
-            value index of label
-
-        Returns
-        -------
-         : numpy.array(str)
-        """
-        if isinstance(index, int):
-            return self._labs(level)[index]
-        else:
-            return [self._labs(level)[idx] for idx in index]

-
-
[docs]    def translate_arr(self, coords):
-        """
-        Translates a single cell in the entity array
-
-        Parameters
-        ----------
-        coords : tuple of ints
-
-        Returns
-        -------
-        list
-        """
-        assert len(coords) == self.dimsize
-        translation = list()
-        for idx in range(self.dimsize):
-            translation.append(self.translate(idx, coords[idx]))
-        return translation

-
-
[docs]    def index(self, category, value=None):
-        """
-        Returns dimension of category and index of value
-
-        Parameters
-        ----------
-        category : string
-        value : string, optional
-
-        Returns
-        -------
-        int or tuple of ints
-        """
-        if value is not None:
-            return self._keyindex(category), self._index(category, value)
-        else:
-            return self._keyindex(category)

-
-
[docs]    def indices(self, category, values):
-        """
-        Returns dimension of category and index of values (array)
-
-        Parameters
-        ----------
-        category : string
-        values : single string or array of strings
-
-        Returns
-        -------
-        list
-        """
-        return [self._index(category, value) for value in values]

-
-
[docs]    def level(self, item, min_level=0, max_level=None, return_index=True):
-        """
-        Returns first level item appears by order of keys from minlevel to maxlevel
-        inclusive
-
-        Parameters
-        ----------
-        item : string
-        min_level : int, optional
-        max_level : int, optional
-
-        return_index : bool, optional
-
-        Returns
-        -------
-        tuple
-        """
-        n = len(self.dimensions)
-        if max_level is not None:
-            n = min([max_level + 1, n])
-        for lev in range(min_level, n):
-            if item in self._labs(lev):
-                if return_index:
-                    return lev, self._index(self._keys[lev], item)
-                else:
-                    return lev
-        else:
-            print(f'"{item}" not found')
-            return None

-
-    # note the depth and registry methods may or may not be useful. We can add these later.
-
-
-
[docs]class StaticEntitySet(StaticEntity):
-
-    """
-    .. _staticentityset:
-    """
-
-    def __init__(
-        self,
-        entity=None,
-        data=None,
-        arr=None,
-        labels=None,
-        uid=None,
-        level1=0,
-        level2=1,
-        **props,
-    ):
-
-        if entity is None:
-            if data is not None:
-                data = data[:, [level1, level2]]
-                arr = None
-            elif arr is not None:
-                data = _turn_tensor_to_data(arr)
-                data = data[:, [level1, level2]]
-                arr = None
-            if labels is not None:
-                keys = np.array(list(labels.keys()))
-                temp = OrderedDict()
-                for lev in [level1, level2]:
-                    if lev < len(keys):
-                        temp[keys[lev]] = labels[keys[lev]]
-                labels = temp
-            super().__init__(data=data, arr=arr, labels=labels, uid=uid, **props)
-        else:
-            E = StaticEntity(entity=entity)
-            E = E.restrict_to_levels([level1, level2])
-            super().__init__(entity=E, uid=uid, **props)
-
-    def __repr__(self):
-        """
-        Returns a string resembling the constructor for entityset without any
-        children
-
-        Returns
-        -------
-        string
-        """
-        return f"StaticEntitySet({self._uid},{list(self.uidset)},{self.properties})"
-
-
[docs]    def incidence_matrix(self, sparse=True, weighted=False, index=False):
-        """
-        Incidence matrix of StaticEntitySet indexed by uidset
-
-        Parameters
-        ----------
-        sparse : bool, optional
-        weighted : bool, optional
-        index : bool, optional
-            give index of rows then columns
-
-        Returns
-        -------
-        matrix
-            scipy.sparse.csr.csr_matrix
-        """
-        if not weighted:
-            temp = remove_row_duplicates(self.data[:, [1, 0]])
-        else:
-            temp = self.data[:, [1, 0]]
-        result = csr_matrix((np.ones(len(temp)), temp.transpose()), dtype=int)
-
-        if index:
-            return (
-                result,
-                {k: v for k, v in enumerate(self._labs(1))},
-                {k: v for k, v in enumerate(self._labs(0))},
-            )
-        else:
-            return result

-
-
[docs]    def restrict_to(self, indices, uid=None):
-        """
-        Limit Static Entityset data to specific indices of keys
-
-        Parameters
-        ----------
-        indices : array
-            array of indices in keys
-        uid : None, optional
-
-        Returns
-        -------
-        StaticEntitySet
-            hnx.classes.staticentity.StaticEntitySet
-
-        """
-        return self.restrict_to_indices(indices, level=0, uid=uid)

-
-
[docs]    def convert_to_entityset(self, uid):
-        """
-        Convert given uid of Static EntitySet into EntitySet
-
-        Parameters
-        ----------
-        uid : string
-
-        Returns
-        -------
-        EntitySet
-            hnx.classes.entity.EntitySet
-        """
-        return EntitySet(uid, self.incidence_dict)

-
-
[docs]    def collapse_identical_elements(
-        self,
-        uid=None,
-        return_equivalence_classes=False,
-    ):
-        """
-        Returns StaticEntitySet after collapsing elements if they have same children
-        If no elements share same children, a copy of the original StaticEntitySet is returned
-        Parameters
-        ----------
-        uid : None, optional
-        return_equivalence_classes : bool, optional
-            If True, return a dictionary of equivalence classes keyed by new edge names
-
-
-        Returns
-        -------
-        StaticEntitySet
-            hnx.classes.staticentity.StaticEntitySet
-        """
-        shared_children = DefaultOrderedDict(list)
-        for k, v in self.elements.items():
-            shared_children[frozenset(v)].append(k)
-        new_entity_dict = OrderedDict(
-            [
-                (
-                    f"{next(iter(v))}:{len(v)}",
-                    sorted(set(k), key=lambda x: list(self.labs(1)).index(x)),
-                )
-                for k, v in shared_children.items()
-            ]
-        )
-        if return_equivalence_classes:
-            eq_classes = OrderedDict(
-                [
-                    (
-                        f"{next(iter(v))}:{len(v)}",
-                        sorted(v, key=lambda x: list(self.labs(0)).index(x)),
-                    )
-                    for k, v in shared_children.items()
-                ]
-            )
-            return StaticEntitySet(uid=uid, entity=new_entity_dict), eq_classes
-        else:
-            return StaticEntitySet(uid=uid, entity=new_entity_dict)

-
-
-def _turn_tensor_to_data(arr, remove_duplicates=True):
-    """
-    Return list of nonzero coordinates in arr.
-
-    Parameters
-    ----------
-    arr : numpy.ndarray
-        Tensor corresponding to incidence of co-occurring labels.
-    """
-    return np.array(arr.nonzero()).transpose()
-
-
-def _turn_dict_to_staticentity(dict_object, remove_duplicates=True):
-    """Create a static entity directly from a dictionary of hashables"""
-    d = OrderedDict(dict_object)
-    level2ctr = HNXCount()
-    level1ctr = HNXCount()
-    level2 = DefaultOrderedDict(level2ctr)
-    level1 = DefaultOrderedDict(level1ctr)
-    coords = list()
-    for k, val in d.items():
-        level1[k]
-        for v in val:
-            level2[v]
-            coords.append((level1[k], level2[v]))
-    if remove_duplicates:
-        coords = remove_row_duplicates(coords)
-    level1 = list(level1)
-    level2 = list(level2)
-    data = np.array(coords, dtype=int)
-    labels = OrderedDict({"0": level1, "1": level2})
-    return data, labels
-
-
-def _turn_iterable_to_staticentity(iter_object, remove_duplicates=True):
-    for s in iter_object:
-        if not isinstance(s, Iterable):
-            raise HyperNetXError(
-                "StaticEntity constructor requires an iterable of iterables."
-            )
-    else:
-        labels = [f"e{str(x)}" for x in range(len(iter_object))]
-        dict_object = dict(zip(labels, iter_object))
-    return _turn_dict_to_staticentity(dict_object, remove_duplicates=remove_duplicates)
-
-
-def _turn_dataframe_into_entity(df, return_counts=False, include_unknowns=False):
-    """
-    Convenience method to reformat dataframe object into data,labels format
-    for construction of a static entity
-
-    Parameters
-    ----------
-    df : pandas.DataFrame
-        May not contain nans
-    return_counts : bool, optional, default : False
-        Used for keeping weights
-    include_unknowns : bool, optional, default : False
-        If Unknown <column name> was used to fill in nans
-
-    Returns
-    -------
-    outputdata : numpy.ndarray
-    counts : numpy.array of ints
-    slabels : numpy.array of strings
-
-    """
-    columns = df.columns
-    ctr = [HNXCount() for c in range(len(columns))]
-    ldict = OrderedDict()
-    rdict = OrderedDict()
-    for idx, c in enumerate(columns):
-        ldict[c] = defaultdict(ctr[idx])  # TODO make this an Ordered default dict
-        rdict[c] = OrderedDict()
-        if include_unknowns:
-            ldict[c][
-                f"Unknown {c}"
-            ]  # TODO: update this to take a dict assign for each column
-            rdict[c][0] = f"Unknown {c}"
-        for k in df[c]:
-            ldict[c][k]
-            rdict[c][ldict[c][k]] = k
-        ldict[c] = dict(ldict[c])
-    dims = tuple([len(ldict[c]) for c in columns])
-
-    m = len(df)
-    n = len(columns)
-    data = np.zeros((m, n), dtype=int)
-    for rid in range(m):
-        for cid in range(n):
-            c = columns[cid]
-            data[rid, cid] = ldict[c][df.iloc[rid][c]]
-
-    output_data = remove_row_duplicates(data, return_counts=return_counts)
-
-    slabels = OrderedDict()
-    for cdx, c in enumerate(columns):
-        slabels.update({c: np.array(list(ldict[c].keys()))})
-    if return_counts:
-        return output_data[0], slabels, output_data[1]
-    else:
-        return output_data, slabels
-
- -
- -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_modules/drawing/rubber_band.html b/docs/build/_modules/drawing/rubber_band.html deleted file mode 100644 index 7f56ef56..00000000 --- a/docs/build/_modules/drawing/rubber_band.html +++ /dev/null @@ -1,715 +0,0 @@ - - - - - - - - - - drawing.rubber_band — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - -
- - - - - -
- -
- - - - - - - - - - - - - - - - - - - -
- -
    - -
  • »
    • - -
  • Module code »
    • - -
  • drawing.rubber_band
    • - - -
  • - -
    • - -
- - -
-
-
-
- -

Source code for drawing.rubber_band

-# Copyright © 2018 Battelle Memorial Institute
-# All rights reserved.
-
-from hypernetx import Hypergraph
-from .util import (
-    get_frozenset_label,
-    get_set_layering,
-    inflate_kwargs,
-    transpose_inflated_kwargs,
-)
-
-import matplotlib.pyplot as plt
-from matplotlib.collections import PolyCollection, LineCollection, CircleCollection
-
-import networkx as nx
-
-from itertools import combinations
-from collections import defaultdict
-
-import numpy as np
-from scipy.spatial.distance import pdist
-from scipy.spatial import ConvexHull
-from scipy.spatial import Voronoi
-
-# increases the default figure size to 8in square.
-plt.rcParams["figure.figsize"] = (8, 8)
-
-N_CONTROL_POINTS = 24
-
-theta = np.linspace(0, 2 * np.pi, N_CONTROL_POINTS + 1)[:-1]
-
-cp = np.vstack((np.cos(theta), np.sin(theta))).T
-
-
-
-
-
-
[docs]def get_default_radius(H, pos):
-    """
-    Calculate a reasonable default node radius
-
-    This function iterates over the hyper edges and finds the most distant
-    pair of points given the positions provided. Then, the node radius is a fraction
-    of the median of this distance take across all hyper-edges.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    pos: dict
-        mapping of node and edge positions to R^2
-
-    Returns
-    -------
-    float
-        the recommended radius
-
-    """
-    if len(H) > 1:
-        return 0.0125 * np.median(
-            [pdist(np.vstack(list(map(pos.get, H.nodes)))).max() for nodes in H.edges()]
-        )
-    return 1

-
-
-
[docs]def draw_hyper_edge_labels(H, polys, labels={}, ax=None, **kwargs):
-    """
-    Draws a label on the hyper edge boundary.
-
-    Should be passed Matplotlib PolyCollection representing the hyper-edges, see
-    the return value of draw_hyper_edges.
-
-    The label will be draw on the least curvy part of the polygon, and will be
-    aligned parallel to the orientation of the polygon where it is drawn.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    polys: PolyCollection
-        collection of polygons returned by draw_hyper_edges
-    labels: dict
-        mapping of node id to string label
-    ax: Axis
-        matplotlib axis on which the plot is rendered
-    kwargs: dict
-        Keyword arguments are passed through to Matplotlib's annotate function.
-
-    """
-    ax = ax or plt.gca()
-
-    params = transpose_inflated_kwargs(inflate_kwargs(H.edges, kwargs))
-
-    for edge, path, params in zip(H.edges, polys.get_paths(), params):
-        s = labels.get(edge, edge)
-
-        # calculate the xy location of the annotation
-        # this is the midpoint of the pair of adjacent points the most distant
-        d = ((path.vertices[:-1] - path.vertices[1:]) ** 2).sum(axis=1)
-        i = d.argmax()
-
-        x1, x2 = path.vertices[i : i + 2]
-        x, y = x2 - x1
-        theta = 360 * np.arctan2(y, x) / (2 * np.pi)
-        theta = (theta + 360) % 360
-
-        while theta > 90:
-            theta -= 180
-
-        # the string is a comma separated list of the edge uid
-        ax.annotate(
-            s, (x1 + x2) / 2, rotation=theta, ha="center", va="center", **params
-        )

-
-
-
[docs]def layout_hyper_edges(H, pos, node_radius={}, dr=None):
-    """
-    Draws a convex hull for each edge in H.
-
-    Position of the nodes in the graph is specified by the position dictionary,
-    pos. Convex hulls are spaced out such that if one set contains another, the
-    convex hull will surround the contained set. The amount of spacing added
-    between hulls is specified by the parameter, dr.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    pos: dict
-        mapping of node and edge positions to R^2
-    node_radius: dict
-        mapping of node to R^1 (radius of each node)
-    dr: float
-        the spacing between concentric rings
-    ax: Axis
-        matplotlib axis on which the plot is rendered
-
-    Returns
-    -------
-    dict
-        A mapping from hyper edge ids to paths (Nx2 numpy matrices)
-    """
-
-    if len(node_radius):
-        r0 = min(node_radius.values())
-    else:
-        r0 = get_default_radius(H, pos)
-
-    dr = dr or r0
-
-    levels = get_set_layering(H)
-
-    radii = {
-        v: {v: i for i, v in enumerate(sorted(e, key=levels.get))}
-        for v, e in H.dual().edges.elements.items()
-    }
-
-    def get_padded_hull(uid, edge):
-        # make sure the edge contains at least one node
-        if len(edge):
-            points = np.vstack(
-                [
-                    cp * (node_radius.get(v, r0) + dr * (2 + radii[v][uid])) + pos[v]
-                    for v in edge
-                ]
-            )
-        # if not, draw an empty edge centered around the location of the edge node (in the bipartite graph)
-        else:
-            points = 4 * r0 * cp + pos[uid]
-
-        hull = ConvexHull(points)
-
-        return hull.points[hull.vertices]
-
-    return [get_padded_hull(uid, list(H.edges[uid])) for uid in H.edges]

-
-
-
[docs]def draw_hyper_edges(H, pos, ax=None, node_radius={}, dr=None, **kwargs):
-    """
-    Draws a convex hull around the nodes contained within each edge in H
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    pos: dict
-        mapping of node and edge positions to R^2
-    node_radius: dict
-        mapping of node to R^1 (radius of each node)
-    dr: float
-        the spacing between concentric rings
-    ax: Axis
-        matplotlib axis on which the plot is rendered
-    kwargs: dict
-        keyword arguments, e.g., linewidth, facecolors, are passed through to the PolyCollection constructor
-
-    Returns
-    -------
-    PolyCollection
-        a Matplotlib PolyCollection that can be further styled
-    """
-    points = layout_hyper_edges(H, pos, node_radius=node_radius, dr=dr)
-
-    polys = PolyCollection(points, **inflate_kwargs(H.edges, kwargs))
-
-    (ax or plt.gca()).add_collection(polys)
-
-    return polys

-
-
-
[docs]def draw_hyper_nodes(H, pos, node_radius={}, r0=None, ax=None, **kwargs):
-    """
-    Draws a circle for each node in H.
-
-    The position of each node is specified by the a dictionary/list-like, pos,
-    where pos[v] is the xy-coordinate for the vertex. The radius of each node
-    can be specified as a dictionary where node_radius[v] is the radius. If a
-    node is missing from this dictionary, or the node_radius is not specified at
-    all, a sensible default radius is chosen based on distances between nodes
-    given by pos.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    pos: dict
-        mapping of node and edge positions to R^2
-    node_radius: dict
-        mapping of node to R^1 (radius of each node)
-    r0: float
-        minimum distance that concentric rings start from the node position
-    ax: Axis
-        matplotlib axis on which the plot is rendered
-    kwargs: dict
-        keyword arguments, e.g., linewidth, facecolors, are passed through to the PolyCollection constructor
-
-    Returns
-    -------
-    PolyCollection
-        a Matplotlib PolyCollection that can be further styled
-    """
-
-    ax = ax or plt.gca()
-
-    r0 = r0 or get_default_radius(H, pos)
-
-    points = [node_radius.get(v, r0) * cp + pos[v] for v in H.nodes]
-
-    kwargs.setdefault("facecolors", "black")
-
-    circles = PolyCollection(points, **inflate_kwargs(H, kwargs))
-
-    ax.add_collection(circles)
-
-    return circles

-
-
-
[docs]def draw_hyper_labels(H, pos, node_radius={}, ax=None, labels={}, **kwargs):
-    """
-    Draws text labels for the hypergraph nodes.
-
-    The label is drawn to the right of the node. The node radius is needed (see
-    draw_hyper_nodes) so the text can be offset appropriately as the node size
-    changes.
-
-    The text label can be customized by passing in a dictionary, labels, mapping
-    a node to its custom label. By default, the label is the string
-    representation of the node.
-
-    Keyword arguments are passed through to Matplotlib's annotate function.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    pos: dict
-        mapping of node and edge positions to R^2
-    node_radius: dict
-        mapping of node to R^1 (radius of each node)
-    ax: Axis
-        matplotlib axis on which the plot is rendered
-    labels: dict
-        mapping of node to text label
-    kwargs: dict
-        keyword arguments passed to matplotlib.annotate
-
-    """
-    ax = ax or plt.gca()
-
-    params = transpose_inflated_kwargs(inflate_kwargs(H.nodes, kwargs))
-
-    for v, v_kwargs in zip(H.nodes, params):
-        xy = np.array([node_radius.get(v, 0), 0]) + pos[v]
-        ax.annotate(
-            labels.get(v, v),
-            xy,
-            **{
-                k: (
-                    d[v]
-                    if hasattr(d, "__getitem__") and type(d) not in {str, tuple}
-                    else d
-                )
-                for k, d in kwargs.items()
-            }
-        )

-
-
-
[docs]def draw(
-    H,
-    pos=None,
-    with_color=True,
-    with_node_counts=False,
-    with_edge_counts=False,
-    layout=nx.spring_layout,
-    layout_kwargs={},
-    ax=None,
-    node_radius=None,
-    edges_kwargs={},
-    nodes_kwargs={},
-    edge_labels={},
-    edge_labels_kwargs={},
-    node_labels={},
-    node_labels_kwargs={},
-    with_edge_labels=True,
-    with_node_labels=True,
-    label_alpha=0.35,
-    return_pos=False,
-):
-    """
-    Draw a hypergraph as a Matplotlib figure
-
-    By default this will draw a colorful "rubber band" like hypergraph, where
-    convex hulls represent edges and are drawn around the nodes they contain.
-
-    This is a convenience function that wraps calls with sensible parameters to
-    the following lower-level drawing functions:
-
-    * draw_hyper_edges,
-    * draw_hyper_edge_labels,
-    * draw_hyper_labels, and
-    * draw_hyper_nodes
-
-    The default layout algorithm is nx.spring_layout, but other layouts can be
-    passed in. The Hypergraph is converted to a bipartite graph, and the layout
-    algorithm is passed the bipartite graph.
-
-    If you have a pre-determined layout, you can pass in a "pos" dictionary.
-    This is a dictionary mapping from node id's to x-y coordinates. For example:
-
-        >>> pos = {
-        >>> 'A': (0, 0),
-        >>> 'B': (1, 2),
-        >>> 'C': (5, -3)
-        >>> }
-
-    will position the nodes {A, B, C} manually at the locations specified. The
-    coordinate system is in Matplotlib "data coordinates", and the figure will
-    be centered within the figure.
-
-    By default, this will draw in a new figure, but the axis to render in can be
-    specified using :code:`ax`.
-
-    This approach works well for small hypergraphs, and does not guarantee
-    a rigorously "correct" drawing. Overlapping of sets in the drawing generally
-    implies that the sets intersect, but sometimes sets overlap if there is no
-    intersection. It is not possible, in general, to draw a "correct" hypergraph
-    this way for an arbitrary hypergraph, in the same way that not all graphs
-    have planar drawings.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    pos: dict
-        mapping of node and edge positions to R^2
-    with_color: bool
-        set to False to disable color cycling of edges
-    with_node_counts: bool
-        set to True to label collapsed nodes with number of elements
-    with_edge_counts: bool
-        set to True to label collapsed edges with number of elements
-    layout: function
-        layout algorithm to compute
-    layout_kwargs: dict
-        keyword arguments passed to layout function
-    ax: Axis
-        matplotlib axis on which the plot is rendered
-    edges_kwargs: dict
-        keyword arguments passed to matplotlib.collections.PolyCollection for edges
-    node_radius: None, int, float, or dict
-        radius of all nodes, or dictionary of node:value; the default (None) calculates radius based on number of collapsed nodes; reasonable values range between 1 and 3
-    nodes_kwargs: dict
-        keyword arguments passed to matplotlib.collections.PolyCollection for nodes
-    edge_labels_kwargs: dict
-        keyword arguments passed to matplotlib.annotate for edge labels
-    node_labels_kwargs: dict
-        keyword argumetns passed to matplotlib.annotate for node labels
-    with_edge_labels: bool
-        set to False to make edge labels invisible
-    with_node_labels: bool
-        set to False to make node labels invisible
-    label_alpha: float
-        the transparency (alpha) of the box behind text drawn in the figure
-    """
-
-    ax = ax or plt.gca()
-
-    if pos is None:
-        pos = layout_node_link(H, layout=layout, **layout_kwargs)
-
-    r0 = get_default_radius(H, pos)
-    a0 = np.pi * r0 ** 2
-
-    def get_node_radius(v):
-        if node_radius is None:
-            return np.sqrt(a0 * (len(v) if type(v) == frozenset else 1) / np.pi)
-        elif hasattr(node_radius, "get"):
-            return node_radius.get(v, 1) * r0
-        return node_radius * r0
-
-    # guarantee that node radius is a dictionary mapping nodes to values
-    node_radius = {v: get_node_radius(v) for v in H.nodes}
-
-    # for convenience, we are using setdefault to mutate the argument
-    # however, we need to copy this to prevent side-effects
-    edges_kwargs = edges_kwargs.copy()
-    edges_kwargs.setdefault("edgecolors", plt.cm.tab10(np.arange(len(H.edges)) % 10))
-    edges_kwargs.setdefault("facecolors", "none")
-
-    polys = draw_hyper_edges(H, pos, node_radius=node_radius, ax=ax, **edges_kwargs)
-
-    if with_edge_labels:
-        labels = get_frozenset_label(
-            H.edges, count=with_edge_counts, override=edge_labels
-        )
-
-        draw_hyper_edge_labels(
-            H,
-            polys,
-            color=edges_kwargs["edgecolors"],
-            backgroundcolor=(1, 1, 1, label_alpha),
-            labels=labels,
-            ax=ax,
-            **edge_labels_kwargs
-        )
-
-    if with_node_labels:
-        labels = get_frozenset_label(
-            H.nodes, count=with_node_counts, override=node_labels
-        )
-
-        draw_hyper_labels(
-            H,
-            pos,
-            node_radius=node_radius,
-            labels=labels,
-            ax=ax,
-            va="center",
-            xytext=(5, 0),
-            textcoords="offset points",
-            backgroundcolor=(1, 1, 1, label_alpha),
-            **node_labels_kwargs
-        )
-
-    draw_hyper_nodes(H, pos, node_radius=node_radius, ax=ax, **nodes_kwargs)
-
-    if len(H.nodes) == 1:
-        x, y = pos[list(H.nodes)[0]]
-        s = 20
-
-        ax.axis([x - s, x + s, y - s, y + s])
-    else:
-        ax.axis("equal")
-
-    ax.axis("off")
-    if return_pos:
-        return pos

-
- -
- -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_modules/drawing/two_column.html b/docs/build/_modules/drawing/two_column.html deleted file mode 100644 index cbc4eaf2..00000000 --- a/docs/build/_modules/drawing/two_column.html +++ /dev/null @@ -1,426 +0,0 @@ - - - - - - - - - - drawing.two_column — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - -
- - - - - -
- -
- - - - - - - - - - - - - - - - - - - -
- -
    - -
  • »
    • - -
  • Module code »
    • - -
  • drawing.two_column
    • - - -
  • - -
    • - -
- - -
-
-
-
- -

Source code for drawing.two_column

-# Copyright © 2018 Battelle Memorial Institute
-# All rights reserved.
-
-import matplotlib.pyplot as plt
-from matplotlib.collections import LineCollection
-
-import networkx as nx
-
-from .util import get_frozenset_label
-
-
-
[docs]def layout_two_column(H, spacing=2):
-    """
-    Two column (bipartite) layout algorithm.
-
-    This algorithm first converts the hypergraph into a bipartite graph and
-    then computes connected components. Disonneccted components are handled
-    independently and then stacked together.
-
-    Within a connected component, the spectral ordering of the bipartite graph
-    provides a quick and dirty ordering that minimizes edge crossings in the
-    diagram.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    spacing: float
-        amount of whitespace between disconnected components
-    """
-    offset = 0
-    pos = {}
-
-    def stack(vertices, x, height):
-        for i, v in enumerate(vertices):
-            pos[v] = (x, i + offset + (height - len(vertices)) / 2)
-
-    G = H.bipartite()
-    for ci in nx.connected_components(G):
-        Gi = G.subgraph(ci)
-        key = {v: i for i, v in enumerate(nx.spectral_ordering(Gi))}.get
-        ci_vertices, ci_edges = [
-            sorted([v for v, d in Gi.nodes(data=True) if d["bipartite"] == j], key=key)
-            for j in [0, 1]
-        ]
-
-        height = max(len(ci_vertices), len(ci_edges))
-
-        stack(ci_vertices, 0, height)
-        stack(ci_edges, 1, height)
-
-        offset += height + spacing
-
-    return pos

-
-
-
[docs]def draw_hyper_edges(H, pos, ax=None, **kwargs):
-    """
-    Renders hyper edges for the two column layout.
-
-    Each node-hyper edge membership is rendered as a line connecting the node
-    in the left column to the edge in the right column.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    pos: dict
-        mapping of node and edge positions to R^2
-    ax: Axis
-        matplotlib axis on which the plot is rendered
-    kwargs: dict
-        keyword arguments passed to matplotlib.LineCollection
-
-    Returns
-    -------
-    LineCollection
-        the hyper edges
-    """
-    ax = ax or plt.gca()
-
-    pairs = [(v, e.uid) for e in H.edges() for v in e]
-
-    kwargs = {
-        k: v if type(v) != dict else [v.get(e) for _, e in pairs]
-        for k, v in kwargs.items()
-    }
-
-    lines = LineCollection([(pos[u], pos[v]) for u, v in pairs], **kwargs)
-
-    ax.add_collection(lines)
-
-    return lines

-
-
-
[docs]def draw_hyper_labels(
-    H, pos, labels={}, with_node_labels=True, with_edge_labels=True, ax=None
-):
-    """
-    Renders hyper labels (nodes and edges) for the two column layout.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    pos: dict
-        mapping of node and edge positions to R^2
-    labels: dict
-        custom labels for nodes and edges can be supplied
-    with_node_labels: bool
-        False to disable node labels
-    with_edge_labels: bool
-        False to disable edge labels
-    ax: Axis
-        matplotlib axis on which the plot is rendered
-    kwargs: dict
-        keyword arguments passed to matplotlib.LineCollection
-
-    """
-
-    ax = ax or plt.gca()
-
-    edges = [e.uid for e in H.edges()]
-
-    to_draw = []
-    if with_node_labels:
-        to_draw.append((H.nodes(), "right"))
-
-    if with_edge_labels:
-        to_draw.append((H.edges(), "left"))
-
-    for points, ha in to_draw:
-        for p in points:
-            ax.annotate(labels.get(p.uid, p.uid), pos[p.uid], ha=ha, va="center")

-
-
-
[docs]def draw(
-    H,
-    with_node_labels=True,
-    with_edge_labels=True,
-    with_node_counts=False,
-    with_edge_counts=False,
-    with_color=True,
-    edge_kwargs=None,
-    ax=None,
-):
-    """
-    Draw a hypergraph using a two-collumn layout.
-
-    This is intended reproduce an illustrative technique for bipartite graphs
-    and hypergraphs that is typically used in papers and textbooks.
-
-    The left column is reserved for nodes and the right column is reserved for
-    edges. A line is drawn between a node an an edge
-
-    The order of nodes and edges is optimized to reduce line crossings between
-    the two columns. Spacing between disconnected components is adjusted to make
-    the diagram easier to read, by reducing the angle of the lines.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    with_node_labels: bool
-        False to disable node labels
-    with_edge_labels: bool
-        False to disable edge labels
-    with_node_counts: bool
-        set to True to label collapsed nodes with number of elements
-    with_edge_counts: bool
-        set to True to label collapsed edges with number of elements
-    with_color: bool
-        set to False to disable color cycling of hyper edges
-    edge_kwargs: dict
-        keyword arguments to pass to matplotlib.LineCollection
-    ax: Axis
-        matplotlib axis on which the plot is rendered
-    """
-
-    edge_kwargs = edge_kwargs or {}
-
-    ax = ax or plt.gca()
-
-    pos = layout_two_column(H)
-
-    V = [v.uid for v in H.nodes()]
-    E = [e.uid for e in H.edges()]
-
-    labels = {}
-    labels.update(get_frozenset_label(V, count=with_node_counts))
-    labels.update(get_frozenset_label(E, count=with_edge_counts))
-
-    if with_color:
-        edge_kwargs["color"] = {
-            e.uid: plt.cm.tab10(i % 10) for i, e in enumerate(H.edges())
-        }
-
-    draw_hyper_edges(H, pos, ax=ax, **edge_kwargs)
-    draw_hyper_labels(
-        H,
-        pos,
-        labels,
-        ax=ax,
-        with_node_labels=with_node_labels,
-        with_edge_labels=with_edge_labels,
-    )
-    ax.autoscale_view()
-
-    ax.axis("off")

-
- -
- -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_modules/drawing/util.html b/docs/build/_modules/drawing/util.html deleted file mode 100644 index 31a5dcab..00000000 --- a/docs/build/_modules/drawing/util.html +++ /dev/null @@ -1,353 +0,0 @@ - - - - - - - - - - drawing.util — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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-
- -

Source code for drawing.util

-# Copyright © 2018 Battelle Memorial Institute
-# All rights reserved.
-
-from itertools import combinations
-
-import numpy as np
-
-import networkx as nx
-
-
-
[docs]def inflate(items, v):
-    if type(v) in {str, tuple, int, float}:
-        return [v] * len(items)
-    elif callable(v):
-        return [v(i) for i in items]
-    elif type(v) not in {list, np.ndarray} and hasattr(v, "__getitem__"):
-        return [v[i] for i in items]
-    return v

-
-
-
[docs]def inflate_kwargs(items, kwargs):
-    """
-    Helper function to expand keyword arguments.
-
-    Parameters
-    ----------
-    n: int
-        length of resulting list if argument is expanded
-    kwargs: dict
-        keyword arguments to be expanded
-
-    Returns
-    -------
-    dict
-        dictionary with same keys as kwargs and whose values are lists of length n
-    """
-
-    return {k: inflate(items, v) for k, v in kwargs.items()}

-
-
-
[docs]def transpose_inflated_kwargs(inflated):
-    return [dict(zip(inflated, v)) for v in zip(*inflated.values())]

-
-
-
[docs]def get_frozenset_label(S, count=False, override={}):
-    """
-    Helper function for rendering the labels of possibly collapsed nodes and edges
-
-    Parameters
-    ----------
-    S: iterable
-        list of entities to be labeled
-    count: bool
-        True if labels should be counts of entities instead of list
-
-    Returns
-    -------
-    dict
-        mapping of entity to its string representation
-    """
-
-    def helper(v):
-        if type(v) == frozenset:
-            if count and len(v) > 1:
-                return f"x {len(v)}"
-            elif count:
-                return ""
-            else:
-                return ", ".join([str(override.get(s, s)) for s in v])
-        return str(v)
-
-    return {v: override.get(v, helper(v)) for v in S}

-
-
-
[docs]def get_line_graph(H, collapse=True):
-    """
-    Computes the line graph, a directed graph, where a directed edge (u, v)
-    exists if the edge u is a subset of the edge v in the hypergraph.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    collapse: bool
-        True if edges should be added if hyper edges are identical
-
-    Returns
-    -------
-    networkx.DiGraph
-        A directed graph
-    """
-    D = nx.DiGraph()
-
-    V = {edge: set(nodes) for edge, nodes in H.edges.elements.items()}
-
-    D.add_nodes_from(V)
-
-    for u, v in combinations(V, 2):
-        if V[u] != V[v] or not collapse:
-            if V[u].issubset(V[v]):
-                D.add_edge(u, v)
-            elif V[v].issubset(V[u]):
-                D.add_edge(v, u)
-
-    return D

-
-
-
[docs]def get_set_layering(H, collapse=True):
-    """
-    Computes a layering of the edges in the hyper graph.
-
-    In this layering, each edge is assigned a level. An edge u will be above
-    (e.g., have a smaller level value) another edge v if v is a subset of u.
-
-    Parameters
-    ----------
-    H: Hypergraph
-        the entity to be drawn
-    collapse: bool
-        True if edges should be added if hyper edges are identical
-
-    Returns
-    -------
-    dict
-        a mapping of vertices in H to integer levels
-    """
-
-    D = get_line_graph(H, collapse=collapse)
-
-    levels = {}
-
-    for v in nx.topological_sort(D):
-        parent_levels = [levels[u] for u, _ in D.in_edges(v)]
-        levels[v] = max(parent_levels) + 1 if len(parent_levels) else 0
-
-    return levels

-
- -
- -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_modules/index.html b/docs/build/_modules/index.html deleted file mode 100644 index 63f60b69..00000000 --- a/docs/build/_modules/index.html +++ /dev/null @@ -1,224 +0,0 @@ - - - - - - - - - - Overview: module code — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - -
- - - - - -
- -
- - - - - - - - - - - - - - - - - - - -
- -
    - -
  • »
    • - -
  • Overview: module code
    • - - -
  • - -
    • - -
- - -
-
-
- - -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_modules/reports/descriptive_stats.html b/docs/build/_modules/reports/descriptive_stats.html deleted file mode 100644 index 66ea9889..00000000 --- a/docs/build/_modules/reports/descriptive_stats.html +++ /dev/null @@ -1,629 +0,0 @@ - - - - - - - - - - reports.descriptive_stats — HyperNetX 1.0.0 documentation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - -
- - - - - -
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    • - -
  • reports.descriptive_stats
    • - - -
  • - -
    • - -
- - -
-
-
-
- -

Source code for reports.descriptive_stats

-"""
-This module contains methods which compute various distributions for hypergraphs:
-    * Edge size distribution
-    * Node degree distribution
-    * Component size distribution
-    * Toplex size distribution
-    * Diameter
-
-Also computes general hypergraph information: number of nodes, edges, cells, aspect ratio, incidence matrix density
-"""
-from collections import Counter
-import numpy as np
-import networkx as nx
-from hypernetx import *
-from hypernetx.utils.decorators import not_implemented_for
-
-__all__ = [
-    "centrality_stats",
-    "edge_size_dist",
-    "degree_dist",
-    "comp_dist",
-    "s_comp_dist",
-    "toplex_dist",
-    "s_node_diameter_dist",
-    "s_edge_diameter_dist",
-    "info",
-    "info_dict",
-    "dist_stats",
-]
-
-
-
[docs]def centrality_stats(X):
-    """
-    Computes basic centrality statistics for X
-
-    Parameters
-    ----------
-    X :
-        an iterable of numbers
-
-    Returns
-    -------
-    [min, max, mean, median, standard deviation] : list
-        List of centrality statistics for X
-    """
-    return [min(X), max(X), np.mean(X), np.median(X), np.std(X)]

-
-
-
[docs]def edge_size_dist(H, aggregated=False):
-    """
-    Computes edge sizes of a hypergraph.
-
-    Parameters
-    ----------
-    H : Hypergraph
-    aggregated :
-        If aggregated is True, returns a dictionary of
-        edge sizes and counts. If aggregated is False, returns a
-        list of edge sizes in H.
-
-    Returns
-    -------
-     edge_size_dist : list or dict
-        List of edge sizes or dictionary of edge size distribution.
-
-    """
-    if aggregated:
-        return Counter(H.edge_size_dist())
-    else:
-        return H.edge_size_dist()

-
-
-
[docs]def degree_dist(H, aggregated=False):
-    """
-    Computes degrees of nodes of a hypergraph.
-
-    Parameters
-    ----------
-    H : Hypergraph
-    aggregated :
-        If aggregated is True, returns a dictionary of
-        degrees and counts. If aggregated is False, returns a
-        list of degrees in H.
-
-    Returns
-    -------
-     degree_dist : list or dict
-        List of degrees or dictionary of degree distribution
-    """
-    if H.nwhy:
-        distr = H.g.node_size_dist()
-    else:
-        distr = [H.degree(n) for n in H.nodes]
-    if aggregated:
-        return Counter(distr)
-    else:
-        return distr

-
-
-
[docs]def comp_dist(H, aggregated=False):
-    """
-    Computes component sizes, number of nodes.
-
-    Parameters
-    ----------
-    H : Hypergraph
-    aggregated :
-        If aggregated is True, returns a dictionary of
-        component sizes (number of nodes) and counts. If aggregated
-        is False, returns a list of components sizes in H.
-
-    Returns
-    -------
-     comp_dist : list or dictionary
-        List of component sizes or dictionary of component size distribution
-
-    See Also
-    --------
-    s_comp_dist
-
-    """
-
-    distr = [len(c) for c in H.components()]
-    if aggregated:
-        return Counter(distr)
-    else:
-        return distr

-
-
-
[docs]def s_comp_dist(H, s=1, aggregated=False, edges=True, return_singletons=True):
-    """
-    Computes s-component sizes, counting nodes or edges.
-
-    Parameters
-    ----------
-    H : Hypergraph
-    s : positive integer, default is 1
-    aggregated :
-        If aggregated is True, returns a dictionary of
-        s-component sizes and counts in H. If aggregated is
-        False, returns a list of s-component sizes in H.
-    edges :
-        If edges is True, the component size is number of edges.
-        If edges is False, the component size is number of nodes.
-    return_singletons : bool, optional, default=True
-
-    Returns
-    -------
-     s_comp_dist : list or dictionary
-        List of component sizes or dictionary of component size distribution in H
-
-    See Also
-    --------
-    comp_dist
-
-    """
-    distr = list()
-    comps = H.s_connected_components(
-        s=s, edges=edges, return_singletons=return_singletons
-    )
-
-    distr = [len(c) for c in comps]
-
-    if aggregated:
-        return Counter(distr)
-    else:
-        return distr

-
-
-
[docs]@not_implemented_for("static")
-def toplex_dist(H, aggregated=False):
-    """
-
-    Computes toplex sizes for hypergraph H.
-
-    Parameters
-    ----------
-    H : Hypergraph
-    aggregated :
-        If aggregated is True, returns a dictionary of
-        toplex sizes and counts in H. If aggregated
-        is False, returns a list of toplex sizes in H.
-
-    Returns
-    -------
-     toplex_dist : list or dictionary
-        List of toplex sizes or dictionary of toplex size distribution in H
-    """
-    distr = [H.size(e) for e in H.toplexes().edges]
-    if aggregated:
-        return Counter(distr)
-    else:
-        return distr

-
-
-
[docs]def s_node_diameter_dist(H):
-    """
-    Parameters
-    ----------
-    H : Hypergraph
-
-    Returns
-    -------
-     s_node_diameter_dist : list
-        List of s-node-diameters for hypergraph H starting with s=1
-        and going up as long as the hypergraph is s-node-connected
-    """
-    i = 1
-    diams = []
-    while H.is_connected(s=i):
-        diams.append(H.diameter(s=i))
-        i += 1
-    return diams

-
-
-
[docs]def s_edge_diameter_dist(H):
-    """
-    Parameters
-    ----------
-    H : Hypergraph
-
-    Returns
-    -------
-     s_edge_diameter_dist : list
-        List of s-edge-diameters for hypergraph H starting with s=1
-        and going up as long as the hypergraph is s-edge-connected
-    """
-    i = 1
-    diams = []
-    while H.is_connected(s=i, edges=True):
-        diams.append(H.edge_diameter(s=i))
-        i += 1
-    return diams

-
-
-
[docs]def info(H, node=None, edge=None):
-    """
-    Print a summary of simple statistics for H
-
-    Parameters
-    ----------
-    H : Hypergraph
-    obj : optional
-        either a node or edge uid from the hypergraph
-    dictionary : optional
-        If True then returns the info as a dictionary rather
-        than a string
-        If False (default) returns the info as a string
-
-    Returns
-    -------
-     info : string
-        Returns a string of statistics of the size,
-        aspect ratio, and density of the hypergraph.
-        Print the string to see it formatted.
-
-    """
-    if not H.edges.elements:
-        return f"Hypergraph {H.name} is empty."
-    report = info_dict(H, node=node, edge=edge)
-    info = ""
-    if node:
-        info += f"Node '{node}' has the following properties:\n"
-        info += f"Degree: {report['degree']}\n"
-        info += f"Contained in: {report['membs']}\n"
-        info += f"Neighbors: {report['neighbors']}"
-    elif edge:
-        info += f"Edge '{edge}' has the following properties:\n"
-        info += f"Size: {report['size']}\n"
-        info += f"Elements: {report['elements']}"
-    else:
-        info += f"Number of Rows: {report['nrows']}\n"
-        info += f"Number of Columns: {report['ncols']}\n"
-        info += f"Aspect Ratio: {report['aspect ratio']}\n"
-        info += f"Number of non-empty Cells: {report['ncells']}\n"
-        info += f"Density: {report['density']}"
-    return info

-
-
-
[docs]def info_dict(H, node=None, edge=None):
-    """
-    Create a summary of simple statistics for H
-
-    Parameters
-    ----------
-    H : Hypergraph
-    obj : optional
-        either a node or edge uid from the hypergraph
-
-    Returns
-    -------
-     info_dict : dict
-        Returns a dictionary of statistics of the size,
-        aspect ratio, and density of the hypergraph.
-
-    """
-    report = dict()
-    if len(H.edges.elements) == 0:
-        return {}
-
-    if node:
-        report["membs"] = list(H.dual().edges[node])
-        report["degree"] = len(report["membs"])
-        report["neighbors"] = H.neighbors(node)
-        return report
-    if edge:
-        report["size"] = H.size(edge)
-        report["elements"] = list(H.edges[edge])
-        return report
-    else:
-        lnodes, ledges = H.shape
-        M = H.incidence_matrix(index=False)
-        ncells = M.nnz
-
-        report["nrows"] = lnodes
-        report["ncols"] = ledges
-        report["aspect ratio"] = lnodes / ledges
-        report["ncells"] = ncells
-        report["density"] = ncells / (lnodes * ledges)
-        return report

-
-
-
[docs]def dist_stats(H):
-    """
-    Computes many basic hypergraph stats and puts them all into a single dictionary object
-
-        * nrows = number of nodes (rows in the incidence matrix)
-        * ncols = number of edges (columns in the incidence matrix)
-        * aspect ratio = nrows/ncols
-        * ncells = number of filled cells in incidence matrix
-        * density = ncells/(nrows*ncols)
-        * node degree list = degree_dist(H)
-        * node degree dist = centrality_stats(degree_dist(H))
-        * node degree hist = Counter(degree_dist(H))
-        * max node degree = max(degree_dist(H))
-        * edge size list = edge_size_dist(H)
-        * edge size dist = centrality_stats(edge_size_dist(H))
-        * edge size hist = Counter(edge_size_dist(H))
-        * max edge size = max(edge_size_dist(H))
-        * comp nodes list = s_comp_dist(H, s=1, edges=False)
-        * comp nodes dist = centrality_stats(s_comp_dist(H, s=1, edges=False))
-        * comp nodes hist = Counter(s_comp_dist(H, s=1, edges=False))
-        * comp edges list = s_comp_dist(H, s=1, edges=True)
-        * comp edges dist = centrality_stats(s_comp_dist(H, s=1, edges=True))
-        * comp edges hist = Counter(s_comp_dist(H, s=1, edges=True))
-        * num comps = len(s_comp_dist(H))
-
-    Parameters
-    ----------
-    H : Hypergraph
-
-    Returns
-    -------
-     dist_stats : dict
-        Dictionary which keeps track of each of the above items (e.g., basic['nrows'] = the number of nodes in H)
-    """
-    stats = H.state_dict.get("dist_stats", None)
-    if stats is not None:
-        return H.state_dict["dist_stats"]
-    else:
-        cstats = ["min", "max", "mean", "median", "std"]
-        basic = dict()
-
-        # Number of rows (nodes), columns (edges), and aspect ratio
-        basic["nrows"] = len(H.nodes)
-        basic["ncols"] = len(H.edges)
-        basic["aspect ratio"] = basic["nrows"] / basic["ncols"]
-
-        # Number of cells and density
-        M = H.incidence_matrix(index=False)
-        basic["ncells"] = M.nnz
-        basic["density"] = basic["ncells"] / (basic["nrows"] * basic["ncols"])
-
-        # Node degree distribution
-        basic["node degree list"] = sorted(degree_dist(H), reverse=True)
-        basic["node degree centrality stats"] = dict(
-            zip(cstats, centrality_stats(basic["node degree list"]))
-        )
-        basic["node degree hist"] = Counter(basic["node degree list"])
-        basic["max node degree"] = max(basic["node degree list"])
-
-        # Edge size distribution
-        basic["edge size list"] = sorted(H.edge_size_dist(), reverse=True)
-        basic["edge size centrality stats"] = dict(
-            zip(cstats, centrality_stats(basic["edge size list"]))
-        )
-        basic["edge size hist"] = Counter(basic["edge size list"])
-        basic["max edge size"] = max(basic["edge size hist"])
-
-        # Component size distribution (nodes)
-        basic["comp nodes list"] = sorted(s_comp_dist(H, edges=False), reverse=True)
-        basic["comp nodes hist"] = Counter(basic["comp nodes list"])
-        basic["comp nodes centrality stats"] = dict(
-            zip(cstats, centrality_stats(basic["comp nodes list"]))
-        )
-
-        # Component size distribution (edges)
-        basic["comp edges list"] = sorted(s_comp_dist(H, edges=True), reverse=True)
-        basic["comp edges hist"] = Counter(basic["comp edges list"])
-        basic["comp edges centrality stats"] = dict(
-            zip(cstats, centrality_stats(basic["comp edges list"]))
-        )
-
-        # Number of components
-        basic["num comps"] = len(basic["comp nodes list"])
-
-        # # Diameters
-        # basic['s edge diam list'] = s_edge_diameter_dist(H)
-        # basic['s node diam list'] = s_node_diameter_dist(H)
-        if H.isstatic:
-            H.set_state(dist_stats=basic)
-        return basic

-
- -
- -
-
- -
- -
-

- © Copyright 2018 Battelle Memorial Institute. - -

-
- - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
-
-
- -
- -
- - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/_static/documentation_options.js b/docs/build/_static/documentation_options.js index 2f08d25f..9fd31e43 100644 --- a/docs/build/_static/documentation_options.js +++ b/docs/build/_static/documentation_options.js @@ -1,6 +1,6 @@ var DOCUMENTATION_OPTIONS = { URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), - VERSION: '1.0.0', + VERSION: '1.0.1', LANGUAGE: 'None', COLLAPSE_INDEX: false, BUILDER: 'html', diff --git a/docs/build/algorithms/algorithms.html b/docs/build/algorithms/algorithms.html index 5a70cab4..4549a2f7 100644 --- a/docs/build/algorithms/algorithms.html +++ b/docs/build/algorithms/algorithms.html @@ -7,7 +7,7 @@ - algorithms package — HyperNetX 1.0.0 documentation + algorithms package — HyperNetX 1.0.1 documentation @@ -36,7 +36,6 @@ - @@ -106,9 +105,9 @@
  • Algorithms @@ -197,667 +196,14 @@

    algorithms package

    Submodules

    -
    -

    algorithms.homology_mod2 module

    -
    -

    Homology and Smith Normal Form

    -

    The purpose of computing the Homology groups for data generated -hypergraphs is to identify data sources that correspond to interesting -features in the topology of the hypergraph.

    -

    The elements of one of these Homology groups are generated by \(k\) -dimensional cycles of relationships in the original data that are not -bound together by higher order relationships. Ideally, we want the -briefest description of these cycles; we want a minimal set of -relationships exhibiting interesting cyclic behavior. This minimal set -will be a bases for the Homology group.

    -

    The cyclic relationships in the data are discovered using a boundary -map represented as a matrix. To discover the bases we compute the -Smith Normal Form of the boundary map.

    -
    -

    Homology Mod2

    -

    This module computes the homology groups for data represented as an -abstract simplicial complex with chain groups \(\{C_k\}\) and \(Z_2\) additions. -The boundary matrices are represented as rectangular matrices over \(Z_2\). -These matrices are diagonalized and represented in Smith -Normal Form. The kernel and image bases are computed and the Betti -numbers and homology bases are returned.

    -

    Methods for obtaining SNF for Z/2Z are based on Ferrario’s work: -http://www.dlfer.xyz/post/2016-10-27-smith-normal-form/

    -
    -
    -algorithms.homology_mod2.add_to_column(M, i, j)[source]
    -

    Replaces column i (of M) with logical xor between column i and j

    -
    -
    Parameters
    -
      -

    • M (np.array) – matrix

      • -

    • i (int) – index of column being altered

      • -

    • j (int) – index of column being added to altered

      • -
    -
    -
    Returns
    -

    N

    -
    -
    Return type
    -

    np.array

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.add_to_row(M, i, j)[source]
    -

    Replaces row i with logical xor between row i and j

    -
    -
    Parameters
    -
      -

    • M (np.array) –

      • -

    • i (int) – index of row being altered

      • -

    • j (int) – index of row being added to altered

      • -
    -
    -
    Returns
    -

    N

    -
    -
    Return type
    -

    np.array

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.betti(bd, k=None)[source]
    -

    Generate the kth-betti numbers for a chain complex with boundary -matrices given by bd

    -
    -
    Parameters
    -
      -

    • bd (dict of k-boundary matrices keyed on dimension of domain) –

      • -

    • k (int, list or tuple, optional, default=None) – list must be min value and max value of k values inclusive -if None, then all betti numbers for dimensions of existing cells will be -computed.

      • -
    -
    -
    Returns
    -

    betti – Description

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.betti_numbers(h, k=None)[source]
    -

    Return the kth betti numbers for the simplicial homology of the ASC -associated to h

    -
    -
    Parameters
    -
      -

    • h (hnx.Hypergraph) – Hypergraph to compute the betti numbers from

      • -

    • k (int or list, optional, default=None) – list must be min value and max value of k values inclusive -if None, then all betti numbers for dimensions of existing cells will be -computed.

      • -
    -
    -
    Returns
    -

    betti – A dictionary of betti numbers keyed by dimension

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.bkMatrix(km1basis, kbasis)[source]
    -

    Compute the boundary map from \(C_{k-1}\)-basis to \(C_k\) basis with -respect to \(Z_2\)

    -
    -
    Parameters
    -
      -

    • km1basis (indexable iterable) – Ordered list of \(k-1\) dimensional cell

      • -

    • kbasis (indexable iterable) – Ordered list of \(k\) dimensional cells

      • -
    -
    -
    Returns
    -

    bk – boundary matrix in \(Z_2\) stored as boolean

    -
    -
    Return type
    -

    np.array

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.boundary_group(image_basis)[source]
    -

    Returns a csr_matrix with rows corresponding to the elements of the -group generated by image basis over \(\mathbb{Z}_2\)

    -
    -
    Parameters
    -

    image_basis (numpy.ndarray or scipy.sparse.csr_matrix) – 2d-array of basis elements

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    scipy.sparse.csr_matrix

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.chain_complex(h, k=None)[source]
    -

    Compute the k-chains and k-boundary maps required to compute homology -for all values in k

    -
    -
    Parameters
    -
      -

    • h (hnx.Hypergraph) –

      • -

    • k (int or list of length 2, optional, default=None) – k must be an integer greater than 0 or a list of -length 2 indicating min and max dimensions to be -computed. eg. if k = [1,2] then 0,1,2,3-chains -and boundary maps for k=1,2,3 will be returned, -if None than k = [1,max dimension of edge in h]

      • -
    -
    -
    Returns
    -

    C, bd – C is a dictionary of lists -bd is a dictionary of numpy arrays

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.homology_basis(bd, k=None, boundary=False, **kwargs)[source]
    -

    Compute a basis for the kth-simplicial homology group, \(H_k\), defined by a -chain complex \(C\) with boundary maps given by bd \(= \{k:\partial_k\)}$

    -
    -
    Parameters
    -
      -

    • bd (dict) – dict of boundary matrices on k-chains to k-1 chains keyed on k -if krange is a tuple then all boundary matrices k in [krange[0],..,krange[1]] -inclusive must be in the dictionary

      • -

    • k (int or list of ints, optional, default=None) – k must be a positive integer or a list of -2 integers indicating min and max dimensions to be -computed, if none given all homology groups will be computed from -available boundary matrices in bd

      • -

    • boundary (bool) – option to return a basis for the boundary group from each dimension. -Needed to compute the shortest generators in the homology group.

      • -
    -
    -
    Returns
    -

      -

    • basis (dict) – dict of generators as 0-1 tuples keyed by dim -basis for dimension k will be returned only if bd[k] and bd[k+1] have -been provided.

      • -

    • im (dict) – dict of boundary group generators keyed by dim

      • -
    -

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.hypergraph_homology_basis(h, k=None, shortest=False, interpreted=True)[source]
    -

    Computes the kth-homology groups mod 2 for the ASC -associated with the hypergraph h for k in krange inclusive

    -
    -
    Parameters
    -
      -

    • h (hnx.Hypergraph) –

      • -

    • k (int or list of length 2, optional, default = None) – k must be an integer greater than 0 or a list of -length 2 indicating min and max dimensions to be -computed

      • -

    • shortest (bool, optional, default=False) – option to look for shortest representative for each coset in the -homology group, only good for relatively small examples

      • -

    • interpreted (bool, optional, default = True) – if True will return an explicit basis in terms of the k-chains

      • -
    -
    -
    Returns
    -

      -

    • basis (list) – list of generators as k-chains as boolean vectors

      • -

    • interpreted_basis – lists of kchains in basis

      • -
    -

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.interpret(Ck, arr, labels=None)[source]
    -

    Returns the data as represented in Ck associated with the arr

    -
    -
    Parameters
    -
      -

    • Ck (list) – a list of k-cells being referenced by arr

      • -

    • arr (np.array) – array of 0-1 vectors

      • -

    • labels (dict, optional) – dictionary of labels to associate to the nodes in the cells

      • -
    -
    -
    Returns
    -

    list of k-cells referenced by data in Ck

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.kchainbasis(h, k)[source]
    -

    Compute the set of k dimensional cells in the abstract simplicial -complex associated with the hypergraph.

    -
    -
    Parameters
    -
      -

    • h (hnx.Hypergraph) –

      • -

    • k (int) – dimension of cell

      • -
    -
    -
    Returns
    -

    an ordered list of kchains represented as tuples of length k+1

    -
    -
    Return type
    -

    list

    -
    -
    -
    -

    See also

    -

    hnx.hypergraph.toplexes

    -
    -

    Notes

    -
      -

    • Method works best if h is simple [Berge], i.e. no edge contains another and there are no duplicate edges (toplexes).

      • -

    • Hypergraph node uids must be sortable.

      • -
    -
    - -
    -
    -algorithms.homology_mod2.logical_dot(ar1, ar2)[source]
    -

    Returns the boolean equivalent of the dot product mod 2 on two 1-d arrays of -the same length.

    -
    -
    Parameters
    -
      -

    • ar1 (numpy.ndarray) – 1-d array

      • -

    • ar2 (numpy.ndarray) – 1-d array

      • -
    -
    -
    Returns
    -

    boolean value associated with dot product mod 2

    -
    -
    Return type
    -

    bool

    -
    -
    Raises
    -

    HyperNetXError – If arrays are not of the same length an error will be raised.

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.logical_matadd(mat1, mat2)[source]
    -

    Returns the boolean equivalent of matrix addition mod 2 on two -binary arrays stored as type boolean

    -
    -
    Parameters
    -
      -

    • mat1 (np.ndarray) – 2-d array of boolean values

      • -

    • mat2 (np.ndarray) – 2-d array of boolean values

      • -
    -
    -
    Returns
    -

    mat – boolean matrix equivalent to the mod 2 matrix addition of the -matrices as matrices over Z/2Z

    -
    -
    Return type
    -

    np.ndarray

    -
    -
    Raises
    -

    HyperNetXError – If dimensions are not equal an error will be raised.

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.logical_matmul(mat1, mat2)[source]
    -

    Returns the boolean equivalent of matrix multiplication mod 2 on two -binary arrays stored as type boolean

    -
    -
    Parameters
    -
      -

    • mat1 (np.ndarray) – 2-d array of boolean values

      • -

    • mat2 (np.ndarray) – 2-d array of boolean values

      • -
    -
    -
    Returns
    -

    mat – boolean matrix equivalent to the mod 2 matrix multiplication of the -matrices as matrices over Z/2Z

    -
    -
    Return type
    -

    np.ndarray

    -
    -
    Raises
    -

    HyperNetXError – If inner dimensions are not equal an error will be raised.

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.matmulreduce(arr, reverse=False)[source]
    -

    Recursively applies a ‘logical multiplication’ to a list of boolean arrays.

    -

    For arr = [arr[0],arr[1],arr[2]…arr[n]] returns product arr[0]arr[1]…arr[n] -If reverse = True, returns product arr[n]arr[n-1]…arr[0]

    -
    -
    Parameters
    -
      -

    • arr (list of np.array) – list of nxm matrices represented as np.array

      • -

    • reverse (bool, optional) – order to multiply the matrices

      • -
    -
    -
    Returns
    -

    P – Product of matrices in the list

    -
    -
    Return type
    -

    np.array

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.reduced_row_echelon_form_mod2(M)[source]
    -

    Computes the invertible transformation matrices needed to compute -the reduced row echelon form of M modulo 2

    -
    -
    Parameters
    -

    M (np.array) – a rectangular matrix with elements in \(Z_2\)

    -
    -
    Returns
    -

    L, S, Linv – LM = S where S is the reduced echelon form of M -and M = LinvS

    -
    -
    Return type
    -

    np.arrays

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.smith_normal_form_mod2(M)[source]
    -

    Computes the invertible transformation matrices needed to compute the -Smith Normal Form of M modulo 2

    -
    -
    Parameters
    -
      -

    • M (np.array) – a rectangular matrix with data type bool

      • -

    • track (bool) – if track=True will print out the transformation as Z/2Z matrix as it -discovers L[i] and R[j]

      • -
    -
    -
    Returns
    -

    L, R, S, Linv – LMR = S is the Smith Normal Form of the matrix M.

    -
    -
    Return type
    -

    np.arrays

    -
    -
    -
    -

    Note

    -

    Given a mxn matrix \(M\) with -entries in \(Z_2\) we start with the equation: \(L M R = S\), where -\(L = I_m\), and \(R=I_n\) are identity matrices and \(S = M\). We -repeatedly apply actions to the left and right side of the equation -to transform S into a diagonal matrix. -For each action applied to the left side we apply its inverse -action to the right side of I_m to generate \(L^{-1}\). -Finally we verify: -\(L M R = S\) and \(LLinv = I_m\).

    -
    -
    - -
    -
    -algorithms.homology_mod2.swap_columns(i, j, *args)[source]
    -

    Swaps ith and jth column of each matrix in args -Returns a list of new matrices

    -
    -
    Parameters
    -
      -

    • i (int) –

      • -

    • j (int) –

      • -

    • args (np.arrays) –

      • -
    -
    -
    Returns
    -

    list of copies of args with ith and jth row swapped

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -algorithms.homology_mod2.swap_rows(i, j, *args)[source]
    -

    Swaps ith and jth row of each matrix in args -Returns a list of new matrices

    -
    -
    Parameters
    -
      -

    • i (int) –

      • -

    • j (int) –

      • -

    • args (np.arrays) –

      • -
    -
    -
    Returns
    -

    list of copies of args with ith and jth row swapped

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -
    -
    -

    algorithms.s_centrality_measures module

    -
    -

    S-Centrality Measures

    -

    We generalize graph metrics to s-metrics for a hypergraph by using its s-connected -components. This is accomplished by computing the s edge-adjacency matrix and -constructing the corresponding graph of the matrix. We then use existing graph metrics -on this representation of the hypergraph. In essence we construct an s-line graph -corresponding to the hypergraph on which to apply our methods.

    -

    S-Metrics for hypergraphs are discussed in depth in: -Aksoy, S.G., Joslyn, C., Ortiz Marrero, C. et al. Hypernetwork science via high-order hypergraph walks. -EPJ Data Sci. 9, 16 (2020). https://doi.org/10.1140/epjds/s13688-020-00231-0

    -
    -
    -algorithms.s_centrality_measures.s_betweenness_centrality(H, s=1, edges=True, normalized=True, return_singletons=True, use_nwhy=True)[source]
    -
    -

    A centrality measure for an s-edge(node) subgraph of H based on shortest paths. -Equals the betweenness centrality of vertices in the edge(node) s-linegraph.

    -

    In a graph (2-uniform hypergraph) the betweenness centrality of a vertex \(v\) -is the ratio of the number of non-trivial shortest paths between any pair of -vertices in the graph that pass through \(v\) divided by the total number of -non-trivial shortest paths in the graph.

    -

    The centrality of edge to all shortest s-edge paths -\(V\) = the set of vertices in the linegraph. -\(\sigma(s,t)\) = the number of shortest paths between vertices \(s\) and \(t\). -\(\sigma(s, t|v)\) = the number of those paths that pass through vertex \(v\) -$$c_B(v) =sum_{s

    -
    -

    eq t in V} -rac{sigma(s, t|v)}{sigma(s, t)}$$

    -
    -

    H : hnx.Hypergraph -s : int

    -
    -

    s connectedness requirement

    -
    -
    -
    edgesbool, optional

    determines if edge or node linegraph

    -
    -
    normalized

    bool, default=False, -If true the betweenness values are normalized by 2/((n-1)(n-2)), -where n is the number of edges in H

    -
    -
    return_singletonsbool, optional

    if False will ignore singleton components of linegraph

    -
    -
    -
    -
    -
    : dict

    A dictionary of s-betweenness centrality value of the edges.

    -
    -
    -
    -
    -
    - -
    -
    -algorithms.s_centrality_measures.s_closeness_centrality(H, s=1, edges=True, return_singletons=True, source=None, use_nwhy=True)[source]
    -
    -

    In a connected component the reciprocal of the sum of the distance between an -edge(node) and all other edges(nodes) in the component times the number of edges(nodes) -in the component minus 1.

    -

    \(V\) = the set of vertices in the linegraph. -\(n = |V|\) -\(d\) = shortest path distance -$$C(u) =

    -
    -

    rac{n - 1}{sum_{v -eq u in V} d(v, u)}$$

    -
    -

    H : hnx.Hypergraph

    -

    s : int, optional

    -
    -
    edgesbool, optional

    Indicates if method should compute edge linegraph (default) or node linegraph.

    -
    -
    return_singletonsbool, optional

    Indicates if method should return values for singleton components.

    -
    -
    sourcestr, optional

    Identifier of node or edge of interest for computing centrality

    -
    -
    use_nwhybool, optional

    If true will use the NWHy library if available.

    -
    -
    -
    -
    -
    : dict or float

    returns the s-closeness centrality value of the edges(nodes). -If source=None a dictionary of values for each s-edge in H is returned. -If source then a single value is returned.

    -
    -
    -
    -
    -
    - -
    -
    -algorithms.s_centrality_measures.s_eccentricity(H, s=1, edges=True, source=None, return_singletons=True, use_nwhy=True)[source]
    -

    The length of the longest shortest path from a vertex \(u\) to every other vertex in the linegraph. -\(V\) = set of vertices in the linegraph -\(d\) = shortest path distance -$$ ext{s-ecc}(u) = ext{max}{d(u,v): v in V} $$

    -
    -
    Parameters
    -
      -

    • H (hnx.Hypergraph) –

      • -

    • s (int, optional) –

      • -

    • edges (bool, optional) – Indicates if method should compute edge linegraph (default) or node linegraph.

      • -

    • return_singletons (bool, optional) – Indicates if method should return values for singleton components.

      • -

    • source (str, optional) – Identifier of node or edge of interest for computing centrality

      • -

    • use_nwhy (bool, optional) – If true will use the NWHy library if available.

      • -
    -
    -
    Returns
    -

    returns the s-eccentricity value of the edges(nodes). -If source=None a dictionary of values for each s-edge in H is returned. -If source then a single value is returned.

    -
    -
    Return type
    -

    dict or float

    -
    -
    -
    - -
    -
    -algorithms.s_centrality_measures.s_harmonic_centrality(H, s=1, edges=True, source=None, normalized=False, return_singletons=True, use_nwhy=True)[source]
    -
    -

    A centrality measure for an s-edge subgraph of H. A value equal to 1 means the s-edge -intersects every other s-edge in H. All values range between 0 and 1. -Edges of size less than s return 0. If H contains only one s-edge a 0 is returned.

    -

    The denormalized reciprocal of the harmonic mean of all distances from \(u\) to all other vertices. -\(V\) = the set of vertices in the linegraph. -\(d\) = shortest path distance -$$C(u) = sum_{v

    -
    -

    eq u in V} -rac{1}{d(v, u)}$$

    -
    -

    Normalized this becomes: -$$C(u) = sum_{v

    -
    -

    eq u in V} -rac{1}{d(v, u)}cdot -rac{2}{(n-1)(n-2)}$$

    -
    -

    where \(n\) is the number vertices.

    -

    H : hnx.Hypergraph

    -

    s : int, optional

    -
    -
    edgesbool, optional

    Indicates if method should compute edge linegraph (default) or node linegraph.

    -
    -
    return_singletonsbool, optional

    Indicates if method should return values for singleton components.

    -
    -
    sourcestr, optional

    Identifier of node or edge of interest for computing centrality

    -
    -
    use_nwhybool, optional

    If true will use the NWHy library if available.

    -
    -
    -
    -
    -
    : dict or float

    returns the s-harmonic closeness centrality value of the edges, a number between 0 and 1 inclusive. -If source=None a dictionary of values for each s-edge in H is returned. -If source then a single value is returned.

    -
    -
    -
    -
    -
    - -
    -
    -algorithms.s_centrality_measures.s_harmonic_closeness_centrality(H, s=1, edge=None, use_nwhy=True)[source]
    -
    - +
    +

    algorithms.homology_mod2 module

    +
    +

    algorithms.s_centrality_measures module

    -
    -

    Module contents

    +
    +

    Module contents

    diff --git a/docs/build/algorithms/modules.html b/docs/build/algorithms/modules.html index f1aa2059..b14efc19 100644 --- a/docs/build/algorithms/modules.html +++ b/docs/build/algorithms/modules.html @@ -7,7 +7,7 @@ - algorithms — HyperNetX 1.0.0 documentation + algorithms — HyperNetX 1.0.1 documentation @@ -189,18 +189,9 @@

    algorithmsalgorithms package

    • diff --git a/docs/build/classes/classes.html b/docs/build/classes/classes.html index 973749c0..7c35d04f 100644 --- a/docs/build/classes/classes.html +++ b/docs/build/classes/classes.html @@ -7,7 +7,7 @@ - classes package — HyperNetX 1.0.0 documentation + classes package — HyperNetX 1.0.1 documentation @@ -104,10 +104,10 @@
  • Hypergraphs @@ -197,2692 +197,17 @@

    classes package

    Submodules

    -
    -

    classes.entity module

    -
    -
    -class classes.entity.Entity(uid, elements=[], entity=None, **props)[source]
    -

    Bases: object

    -

    Base class for objects used in building network-like objects including -Hypergraphs, Posets, Cell Complexes.

    -
    -
    Parameters
    -
      -

    • uid (hashable) – a unique identifier

      • -

    • elements (list or dict, optional, default: None) – a list of entities with identifiers different than uid and/or -hashables different than uid, see Honor System

      • -

    • entity (Entity) – an Entity object to be cloned into a new Entity with uid. If the uid is the same as -Entity.uid then the entities will not be distinguishable and error will be raised. -The elements in the signature will be added to the cloned entity.

      • -

    • props (keyword arguments, optional, default: {}) – properties belonging to the entity added as key=value pairs. -Both key and value must be hashable.

      • -
    -
    -
    -

    Notes

    -

    An Entity is a container-like object, which has a unique identifier and -may contain elements and have properties. -The Entity class was created as a generic object providing structure for -Hypergraph nodes and edges.

    - -

    Honor System

    -

    HyperNetX has an Honor System that applies to Entity uid values. -Two entities are equal if their __dict__ objects match. -For performance reasons many methods distinguish entities by their uids. -It is, therefore, up to the user to ensure entities with the same uids are indeed the same. -Not doing so may cause undesirable side effects. -In particular, the methods in the Hypergraph class assume distinct nodes and edges -have distinct uids.

    -

    Examples

    -
    >>> x = Entity('x')
->>> y = Entity('y',[x])
->>> z = Entity('z',[x,y],weight=1)
->>> z
-Entity(z,['y', 'x'],{'weight': 1})
->>> z.uid
-'z'
->>> z.elements
-{'x': Entity(x,[],{}), 'y': Entity(y,['x'],{})}
->>> z.properties
-{'weight': 1}
->>> z.children
-{'x'}
->>> x.memberships
-{'y': Entity(y,['x'],{}), 'z': Entity(z,['y', 'x'],{'weight': 1})}
->>> z.fullregistry()
-{'x': Entity(x,[],{}), 'y': Entity(y,['x'],{})}
-
    -
    -
    -

    See also

    -

    EntitySet

    -
    -
    -
    -add(*args)[source]
    -

    Adds unpacked args to entity elements. Depends on add_element()

    -
    -
    Parameters
    -

    args (One or more entities or hashables) –

    -
    -
    Returns
    -

    self

    -
    -
    Return type
    -

    Entity

    -
    -
    -
    -

    Note

    -

    Adding an element to an object in a hypergraph will not add the -element to the hypergraph and will cause an error. Use Hypergraph.add_edge -or Hypergraph.add_node_to_edge instead.

    -
    -
    - -
    -
    -add_element(item)[source]
    -

    Adds item to entity elements and adds entity to item.memberships.

    -
    -
    Parameters
    -

    item (hashable or Entity) – If hashable, will be replaced with empty Entity using hashable as uid

    -
    -
    Returns
    -

    self

    -
    -
    Return type
    -

    Entity

    -
    -
    -

    Notes

    -

    If item is in entity elements, no new element is added but properties -will be updated. -If item is in complete_registry(), only the item already known to self will be added. -This method employs the Honor System since membership in complete_registry is checked -using the item’s uid. It is assumed that the user will only use the same uid -for identical instances within the entities registry.

    -
    - -
    -
    -add_elements_from(arg_set)[source]
    -

    Similar to add() it allows for adding from an interable.

    -
    -
    Parameters
    -

    arg_set (Iterable of hashables or entities) –

    -
    -
    Returns
    -

    self

    -
    -
    Return type
    -

    Entity

    -
    -
    -
    - -
    -
    -property children
    -

    Set of uids of the elements of elements of entity.

    -

    To return set of ids for deeper level use: -Entity.levelset(level).keys() -see: Entity.levelset()

    -
    - -
    -
    -clone(newuid)[source]
    -

    Returns shallow copy of entity with newuid. Entity’s elements will -belong to two distinct Entities.

    -
    -
    Parameters
    -

    newuid (hashable) – Name of the new entity

    -
    -
    Returns
    -

    clone

    -
    -
    Return type
    -

    Entity

    -
    -
    -
    - -
    -
    -complete_registry()[source]
    -

    A dictionary of all entities appearing in any level of -entity

    -
    -
    Returns
    -

    complete_registry

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -depth(max_depth=10)[source]
    -

    Returns the number of nonempty level sets of level <= max_depth

    -
    -
    Parameters
    -

    max_depth (int, optional, default: 10) – If full depth is desired set max_depth to number of entities in -system + 1.

    -
    -
    Returns
    -

    depth – If max_depth is exceeded output will be numpy infinity. -If there is a cycle output will be numpy infinity.

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -property elements
    -

    Dictionary of elements belonging to entity.

    -
    - -
    -
    -fullregistry(lastlevel=10, firstlevel=1)[source]
    -

    A dictionary of all entities appearing in levels firstlevel -to lastlevel.

    -
    -
    Parameters
    -
      -

    • lastlevel (int, optional, default: 10) –

      • -

    • firstlevel (int, optional, default: 1) –

      • -
    -
    -
    Returns
    -

    fullregistry

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -property incidence_dict
    -

    element.uidset for each element in entity

    -

    To return an incidence dictionary of all nested entities in entity -use nested_incidence_dict

    -
    -
    Type
    -

    Dictionary of element.uid

    -
    -
    -
    - -
    -
    -intersection(other)[source]
    -

    A dictionary of elements belonging to entity and other.

    -
    -
    Parameters
    -

    other (Entity) –

    -
    -
    Returns
    -

    Dictionary of elements

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -property is_bipartite
    -

    Returns boolean indicating if the entity satisfies the Bipartite Condition

    -
    - -
    -
    -property is_empty
    -

    Boolean indicating if entity.elements is empty

    -
    - -
    -
    -level(item, max_depth=10)[source]
    -

    The first level where item appears in self.

    -
    -
    Parameters
    -
      -

    • item (hashable) – uid for an entity

      • -

    • max_depth (int, default: 10) – last level to check for entity

      • -
    -
    -
    Returns
    -

    level

    -
    -
    Return type
    -

    int

    -
    -
    -
    -

    Note

    -

    Item must be the uid of an entity listed -in fullregistry()

    +
    +

    classes.entity module

    -
    - -
    -
    -levelset(k=1)[source]
    -

    A dictionary of level k of self.

    -
    -
    Parameters
    -

    k (int, optional, default: 1) –

    -
    -
    Returns
    -

    levelset

    -
    -
    Return type
    -

    dict

    -
    -
    -
    -

    Note

    -

    An Entity contains other entities, hence the relationships between entities -and their elements may be represented in a directed graph with entity as root. -The levelsets are sets of entities which make up the elements appearing at -a certain level.

    +
    +

    classes.hypergraph module

    -
    - -
    -
    -property memberships
    -

    Dictionary of elements to which entity belongs.

    -

    This assignment is done on construction and controlled by -Entity.add_element() -and Entity.remove_element() methods.

    -
    - -
    -
    -static merge_entities(name, ent1, ent2)[source]
    -

    Merge two entities making sure they do not conflict.

    -
    -
    Parameters
    -
      -

    • name (hashable) –

      • -

    • ent1 (Entity) – First entity to have elements and properties added to new -entity

      • -

    • ent2 (Entity) – elements of ent2 will be checked against ent1.complete_registry() -and only nonexisting elements will be added using add() method. -Properties of ent2 will update properties of ent1 in new entity.

      • -
    -
    -
    Returns
    -

    a new entity

    -
    -
    Return type
    -

    Entity

    -
    -
    -
    - -
    -
    -nested_incidence_dict(level=10)[source]
    -

    Returns a nested dictionary with keys up to level

    -
    -
    Parameters
    -

    level (int, optional, default: 10) – If level<=1, returns the incidence_dict.

    -
    -
    Returns
    -

    nested_incidence_dict

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -property properties
    -

    Dictionary of properties of entity

    -
    - -
    -
    -property registry
    -

    Entity pairs for children entity.

    -

    To return a dictionary of all entities at all depths -Entity.complete_registry()

    -
    -
    Type
    -

    Dictionary of uid

    -
    -
    -
    - -
    -
    -remove(*args)[source]
    -

    Removes args from entitie’s elements if they belong. -Does nothing with args not in entity.

    -
    -
    Parameters
    -

    args (One or more hashables or entities) –

    -
    -
    Returns
    -

    self

    -
    -
    Return type
    -

    Entity

    -
    -
    -
    - -
    -
    -remove_element(item)[source]
    -

    Removes item from entity and reference to entity from -item.memberships

    -
    -
    Parameters
    -

    item (Hashable or Entity) –

    -
    -
    Returns
    -

    self

    -
    -
    Return type
    -

    Entity

    -
    -
    -
    - -
    -
    -remove_elements_from(arg_set)[source]
    -

    Similar to remove(). Removes elements in arg_set.

    -
    -
    Parameters
    -

    arg_set (Iterable of hashables or entities) –

    -
    -
    Returns
    -

    self

    -
    -
    Return type
    -

    Entity

    -
    -
    -
    - -
    -
    -restrict_to(element_subset, name=None)[source]
    -

    Shallow copy of entity removing elements not in element_subset.

    -
    -
    Parameters
    -
      -

    • element_subset (iterable) – A subset of entities elements

      • -

    • name (hashable, optional) – If not given, a name is generated to reflect entity uid

      • -
    -
    -
    Returns
    -

    New Entity – Could be empty.

    -
    -
    Return type
    -

    Entity

    -
    -
    -
    - -
    -
    -size()[source]
    -

    Returns the number of elements in entity

    -
    - -
    -
    -property uid
    -

    String identifier for entity

    -
    - -
    -
    -property uidset
    -

    Set of uids of elements of entity.

    -
    - -
    - -
    -
    -class classes.entity.EntitySet(uid, elements=[], **props)[source]
    -

    Bases: classes.entity.Entity

    -
    -
    Parameters
    -
      -

    • uid (hashable) – a unique identifier

      • -

    • elements (list or dict, optional, default: None) – a list of entities with identifiers different than uid and/or -hashables different than uid, see Honor System

      • -

    • props (keyword arguments, optional, default: {}) – properties belonging to the entity added as key=value pairs. -Both key and value must be hashable.

      • -
    -
    -
    -

    Notes

    -

    The EntitySet class was created to distinguish Entities satifying the Bipartite Condition.

    -

    Bipartite Condition

    -

    Entities that are elements of the same EntitySet, may not contain each other as elements. -The elements and children of an EntitySet generate a specific partition for a bipartite graph. -The partition is isomorphic to a Hypergraph where the elements correspond to hyperedges and -the children correspond to the nodes. EntitySets are the basic objects used to construct hypergraphs -in HNX.

    -

    Example:

    -
    >>> y = Entity('y')
->>> x = Entity('x')
->>> x.add(y)
->>> y.add(x)
->>> w = EntitySet('w',[x,y])
-HyperNetXError: Error: Fails the Bipartite Condition for EntitySet.
-y references a child of an existing Entity in the EntitySet.
-
    -
    -
    -
    -add(*args)[source]
    -

    Adds args to entityset’s elements, checking to make sure no self references are -made to element ids. -Ensures Bipartite Condition of EntitySet.

    -
    -
    Parameters
    -

    args (One or more entities or hashables) –

    -
    -
    Returns
    -

    self

    -
    -
    Return type
    -

    EntitySet

    -
    -
    -
    - -
    -
    -clone(newuid)[source]
    -

    Returns shallow copy of entityset with newuid. Entityset’s -elements will belong to two distinct entitysets.

    -
    -
    Parameters
    -

    newuid (hashable) – Name of the new entityset

    -
    -
    Returns
    -

    clone

    -
    -
    Return type
    -

    EntitySet

    -
    -
    -
    - -
    -
    -collapse_identical_elements(newuid, return_equivalence_classes=False)[source]
    -

    Returns a deduped copy of the entityset, using representatives of equivalence classes as element keys. -Two elements of an EntitySet are collapsed if they share the same children.

    -
    -
    Parameters
    -
      -

    • newuid (hashable) –

      • -

    • return_equivalence_classes (boolean, default=False) – If True, return a dictionary of equivalence classes keyed by new edge names

      • -
    -
    -
    Returns
    -

    -
    -
    Return type
    -

    EntitySet

    -
    -
    -
    -
    eq_classesdict

    if return_equivalence_classes = True

    -
    -
    -

    Notes

    -

    Treats elements of the entityset as equal if they have the same uidsets. Using this -as an equivalence relation, the entityset’s uidset is partitioned into equivalence classes. -The equivalent elements are identified using a single entity by using the -frozenset of uids associated to these elements as the uid for the new element -and dropping the properties. -If use_reps is set to True a representative element of the equivalence class is -used as identifier instead of the frozenset.

    -

    Example:

    -
    >>> E = EntitySet('E',elements=[Entity('E1', ['a','b']),Entity('E2',['a','b'])])
->>> E.incidence_dict
-{'E1': {'a', 'b'}, 'E2': {'a', 'b'}}
->>> E.collapse_identical_elements('_',).incidence_dict
-{'E2': {'a', 'b'}}
-
    -
    -
    - -
    -
    -incidence_matrix(sparse=True, index=False)[source]
    -

    An incidence matrix for the EntitySet indexed by children x uidset.

    -
    -
    Parameters
    -
      -

    • sparse (boolean, optional, default: True) –

      • -

    • index (boolean, optional, default False) – If True return will include a dictionary of children uid : row number -and element uid : column number

      • -
    -
    -
    Returns
    -

      -

    • incidence_matrix (scipy.sparse.csr.csr_matrix or np.ndarray)

      • -

    • row dictionary (dict) – Dictionary identifying row with item in entityset’s children

      • -

    • column dictionary (dict) – Dictionary identifying column with item in entityset’s uidset

      • -
    -

    -
    -
    -

    Notes

    -

    Example:

    -
    >>> E = EntitySet('E',{'a':{1,2,3},'b':{2,3},'c':{1,4}})
->>> E.incidence_matrix(sparse=False, index=True)
-(array([[0, 1, 1],
-        [1, 1, 0],
-        [1, 1, 0],
-        [0, 0, 1]]), {0: 1, 1: 2, 2: 3, 3: 4}, {0: 'b', 1: 'a', 2: 'c'})
-
    -
    -
    - -
    -
    -restrict_to(element_subset, name=None)[source]
    -

    Shallow copy of entityset removing elements not in element_subset.

    -
    -
    Parameters
    -
      -

    • element_subset (iterable) – A subset of the entityset’s elements

      • -

    • name (hashable, optional) – If not given, a name is generated to reflect entity uid

      • -
    -
    -
    Returns
    -

    new entityset – Could be empty.

    -
    -
    Return type
    -

    EntitySet

    -
    -
    -
    -

    See also

    -

    Entity.restrict_to

    -
    -
    - -
    - -
    -
    -

    classes.hypergraph module

    -
    -
    -class classes.hypergraph.Hypergraph(setsystem=None, name=None, static=False, use_nwhy=False, filepath=None)[source]
    -

    Bases: object

    -

    Hypergraph H = (V,E) references a pair of disjoint sets: -V = nodes (vertices) and E = (hyper)edges.

    -

    An HNX Hypergraph is either dynamic or static. -Dynamic hypergraphs can change by adding or subtracting objects -from them. Static hypergraphs require that all of the nodes and edges -be known at creation. A hypergraph is dynamic by default.

    -

    Dynamic hypergraphs require the user to keep track of its objects, -by using a unique names for each node and edge. This allows for multi-edge graphs and -inseperable nodes.

    -

    For example: Let V = {1,2,3} and E = {e1,e2,e3}, -where e1 = {1,2}, e2 = {1,2}, and e3 = {1,2,3}. -The edges e1 and e2 contain the same set of nodes and yet -are distinct and must be distinguishable within H.

    -

    In a dynamic hypergraph each node and edge is -instantiated as an Entity and given an identifier or uid. Entities -keep track of inclusion relationships and can be nested. Since -hypergraphs can be quite large, only the entity identifiers will be used -for computation intensive methods, this means the user must take care -to keep a one to one correspondence between their set of uids and -the objects in their hypergraph. See Honor System -Dynamic hypergraphs are most practical for small to modestly sized -hypergraphs (<1000 objects).

    -

    Static hypergraphs store node and edge information in numpy arrays and -are immutable. Each node and edge receives a class generated internal -identifier used for computations so do not require the user to create -different ids for nodes and edges. To create a static hypergraph set -static = True in the signature.

    -

    We will create hypergraphs in multiple ways:

    -
      -

    1. As an empty instance:

      -
      >>> H = hnx.Hypergraph()
->>> H.nodes, H.edges
-({}, {})
-
      -
      -
      2. -

    2. From a dictionary of iterables (elements of iterables must be of type hypernetx.Entity or hashable):

      -
      >>> H = Hypergraph({'a':[1,2,3],'b':[4,5,6]})
->>> H.nodes, H.edges
-# output: (EntitySet(_:Nodes,[1, 2, 3, 4, 5, 6],{}), EntitySet(_:Edges,['b', 'a'],{}))
-
      -
      -
      3. -

    3. From an iterable of iterables: (elements of iterables must be of type hypernetx.Entity or hashable):

      -
      >>> H = Hypergraph([{'a','b'},{'b','c'},{'a','c','d'}])
->>> H.nodes, H.edges
-# output: (EntitySet(_:Nodes,['d', 'b', 'c', 'a'],{}), EntitySet(_:Edges,['_1', '_2', '_0'],{}))
-
      -
      -
      4. -

    4. From a hypernetx.EntitySet or StaticEntitySet:

      -
      >>> a = Entity('a',{1,2}); b = Entity('b',{2,3})
->>> E = EntitySet('sample',elements=[a,b])
->>> H = Hypergraph(E)
->>> H.nodes, H.edges.
-# output: (EntitySet(_:Nodes,[1, 2, 3],{}), EntitySet(_:Edges,['b', 'a'],{}))
-
      -
      -
      5. -
    -

    All of these constructions apply for both dynamic and static hypergraphs. To -create a static hypergraph set the parameter static=True. In addition a static -hypergraph is automatically created if a StaticEntity, StaticEntitySet, or pandas.DataFrame object -is passed to the Hypergraph constructor.

    -
      -
    1. -
      From a pandas.DataFrame. The dataframe must have at least two columns with headers and there can be no nans.
      -
      By default the first column corresponds to the edge names and the second column to the node names.
      -
      You can specify the columns by restricting the dataframe to the columns of interest in the order:
      -
      hnx.Hypergraph(df[[edge_column_name,node_column_name]])
      -
      See Colab Tutorials Tutorial 6 - Static Hypergraphs and Entities for additional information.
      -
      -
      2. -
    -
    -
    Parameters
    -
      -

    • setsystem ((optional) EntitySet, StaticEntitySet, dict, iterable, pandas.dataframe, default: None) – See notes above for setsystem requirements.

      • -

    • name (hashable, optional, default: None) – If None then a placeholder ‘_’ will be inserted as name

      • -

    • static (boolean, optional, default: False) – If True the hypergraph will be immutable, edges and nodes may not be changed.

      • -

    • use_nwhy (boolean, optional, default = False) – If True hypergraph will be static and computations will be done using -C++ backend offered by NWHypergraph. This requires installation of the -NWHypergraph C++ library. Please see the NWHy documentation for more information.

      • -
    -
    -
    -
    -
    -add_edge(edge)[source]
    -

    Adds a single edge to hypergraph.

    -
    -
    Parameters
    -

    edge (hashable or Entity) – If hashable the edge returned will be empty.

    -
    -
    Returns
    -

    hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -

    Notes

    -

    When adding an edge to a hypergraph children must be removed -so that nodes do not have elements. -Each node (element of edge) must be instantiated as a node, -making sure its uid isn’t already present in the self. -If an added edge contains nodes that cannot be added to hypergraph -then an error will be raised.

    -
    - -
    -
    -add_edges_from(edge_set)[source]
    -

    Add edges to hypergraph.

    -
    -
    Parameters
    -

    edge_set (iterable of hashables or Entities) – For hashables the edges returned will be empty.

    -
    -
    Returns
    -

    hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    - -
    -
    -add_node_to_edge(node, edge)[source]
    -

    Adds node to an edge in hypergraph edges

    -
    -
    Parameters
    -
      -

    • node (hashable or Entity) – If Entity, only uid and properties will be used. -If uid is already in nodes then the known node will -be used

      • -

    • edge (uid of edge or edge, must belong to self.edges) –

      • -
    -
    -
    Returns
    -

    hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    - -
    -
    -classmethod add_nwhy(h, fpath=None)[source]
    -

    Add nwhy functionality to a hypergraph.

    -
    -
    Parameters
    -
      -

    • h (hnx.Hypergraph) –

      • -

    • fpath (file path for storage of hypergraph state dictionary) –

      • -
    -
    -
    Returns
    -

    Returns a copy of h with static set to true and nwhy set to True -if it is available.

    -
    -
    Return type
    -

    hnx.Hypergraph

    -
    -
    -
    - -
    -
    -adjacency_matrix(index=False, s=1, weighted=True)[source]
    -

    The sparse weighted s-adjacency matrix

    -
    -
    Parameters
    -
      -

    • s (int, optional, default: 1) –

      • -

    • index (boolean, optional, default: False) – if True, will return a rowdict of row to node uid

      • -

    • weighted (boolean, optional, default: True) –

      • -
    -
    -
    Returns
    -

      -

    • adjacency_matrix (scipy.sparse.csr.csr_matrix)

      • -

    • row dictionary (dict)

      • -
    -

    -
    -
    -

    Notes

    -

    If weighted is True each off diagonal cell will equal the number -of edges shared by the nodes indexing the row and column if that number is -greater than s, otherwise the cell will equal 0. If weighted is False, the off -diagonal cell will equal 1 if the nodes indexed by the row and column share at -least s edges and 0 otherwise.

    -
    - -
    -
    -auxiliary_matrix(s=1, index=False)[source]
    -

    The unweighted s-auxiliary matrix for hypergraph

    -
    -
    Parameters
    -
      -

    • s (int) –

      • -

    • index (bool, optional, default: False) – return a dictionary of labels for the rows of the matrix

      • -
    -
    -
    Returns
    -

    auxiliary_matrix – Will return the same type of matrix as self.arr

    -
    -
    Return type
    -

    scipy.sparse.csr.csr_matrix or numpy.ndarray

    -
    -
    -

    Notes

    -

    Creates subgraph by restricting to edges of cardinality at least s. -Returns the unweighted s-edge adjacency matrix for the subgraph.

    -
    - -
    -
    -bipartite()[source]
    -

    Constructs the networkX bipartite graph associated to hypergraph.

    -
    -
    Returns
    -

    bipartite

    -
    -
    Return type
    -

    nx.Graph()

    -
    -
    -

    Notes

    -

    Creates a bipartite networkx graph from hypergraph. -The nodes and (hyper)edges of hypergraph become the nodes of bipartite graph. -For every (hyper)edge e in the hypergraph and node n in e there is an edge (n,e) -in the graph.

    -
    - -
    -
    -collapse_edges(name=None, use_reps=None, return_counts=None, return_equivalence_classes=False)[source]
    -

    Constructs a new hypergraph gotten by identifying edges containing the same nodes

    -
    -
    Parameters
    -
      -

    • name (hashable, optional, default: None) –

      • -

    • return_equivalence_classes (boolean, optional, default: False) – Returns a dictionary of edge equivalence classes keyed by frozen sets of nodes

      • -
    -
    -
    Returns
    -

      -

    • new hypergraph (Hypergraph) – Equivalent edges are collapsed to a single edge named by a representative of the equivalent -edges followed by a colon and the number of edges it represents.

      • -

    • equivalence_classes (dict) – A dictionary keyed by representative edge names with values equal to the edges in -its equivalence class

      • -
    -

    -
    -
    -

    Notes

    -

    Two edges are identified if their respective elements are the same. -Using this as an equivalence relation, the uids of the edges are partitioned into -equivalence classes.

    -

    A single edge from the collapsed edges followed by a colon and the number of elements -in its equivalence class as uid for the new edge

    -
    - -
    -
    -collapse_nodes(name=None, use_reps=True, return_counts=True, return_equivalence_classes=False)[source]
    -

    Constructs a new hypergraph gotten by identifying nodes contained by the same edges

    -
    -
    Parameters
    -
      -

    • name (str, optional, default: None) –

      • -

    • return_equivalence_classes (boolean, optional, default: False) – Returns a dictionary of node equivalence classes keyed by frozen sets of edges

      • -

    • use_reps (boolean, optional, default: False - Deprecated, this no longer works and will be removed) – Choose a single element from the collapsed nodes as uid for the new node, otherwise uses -a frozen set of the uids of nodes in the equivalence class

      • -

    • return_counts (boolean, - Deprecated, this no longer works and will be removed) – if use_reps is True the new nodes have uids given by a tuple of the rep -and the count

      • -
    -
    -
    Returns
    -

    new hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -

    Notes

    -

    Two nodes are identified if their respective memberships are the same. -Using this as an equivalence relation, the uids of the nodes are partitioned into -equivalence classes. A single member of the equivalence class is chosen to represent -the class followed by the number of members of the class.

    -

    Example

    -
    >>> h = Hypergraph(EntitySet('example',elements=[Entity('E1', ['a','b']),Entity('E2',['a','b'])]))
->>> h.incidence_dict
-{'E1': {'a', 'b'}, 'E2': {'a', 'b'}}
->>> h.collapse_nodes().incidence_dict
-{'E1': {frozenset({'a', 'b'})}, 'E2': {frozenset({'a', 'b'})}} ### Fix this
->>> h.collapse_nodes(use_reps=True).incidence_dict
-{'E1': {('a', 2)}, 'E2': {('a', 2)}}
-
    -
    -
    - -
    -
    -collapse_nodes_and_edges(name=None, use_reps=True, return_counts=True, return_equivalence_classes=False)[source]
    -

    Returns a new hypergraph by collapsing nodes and edges.

    -
    -
    Parameters
    -
      -

    • name (str, optional, default: None) –

      • -

    • use_reps (boolean, optional, default: False) – Choose a single element from the collapsed elements as a representative

      • -

    • return_counts (boolean, optional, default: True) – if use_reps is True the new elements are keyed by a tuple of the rep -and the count

      • -

    • return_equivalence_classes (boolean, optional, default: False) – Returns a dictionary of edge equivalence classes keyed by frozen sets of nodes

      • -
    -
    -
    Returns
    -

    new hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -

    Notes

    -

    Collapses the Nodes and Edges EntitySets. Two nodes(edges) are duplicates -if their respective memberships(elements) are the same. Using this as an -equivalence relation, the uids of the nodes(edges) are partitioned into -equivalence classes. A single member of the equivalence class is chosen to represent -the class followed by the number of members of the class.

    -

    Example

    -
    >>> h = Hypergraph(EntitySet('example',elements=[Entity('E1', ['a','b']),Entity('E2',['a','b'])]))
->>> h.incidence_dict
-{'E1': {'a', 'b'}, 'E2': {'a', 'b'}}
->>> h.collapse_nodes_and_edges().incidence_dict   ### Fix this
-{('E1', 2): {('a', 2)}}
-
    -
    -
    - -
    -
    -component_subgraphs(return_singletons=False)[source]
    -

    Same as s_components_subgraphs() with s=1. Returns iterator.

    -
    -

    See also

    -

    s_component_subgraphs

    -
    -
    - -
    -
    -components(edges=False, return_singletons=True)[source]
    -

    Same as s_connected_components() with s=1, but nodes are returned -by default. Return iterator.

    -
    -

    See also

    -

    s_connected_components

    -
    -
    - -
    -
    -connected_component_subgraphs(return_singletons=True)[source]
    -

    Same as s_component_subgraphs() with s=1. Returns iterator

    -
    -

    See also

    -

    s_component_subgraphs

    -
    -
    - -
    -
    -connected_components(edges=False, return_singletons=True)[source]
    -

    Same as s_connected_components() with s=1, but nodes are returned -by default. Return iterator.

    -
    -

    See also

    -

    s_connected_components

    -
    -
    - -
    -
    -convert_to_static(name=None, nodes_name='nodes', edges_name='edges', use_nwhy=False, filepath=None)[source]
    -

    Returns new static hypergraph with the same dictionary as original hypergraph

    -
    -
    Parameters
    -
      -

    • name (None, optional) – Name

      • -

    • nodes_name (str, optional) – name for list of node labels

      • -

    • edges_name (str, optional) – name for list of edge labels

      • -
    -
    -
    Returns
    -

    Will have attribute static = True

    -
    -
    Return type
    -

    hnx.Hypergraph

    -
    -
    -
    -

    Note

    -

    Static hypergraphs store the user defined node and edge names in -a dictionary of labeled lists. The order of the lists provides an -index, which the hypergraph uses in place of the node and edge names -for fast processing.

    -
    -
    - -
    -
    -dataframe(sort_rows=False, sort_columns=False)[source]
    -

    Returns a pandas dataframe for hypergraph indexed by the nodes and -with column headers given by the edge names.

    -
    -
    Parameters
    -
      -

    • sort_rows (bool, optional, default=True) – sort rows based on hashable node names

      • -

    • sort_columns (bool, optional, default=True) – sort columns based on hashable edge names

      • -
    -
    -
    -
    - -
    -
    -degree(node, s=1, max_size=None)[source]
    -

    The number of edges of size s that contain node.

    -
    -
    Parameters
    -
      -

    • node (hashable) – identifier for the node.

      • -

    • s (positive integer, optional, default: 1) – smallest size of edge to consider in degree

      • -

    • max_size (positive integer or None, optional, default: None) – largest size of edge to consider in degree

      • -
    -
    -
    Returns
    -

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -diameter(s=1)[source]
    -

    Returns the length of the longest shortest s-walk between nodes in hypergraph

    -
    -
    Parameters
    -

    s (int, optional, default: 1) –

    -
    -
    Returns
    -

    diameter

    -
    -
    Return type
    -

    int

    -
    -
    Raises
    -

    HyperNetXError – If hypergraph is not s-edge-connected

    -
    -
    -

    Notes

    -

    Two nodes are s-adjacent if they share s edges. -Two nodes v_start and v_end are s-walk connected if there is a sequence of -nodes v_start, v_1, v_2, … v_n-1, v_end such that consecutive nodes -are s-adjacent. If the graph is not connected, an error will be raised.

    -
    - -
    -
    -dim(edge)[source]
    -

    Same as size(edge)-1.

    -
    - -
    -
    -distance(source, target, s=1)[source]
    -

    Returns the shortest s-walk distance between two nodes in the hypergraph.

    -
    -
    Parameters
    -
      -

    • source (node.uid or node) – a node in the hypergraph

      • -

    • target (node.uid or node) – a node in the hypergraph

      • -

    • s (positive integer) – the number of edges

      • -
    -
    -
    Returns
    -

    s-walk distance

    -
    -
    Return type
    -

    int

    -
    -
    -
    -

    See also

    -

    edge_distance

    -
    -

    Notes

    -

    The s-distance is the shortest s-walk length between the nodes. -An s-walk between nodes is a sequence of nodes that pairwise share -at least s edges. The length of the shortest s-walk is 1 less than -the number of nodes in the path sequence.

    -

    Uses the networkx shortest_path_length method on the graph -generated by the s-adjacency matrix.

    -
    - -
    -
    -dual(name=None)[source]
    -

    Constructs a new hypergraph with roles of edges and nodes of hypergraph reversed.

    -
    -
    Parameters
    -

    name (hashable) –

    -
    -
    Returns
    -

    dual

    -
    -
    Return type
    -

    hypergraph

    -
    -
    -
    - -
    -
    -edge_adjacency_matrix(index=False, s=1, weighted=True)[source]
    -

    The weighted s-adjacency matrix for the dual hypergraph.

    -
    -
    Parameters
    -
      -

    • s (int, optional, default: 1) –

      • -

    • index (boolean, optional, default: False) – if True, will return a coldict of column to edge uid

      • -

    • sparse (boolean, optional, default: True) –

      • -

    • weighted (boolean, optional, default: True) –

      • -
    -
    -
    Returns
    -

      -

    • edge_adjacency_matrix (scipy.sparse.csr.csr_matrix or numpy.ndarray)

      • -

    • column dictionary (dict)

      • -
    -

    -
    -
    -

    Notes

    -

    This is also the adjacency matrix for the line graph. -Two edges are s-adjacent if they share at least s nodes. -If index=True, returns a dictionary column_index:edge_uid

    -
    - -
    -
    -edge_diameter(s=1)[source]
    -

    Returns the length of the longest shortest s-walk between edges in hypergraph

    -
    -
    Parameters
    -

    s (int, optional, default: 1) –

    -
    -
    Returns
    -

    edge_diameter

    -
    -
    Return type
    -

    int

    -
    -
    Raises
    -

    HyperNetXError – If hypergraph is not s-edge-connected

    -
    -
    -

    Notes

    -

    Two edges are s-adjacent if they share s nodes. -Two nodes e_start and e_end are s-walk connected if there is a sequence of -edges e_start, e_1, e_2, … e_n-1, e_end such that consecutive edges -are s-adjacent. If the graph is not connected, an error will be raised.

    -
    - -
    -
    -edge_diameters(s=1)[source]
    -

    Returns the edge diameters of the s_edge_connected component subgraphs -in hypergraph.

    -
    -
    Parameters
    -

    s (int, optional, default: 1) –

    -
    -
    Returns
    -

      -

    • maximum diameter (int)

      • -

    • list of diameters (list) – List of edge_diameters for s-edge component subgraphs in hypergraph

      • -

    • list of component (list) – List of the edge uids in the s-edge component subgraphs.

      • -
    -

    -
    -
    -
    - -
    -
    -edge_distance(source, target, s=1)[source]
    -

    XX TODO: still need to return path and translate into user defined nodes and edges -Returns the shortest s-walk distance between two edges in the hypergraph.

    -
    -
    Parameters
    -
      -

    • source (edge.uid or edge) – an edge in the hypergraph

      • -

    • target (edge.uid or edge) – an edge in the hypergraph

      • -

    • s (positive integer) – the number of intersections between pairwise consecutive edges

      • -

    • TODO (add edge weights) –

      • -

    • weight (None or string, optional, default: None) – if None then all edges have weight 1. If string then edge attribute -string is used if available.

      • -
    -
    -
    Returns
    -

    s- walk distance – A shortest s-walk is computed as a sequence of edges, -the s-walk distance is the number of edges in the sequence -minus 1. If no such path exists returns np.inf.

    -
    -
    Return type
    -

    the shortest s-walk edge distance

    -
    -
    -
    -

    See also

    -

    distance

    -
    -

    Notes

    -

    The s-distance is the shortest s-walk length between the edges. -An s-walk between edges is a sequence of edges such that consecutive pairwise -edges intersect in at least s nodes. The length of the shortest s-walk is 1 less than -the number of edges in the path sequence.

    -

    Uses the networkx shortest_path_length method on the graph -generated by the s-edge_adjacency matrix.

    -
    - -
    -
    -edge_neighbors(edge, s=1)[source]
    -

    The edges in hypergraph which share s nodes(s) with edge.

    -
    -
    Parameters
    -
      -

    • edge (hashable or Entity) – uid for a edge in hypergraph or the edge Entity

      • -

    • s (int, list, optional, default : 1) – Minimum number of nodes shared by neighbors edge node.

      • -
    -
    -
    Returns
    -

    List of edge neighbors

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -edge_size_dist()[source]
    -

    Returns the size for each edge

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    np.array

    -
    -
    -
    - -
    -
    -property edges
    -

    Object associated with self._edges.

    -
    -
    Returns
    -

    If self.isstatic the StaticEntitySet, otherwise EntitySet.

    -
    -
    Return type
    -

    StaticEntitySet or EntitySet

    -
    -
    -
    - -
    -
    -classmethod from_bipartite(B, set_names=('nodes', 'edges'), name=None, static=False, use_nwhy=False)[source]
    -

    Static method creates a Hypergraph from a bipartite graph.

    -
    -
    Parameters
    -
      -

    • B (nx.Graph()) – A networkx bipartite graph. Each node in the graph has a property -‘bipartite’ taking the value of 0 or 1 indicating a 2-coloring of the graph.

      • -

    • set_names (iterable of length 2, optional, default = ['nodes','edges']) – Category names assigned to the graph nodes associated to each bipartite set

      • -

    • name (hashable) –

      • -

    • static (bool) –

      • -
    -
    -
    Returns
    -

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -

    Notes

    -

    A partition for the nodes in a bipartite graph generates a hypergraph.

    -
    >>> import networkx as nx
->>> B = nx.Graph()
->>> B.add_nodes_from([1, 2, 3, 4], bipartite=0)
->>> B.add_nodes_from(['a', 'b', 'c'], bipartite=1)
->>> B.add_edges_from([(1, 'a'), (1, 'b'), (2, 'b'), (2, 'c'), (3, 'c'), (4, 'a')])
->>> H = Hypergraph.from_bipartite(B)
->>> H.nodes, H.edges
-# output: (EntitySet(_:Nodes,[1, 2, 3, 4],{}), EntitySet(_:Edges,['b', 'c', 'a'],{}))
-
    -
    -
    - -
    -
    -classmethod from_dataframe(df, columns=None, rows=None, name=None, fillna=0, transpose=False, transforms=[], key=None, node_label='nodes', edge_label='edges', static=False, use_nwhy=False)[source]
    -

    Create a hypergraph from a Pandas Dataframe object using index to label vertices -and Columns to label edges. The values of the dataframe are transformed into an -incidence matrix. -Note this is different than passing a dataframe directly -into the Hypergraph constructor. The latter automatically generates a static hypergraph -with edge and node labels given by the cell values.

    -
    -
    Parameters
    -
      -

    • df (Pandas.Dataframe) – a real valued dataframe with a single index

      • -

    • columns ((optional) list, default = None) – restricts df to the columns with headers in this list.

      • -

    • rows ((optional) list, default = None) – restricts df to the rows indexed by the elements in this list.

      • -

    • name ((optional) string, default = None) –

      • -

    • fillna (float, default = 0) – a real value to place in empty cell, all-zero columns will not generate -an edge.

      • -

    • transpose ((optional) bool, default = False) – option to transpose the dataframe, in this case df.Index will label the edges -and df.columns will label the nodes, transpose is applied before transforms and -key

      • -

    • transforms ((optional) list, default = []) – optional list of transformations to apply to each column, -of the dataframe using pd.DataFrame.apply(). -Transformations are applied in the order they are -given (ex. abs). To apply transforms to rows or for additional -functionality, consider transforming df using pandas.DataFrame methods -prior to generating the hypergraph.

      • -

    • key ((optional) function, default = None) – boolean function to be applied to dataframe. Must be defined on numpy -arrays.

      • -
    -
    -
    -
    -

    See also

    -

    from_numpy_array

    -
    -
    -
    Returns
    -

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -

    Notes

    -

    The from_dataframe constructor does not generate empty edges. -All-zero columns in df are removed and the names corresponding to these -edges are discarded. -Restrictions and data processing will occur in this order:

    -
    -
      -

    1. column and row restrictions

      2. -

    2. fillna replace NaNs in dataframe

      3. -

    3. transpose the dataframe

      4. -

    4. transforms in the order listed

      5. -

    5. boolean key

      6. -
    -
    -

    This method offers the above options for wrangling a dataframe into an incidence -matrix for a hypergraph. For more flexibility we recommend you use the Pandas -library to format the values of your dataframe before submitting it to this -constructor.

    -
    - -
    -
    -classmethod from_numpy_array(M, node_names=None, edge_names=None, node_label='nodes', edge_label='edges', name=None, key=None, static=False, use_nwhy=False)[source]
    -

    Create a hypergraph from a real valued matrix represented as a 2 dimensionsl numpy array. -The matrix is converted to a matrix of 0’s and 1’s so that any truthy cells are converted to 1’s and -all others to 0’s.

    -
    -
    Parameters
    -
      -

    • M (real valued array-like object, 2 dimensions) – representing a real valued matrix with rows corresponding to nodes and columns to edges

      • -

    • node_names (object, array-like, default=None) – List of node names must be the same length as M.shape[0]. -If None then the node names correspond to row indices with ‘v’ prepended.

      • -

    • edge_names (object, array-like, default=None) – List of edge names must have the same length as M.shape[1]. -If None then the edge names correspond to column indices with ‘e’ prepended.

      • -

    • name (hashable) –

      • -

    • key ((optional) function) – boolean function to be evaluated on each cell of the array, -must be applicable to numpy.array

      • -
    -
    -
    Returns
    -

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    -

    Note

    -

    The constructor does not generate empty edges. -All zero columns in M are removed and the names corresponding to these -edges are discarded.

    -
    -
    - -
    -
    -get_id(uid, edges=False)[source]
    -

    Return the internally assigned id associated with a label.

    -
    -
    Parameters
    -
      -

    • uid (string) – User provided name/id/label for hypergraph object

      • -

    • edges (bool, optional) – Determines if uid is an edge or node name

      • -
    -
    -
    Returns
    -

    internal id assigned at construction

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -get_linegraph(s, edges=True, use_nwhy=True)[source]
    -

    Creates an ::term::s-linegraph for the Hypergraph. -If edges=True (default)then the edges will be the vertices of the line graph. -Two vertices are connected by an s-line-graph edge if the corresponding -hypergraphedges intersect in at least s hypergraph nodes. -If edges=False, the hypergraph nodes will be the vertices of the line graph. -Two vertices are connected if the nodes they correspond to share at least s -incident hyper edges.

    -
    -
    Parameters
    -
      -

    • s (int) – The width of the connections.

      • -

    • edges (bool, optional) – Determine if edges or nodes will be the vertices in the linegraph.

      • -

    • use_nwhy (bool, optional) – Requests that nwhy be used to construct the linegraph. If NWHy is not available this is ignored.

      • -
    -
    -
    Returns
    -

    A NetworkX graph.

    -
    -
    Return type
    -

    nx.Graph

    -
    -
    -
    - -
    -
    -get_name(id, edges=False)[source]
    -

    Return the user defined name/id/label associated to an -internally assigned id.

    -
    -
    Parameters
    -
      -

    • id (int) – Internally assigned id

      • -

    • edges (bool, optional) – Determines if id references an edge or node

      • -
    -
    -
    Returns
    -

    User provided name/id/label for hypergraph object

    -
    -
    Return type
    -

    str

    -
    -
    -
    - -
    -
    -property incidence_dict
    -

    Dictionary keyed by edge uids with values the uids of nodes in each edge

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -incidence_matrix(index=False)[source]
    -

    An incidence matrix for the hypergraph indexed by nodes x edges.

    -
    -
    Parameters
    -

    index (boolean, optional, default False) – If True return will include a dictionary of node uid : row number -and edge uid : column number

    -
    -
    Returns
    -

      -

    • incidence_matrix (scipy.sparse.csr.csr_matrix or np.ndarray)

      • -

    • row dictionary (dict) – Dictionary identifying rows with nodes

      • -

    • column dictionary (dict) – Dictionary identifying columns with edges

      • -
    -

    -
    -
    -
    - -
    -
    -static incidence_to_adjacency(M, s=1, weighted=True)[source]
    -

    Helper method to obtain adjacency matrix from incidence matrix.

    -
    -
    Parameters
    -
      -

    • M (scipy.sparse.csr.csr_matrix) –

      • -

    • s (int, optional, default: 1) –

      • -

    • weighted (boolean, optional, default: True) –

      • -
    -
    -
    Returns
    -

    a matrix

    -
    -
    Return type
    -

    scipy.sparse.csr.csr_matrix

    -
    -
    -
    - -
    -
    -is_connected(s=1, edges=False)[source]
    -

    Determines if hypergraph is s-connected.

    -
    -
    Parameters
    -
      -

    • s (int, optional, default: 1) –

      • -

    • edges (boolean, optional, default: False) – If True, will determine if s-edge-connected. -For s=1 s-edge-connected is the same as s-connected.

      • -
    -
    -
    Returns
    -

    is_connected

    -
    -
    Return type
    -

    boolean

    -
    -
    -

    Notes

    -

    A hypergraph is s node connected if for any two nodes v0,vn -there exists a sequence of nodes v0,v1,v2,…,v(n-1),vn -such that every consecutive pair of nodes v(i),v(i+1) -share at least s edges.

    -

    A hypergraph is s edge connected if for any two edges e0,en -there exists a sequence of edges e0,e1,e2,…,e(n-1),en -such that every consecutive pair of edges e(i),e(i+1) -share at least s nodes.

    -
    - -
    -
    -property isstatic
    -

    Checks whether nodes and edges are immutable

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    Boolean

    -
    -
    -
    - -
    -
    -neighbors(node, s=1)[source]
    -

    The nodes in hypergraph which share s edge(s) with node.

    -
    -
    Parameters
    -
      -

    • node (hashable or Entity) – uid for a node in hypergraph or the node Entity

      • -

    • s (int, list, optional, default : 1) – Minimum number of edges shared by neighbors with node.

      • -
    -
    -
    Returns
    -

    List of neighbors

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -node_diameters(s=1)[source]
    -

    Returns the node diameters of the connected components in hypergraph.

    -
    -
    Parameters
    -
      -

    • of the diameters of the s-components and (list) –

      • -

    • of the s-component nodes (list) –

      • -
    -
    -
    -
    - -
    -
    -property nodes
    -

    Object associated with self._nodes.

    -
    -
    Returns
    -

    If self.isstatic the StaticEntitySet, otherwise EntitySet.

    -
    -
    Return type
    -

    StaticEntitySet or EntitySet

    -
    -
    -
    - -
    -
    -number_of_edges(edgeset=None)[source]
    -

    The number of edges in edgeset belonging to hypergraph.

    -
    -
    Parameters
    -

    edgeset (an interable of Entities, optional, default: None) – If None, then return the number of edges in hypergraph.

    -
    -
    Returns
    -

    number_of_edges

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -number_of_nodes(nodeset=None)[source]
    -

    The number of nodes in nodeset belonging to hypergraph.

    -
    -
    Parameters
    -

    nodeset (an interable of Entities, optional, default: None) – If None, then return the number of nodes in hypergraph.

    -
    -
    Returns
    -

    number_of_nodes

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -order()[source]
    -

    The number of nodes in hypergraph.

    -
    -
    Returns
    -

    order

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -classmethod recover_from_state(fpath='current_state.p', newfpath=None, use_nwhy=True)[source]
    -

    Recover a static hypergraph pickled using save_state.

    -
    -
    Parameters
    -

    fpath (str) – Full path to pickle file containing state_dict and labels -of hypergraph

    -
    -
    Returns
    -

    H – static hypergraph with state dictionary prefilled

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    - -
    -
    -remove_edge(edge)[source]
    -

    Removes a single edge from hypergraph.

    -
    -
    Parameters
    -

    edge (hashable or Entity) –

    -
    -
    Returns
    -

    hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -

    Notes

    -

    Deletes reference to edge from all of its nodes. -If any of its nodes do not belong to any other edges -the node is dropped from self.

    -
    - -
    -
    -remove_edges(edge_set)[source]
    -

    Removes edges from hypergraph.

    -
    -
    Parameters
    -

    edge_set (iterable of hashables or Entities) –

    -
    -
    Returns
    -

    hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    - -
    -
    -remove_node(node)[source]
    -

    Removes node from edges and deletes reference in hypergraph nodes

    -
    -
    Parameters
    -

    node (hashable or Entity) – a node in hypergraph

    -
    -
    Returns
    -

    hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    - -
    -
    -remove_nodes(node_set)[source]
    -

    Removes nodes from edges and deletes references in hypergraph nodes

    -
    -
    Parameters
    -

    node_set (an iterable of hashables or Entities) – Nodes in hypergraph

    -
    -
    Returns
    -

    hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    - -
    -
    -remove_singletons(name=None)[source]
    -

    XX -Constructs clone of hypergraph with singleton edges removed.

    -
    -
    Parameters
    -

    name (str, optional, default: None) –

    -
    -
    Returns
    -

    new hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    - -
    -
    -remove_static(name=None)[source]
    -

    Returns dynamic hypergraph

    -
    -
    Parameters
    -

    name (None, optional) – User defined namae of hypergraph

    -
    -
    Returns
    -

    A new hypergraph with the same dictionary as self but allowing dynamic -changes to nodes and edges. -If hypergraph is not static, returns self.

    -
    -
    Return type
    -

    hnx.Hypergraph

    -
    -
    -
    - -
    -
    -restrict_to_edges(edgeset, name=None)[source]
    -

    Constructs a hypergraph using a subset of the edges in hypergraph

    -
    -
    Parameters
    -
      -

    • edgeset (iterable of hashables or Entities) – A subset of elements of the hypergraph edges

      • -

    • name (str, optional) –

      • -
    -
    -
    Returns
    -

    new hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    - -
    -
    -restrict_to_nodes(nodeset, name=None)[source]
    -

    Constructs a new hypergraph by restricting the edges in the hypergraph to -the nodes referenced by nodeset.

    -
    -
    Parameters
    -
      -

    • nodeset (iterable of hashables) – References a subset of elements of self.nodes

      • -

    • name (string, optional, default: None) –

      • -
    -
    -
    Returns
    -

    new hypergraph

    -
    -
    Return type
    -

    Hypergraph

    -
    -
    -
    - -
    -
    -s_component_subgraphs(s=1, edges=True, return_singletons=False)[source]
    -

    Returns a generator for the induced subgraphs of s_connected components. -Removes singletons unless return_singletons is set to True. Computed using -s-linegraph generated either by the hypergraph (edges=True) or its dual -(edges = False)

    -
    -
    Parameters
    -
      -

    • s (int, optional, default: 1) –

      • -

    • edges (boolean, optional, edges=False) – Determines if edge or node components are desired. Returns -subgraphs equal to the hypergraph restricted to each set of nodes(edges) in the -s-connected components or s-edge-connected components

      • -

    • return_singletons (bool, optional) –

      • -
    -
    -
    Yields
    -

    s_component_subgraphs (iterator) – Iterator returns subgraphs generated by the edges (or nodes) in the -s-edge(node) components of hypergraph.

    -
    -
    -
    - -
    -
    -s_components(s=1, edges=True, return_singletons=True)[source]
    -

    Same as s_connected_components

    -
    -

    See also

    -

    s_connected_components

    -
    -
    - -
    -
    -s_connected_components(s=1, edges=True, return_singletons=False)[source]
    -

    Returns a generator for the s-edge-connected components -or the s-node-connected components -of the hypergraph.

    -
    -
    Parameters
    -
      -

    • s (int, optional, default: 1) –

      • -

    • edges (boolean, optional, default: True) – If True will return edge components, if False will return node components

      • -

    • return_singletons (bool, optional, default : False) –

      • -
    -
    -
    -

    Notes

    -

    If edges=True, this method returns the s-edge-connected components as -lists of lists of edge uids. -An s-edge-component has the property that for any two edges e1 and e2 -there is a sequence of edges starting with e1 and ending with e2 -such that pairwise adjacent edges in the sequence intersect in at least -s nodes. If s=1 these are the path components of the hypergraph.

    -

    If edges=False this method returns s-node-connected components. -A list of sets of uids of the nodes which are s-walk connected. -Two nodes v1 and v2 are s-walk-connected if there is a -sequence of nodes starting with v1 and ending with v2 such that pairwise -adjacent nodes in the sequence share s edges. If s=1 these are the -path components of the hypergraph.

    -

    Example

    -
    >>> S = {'A':{1,2,3},'B':{2,3,4},'C':{5,6},'D':{6}}
->>> H = Hypergraph(S)
-
    -
    -
    >>> list(H.s_components(edges=True))
-[{'C', 'D'}, {'A', 'B'}]
->>> list(H.s_components(edges=False))
-[{1, 2, 3, 4}, {5, 6}]
-
    -
    -
    -
    Yields
    -

    s_connected_components (iterator) – Iterator returns sets of uids of the edges (or nodes) in the s-edge(node) -components of hypergraph.

    -
    -
    -
    - -
    -
    -s_degree(node, s=1)[source]
    -

    Same as degree

    -
    -
    Parameters
    -
      -

    • node (Entity or hashable) – If hashable, then must be uid of node in hypergraph

      • -

    • s (positive integer, optional, default: 1) –

      • -
    -
    -
    Returns
    -

    s_degree – The degree of a node in the subgraph induced by edges -of size s

    -
    -
    Return type
    -

    int

    -
    -
    -
    -

    Note

    -

    The s-degree of a node is the number of edges of size -at least s that contain the node.

    -
    -
    - -
    -
    -save_state(fpath=None)[source]
    -

    Save the hypergraph as an ordered pair: [state_dict,labels] -The hypergraph can be recovered using the command:

    -
    >>> H = hnx.Hypergraph.recover_from_state(fpath)
-
    -
    -
    -
    Parameters
    -

    fpath (str, optional) –

    -
    -
    -
    - -
    -
    -set_state(**kwargs)[source]
    -

    Allow state_dict updates from outside of class. Use with caution.

    -
    -
    Parameters
    -

    **kwargs – key=value pairs to save in state dictionary

    -
    -
    -
    - -
    -
    -property shape
    -

    (number of nodes, number of edges)

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    tuple

    -
    -
    -
    - -
    -
    -singletons()[source]
    -

    Returns a list of singleton edges. A singleton edge is an edge of -size 1 with a node of degree 1.

    -
    -
    Returns
    -

    singles – A list of edge uids.

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -size(edge)[source]
    -

    The number of nodes that belong to edge.

    -
    -
    Parameters
    -

    edge (hashable) – The uid of an edge in the hypergraph

    -
    -
    Returns
    -

    size

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -toplexes(name=None, collapse=False, use_reps=False, return_counts=True)[source]
    -

    Returns a simple hypergraph corresponding to self.

    -
    -

    Warning

    -

    Collapsing is no longer supported inside the toplexes method. Instead generate a new -collapsed hypergraph and compute the toplexes of the new hypergraph.

    -
    -
    -
    Parameters
    -
      -

    • name (str, optional, default: None) –

      • -

    • collapse (#) –

      • -

    • Should the hypergraph be collapsed? This would preserve a link between duplicate maximal sets. (#) –

      • -

    • If False then only one of these sets will be used and uniqueness will be up to sets of equal size. (#) –

      • -

    • use_reps (#) –

      • -

    • If collapse=True then each toplex will be named by a representative of the set of (#) –

      • -

    • equivalent edges (#) –

      • -

    • is False (see collapse_edges) (default) –

      • -

    • return_counts (boolean, optional, default: True) – # If collapse=True then each toplex will be named by a tuple of the representative -# of the set of equivalent edges and their count

      • -
    -
    -
    -
    - -
    -
    -translate(idx, edges=False)[source]
    -

    Returns the translation of numeric values associated with hypergraph. -Only needed if exposing the static identifiers assigned by the class. -If not static then the idx is returned.

    -
    -
    Parameters
    -
      -

    • idx (int) – class assigned integer for internal manipulation of Hypergraph data

      • -

    • edges (bool, optional, default: True) – If True then translates from edge index. Otherwise will translate from -node index, default=False

      • -
    -
    -
    Returns
    -

    User assigned identifier corresponding to idx

    -
    -
    Return type
    -

    int or string

    -
    -
    -
    - -
    - -
    -
    -

    classes.staticentity module

    -
    -
    -class classes.staticentity.StaticEntity(entity=None, data=None, arr=None, labels=None, uid=None, **props)[source]
    -

    Bases: object

    -
    -
    Parameters
    -
      -

    • entity (StaticEntity, StaticEntitySet, Entity, EntitySet, pandas.DataFrame, dict, or list of lists) – If a pandas.DataFrame, an error will be raised if there are nans.

      • -

    • data (array or array-like) – Two dimensional array of integers. Provides sparse tensor indices for incidence -tensor.

      • -

    • arr (numpy.ndarray or scip.sparse.matrix, optional, default=None) – Incidence tensor of data.

      • -

    • labels (OrderedDict of lists, optional, default=None) – User defined labels corresponding to integers in data.

      • -

    • uid (hashable, optional, default=None) –

      • -

    • props (user defined keyword arguments to be added to a properties dictionary, optional) –

      • -
    -
    -
    -
    -
    -properties
    -

    Description

    -
    -
    Type
    -

    dict

    -
    -
    -
    - -
    -
    -property arr
    -
    - -
    -
    -property children
    -

    Labels of keys of first index

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    set

    -
    -
    -
    - -
    -
    -property data
    -

    Data array or tensor array of Static Entity

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    np.ndarray

    -
    -
    -
    - -
    -
    -property dataframe
    -

    Returns the entity data in DataFrame format

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    pandas.core.frame.DataFrame

    -
    -
    -
    - -
    -
    -property dimensions
    -

    Dimension of Static Entity data

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    tuple

    -
    -
    -
    - -
    -
    -property dimsize
    -

    Number of categories in the data

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -property elements
    -

    Keys and values in the order of insertion

    -
    -
    Returns
    -

      -

    • collections.OrderedDict

      • -

    • level1 = elements, level2 = children

      • -
    -

    -
    -
    -
    - -
    -
    -elements_by_level(level1=0, level2=None, translate=False)[source]
    -

    Elements of staticentity by specified column

    -
    -
    Parameters
    -
      -

    • level1 (int, optional) – edges

      • -

    • level2 (int, optional) – nodes

      • -

    • translate (bool, optional) – whether to replace indices with labels

      • -
    -
    -
    Returns
    -

      -

    • collections.defaultdict

      • -

    • think (level1 = edges, level2 = nodes)

      • -
    -

    -
    -
    -
    - -
    -
    -property incidence_dict
    -

    Dictionary using index 0 as nodes and index 1 as edges

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    collections.OrderedDict

    -
    -
    -
    - -
    -
    -incidence_matrix(level1=0, level2=1, weighted=False, index=False)[source]
    -

    Convenience method to navigate large tensor

    -
    -
    Parameters
    -
      -

    • level1 (int, optional) – indexes columns

      • -

    • level2 (int, optional) – indexes rows

      • -

    • weighted (bool, optional) –

      • -

    • index (bool, optional) –

      • -
    -
    -
    Returns
    -

      -

    • scipy.sparse.csr.csr_matrix

      • -

    • think level1 = edges, level2 = nodes

      • -
    -

    -
    -
    -
    - -
    -
    -index(category, value=None)[source]
    -

    Returns dimension of category and index of value

    -
    -
    Parameters
    -
      -

    • category (string) –

      • -

    • value (string, optional) –

      • -
    -
    -
    Returns
    -

    -
    -
    Return type
    -

    int or tuple of ints

    -
    -
    -
    - -
    -
    -indices(category, values)[source]
    -

    Returns dimension of category and index of values (array)

    -
    -
    Parameters
    -
      -

    • category (string) –

      • -

    • values (single string or array of strings) –

      • -
    -
    -
    Returns
    -

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -is_empty(level=0)[source]
    -

    Boolean indicating if entity.elements is empty

    -
    -
    Parameters
    -

    level (int, optional) –

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    bool

    -
    -
    -
    - -
    -
    -property keyindex
    -

    Returns the index of a category in keys array

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -property keys
    -

    Array of keys of labels

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    np.ndarray

    -
    -
    -
    - -
    -
    -property labels
    -

    Ordered dictionary of labels

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    collections.OrderedDict

    -
    -
    -
    - -
    -
    -labs(kdx)[source]
    -

    Retrieve labels by index in keys

    -
    -
    Parameters
    -

    kdx (int) – index of key in E.keys

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    np.ndarray

    -
    -
    -
    - -
    -
    -level(item, min_level=0, max_level=None, return_index=True)[source]
    -

    Returns first level item appears by order of keys from minlevel to maxlevel -inclusive

    -
    -
    Parameters
    -
      -

    • item (string) –

      • -

    • min_level (int, optional) –

      • -

    • max_level (int, optional) –

      • -

    • return_index (bool, optional) –

      • -
    -
    -
    Returns
    -

    -
    -
    Return type
    -

    tuple

    -
    -
    -
    - -
    -
    -restrict_to_indices(indices, level=0, uid=None)[source]
    -

    Limit Static Entity data to specific indices of keys

    -
    -
    Parameters
    -
      -

    • indices (array) – array of category indices

      • -

    • level (int, optional) – index of label

      • -

    • uid (None, optional) –

      • -
    -
    -
    Returns
    -

    hnx.classes.staticentity.StaticEntity

    -
    -
    Return type
    -

    Static Entity class

    -
    -
    -
    - -
    -
    -restrict_to_levels(levels, uid=None)[source]
    -

    Limit Static Entity data to specific labels

    -
    -
    Parameters
    -
      -

    • levels (array) – index of labels in data

      • -

    • uid (None, optional) –

      • -
    -
    -
    Returns
    -

    hnx.classes.staticentity.StaticEntity

    -
    -
    Return type
    -

    Static Entity class

    -
    -
    -
    - -
    -
    -size()[source]
    -

    The number of elements in E, the size of dimension 0 in the E.arr

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    int

    -
    -
    -
    - -
    -
    -translate(level, index)[source]
    -

    Replaces a category index and value index with label

    -
    -
    Parameters
    -
      -

    • level (int) – category index of label

      • -

    • index (int) – value index of label

      • -
    -
    -
    Returns
    -

    -
    -
    Return type
    -

    numpy.array(str)

    -
    -
    -
    - -
    -
    -translate_arr(coords)[source]
    -

    Translates a single cell in the entity array

    -
    -
    Parameters
    -

    coords (tuple of ints) –

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -turn_entity_data_into_dataframe(data_subset)[source]
    -

    Convert rows of original data in StaticEntity to dataframe

    -
    -
    Parameters
    -

    data (numpy.ndarray) – Subset of the rows in the original data held in the StaticEntity

    -
    -
    Returns
    -

    Columns and cell entries are derived from data and self.labels

    -
    -
    Return type
    -

    pandas.core.frame.DataFrame

    -
    -
    -
    - -
    -
    -property uid
    -
    - -
    -
    -property uidset
    -

    Returns a set of the string identifiers for Static Entity

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    frozenset

    -
    -
    -
    - -
    -
    -uidset_by_level(level=0)[source]
    -

    The labels found in columns = level

    -
    -
    Parameters
    -

    level (int, optional) –

    -
    -
    Returns
    -

    -
    -
    Return type
    -

    frozenset

    -
    -
    -
    - -
    - -
    -
    -class classes.staticentity.StaticEntitySet(entity=None, data=None, arr=None, labels=None, uid=None, level1=0, level2=1, **props)[source]
    -

    Bases: classes.staticentity.StaticEntity

    -
    -
    -collapse_identical_elements(uid=None, return_equivalence_classes=False)[source]
    -

    Returns StaticEntitySet after collapsing elements if they have same children -If no elements share same children, a copy of the original StaticEntitySet is returned -:param uid: -:type uid: None, optional -:param return_equivalence_classes: If True, return a dictionary of equivalence classes keyed by new edge names -:type return_equivalence_classes: bool, optional

    -
    -
    Returns
    -

    hnx.classes.staticentity.StaticEntitySet

    -
    -
    Return type
    -

    StaticEntitySet

    -
    -
    -
    - -
    -
    -convert_to_entityset(uid)[source]
    -

    Convert given uid of Static EntitySet into EntitySet

    -
    -
    Parameters
    -

    uid (string) –

    -
    -
    Returns
    -

    hnx.classes.entity.EntitySet

    -
    -
    Return type
    -

    EntitySet

    -
    -
    -
    - -
    -
    -incidence_matrix(sparse=True, weighted=False, index=False)[source]
    -

    Incidence matrix of StaticEntitySet indexed by uidset

    -
    -
    Parameters
    -
      -

    • sparse (bool, optional) –

      • -

    • weighted (bool, optional) –

      • -

    • index (bool, optional) – give index of rows then columns

      • -
    -
    -
    Returns
    -

    scipy.sparse.csr.csr_matrix

    -
    -
    Return type
    -

    matrix

    -
    -
    -
    - -
    -
    -restrict_to(indices, uid=None)[source]
    -

    Limit Static Entityset data to specific indices of keys

    -
    -
    Parameters
    -
      -

    • indices (array) – array of indices in keys

      • -

    • uid (None, optional) –

      • -
    -
    -
    Returns
    -

    hnx.classes.staticentity.StaticEntitySet

    -
    -
    Return type
    -

    StaticEntitySet

    -
    -
    -
    - -
    - +
    +

    classes.staticentity module

    -
    -

    Module contents

    +
    +

    Module contents

    diff --git a/docs/build/classes/modules.html b/docs/build/classes/modules.html index 63cbb63b..77a1e982 100644 --- a/docs/build/classes/modules.html +++ b/docs/build/classes/modules.html @@ -7,7 +7,7 @@ - classes — HyperNetX 1.0.0 documentation + classes — HyperNetX 1.0.1 documentation @@ -189,10 +189,10 @@

    classesclasses package

    • diff --git a/docs/build/core.html b/docs/build/core.html index 67b1f3ef..59a72922 100644 --- a/docs/build/core.html +++ b/docs/build/core.html @@ -7,7 +7,7 @@ - HyperNetX Packages — HyperNetX 1.0.0 documentation + HyperNetX Packages — HyperNetX 1.0.1 documentation @@ -185,10 +185,10 @@
  • Hypergraphs @@ -196,18 +196,9 @@
  • Algorithms @@ -215,10 +206,10 @@
  • Drawing @@ -226,8 +217,8 @@
  • Reports diff --git a/docs/build/drawing/drawing.html b/docs/build/drawing/drawing.html index bdf61e6e..6b70eb59 100644 --- a/docs/build/drawing/drawing.html +++ b/docs/build/drawing/drawing.html @@ -7,7 +7,7 @@ - drawing package — HyperNetX 1.0.0 documentation + drawing package — HyperNetX 1.0.1 documentation @@ -106,10 +106,10 @@
  • Drawing @@ -197,434 +197,17 @@

    drawing package

    Submodules

    -
    -

    drawing.rubber_band module

    -
    -
    -drawing.rubber_band.draw(H, pos=None, with_color=True, with_node_counts=False, with_edge_counts=False, layout=<function fruchterman_reingold_layout>, layout_kwargs={}, ax=None, node_radius=None, edges_kwargs={}, nodes_kwargs={}, edge_labels={}, edge_labels_kwargs={}, node_labels={}, node_labels_kwargs={}, with_edge_labels=True, with_node_labels=True, label_alpha=0.35, return_pos=False)[source]
    -

    Draw a hypergraph as a Matplotlib figure

    -

    By default this will draw a colorful “rubber band” like hypergraph, where -convex hulls represent edges and are drawn around the nodes they contain.

    -

    This is a convenience function that wraps calls with sensible parameters to -the following lower-level drawing functions:

    -
      -

    • draw_hyper_edges,

      • -

    • draw_hyper_edge_labels,

      • -

    • draw_hyper_labels, and

      • -

    • draw_hyper_nodes

      • -
    -

    The default layout algorithm is nx.spring_layout, but other layouts can be -passed in. The Hypergraph is converted to a bipartite graph, and the layout -algorithm is passed the bipartite graph.

    -

    If you have a pre-determined layout, you can pass in a “pos” dictionary. -This is a dictionary mapping from node id’s to x-y coordinates. For example:

    -
    >>> pos = {
->>> 'A': (0, 0),
->>> 'B': (1, 2),
->>> 'C': (5, -3)
->>> }
-
    +
    +

    drawing.rubber_band module

    -

    will position the nodes {A, B, C} manually at the locations specified. The -coordinate system is in Matplotlib “data coordinates”, and the figure will -be centered within the figure.

    -

    By default, this will draw in a new figure, but the axis to render in can be -specified using ax.

    -

    This approach works well for small hypergraphs, and does not guarantee -a rigorously “correct” drawing. Overlapping of sets in the drawing generally -implies that the sets intersect, but sometimes sets overlap if there is no -intersection. It is not possible, in general, to draw a “correct” hypergraph -this way for an arbitrary hypergraph, in the same way that not all graphs -have planar drawings.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • pos (dict) – mapping of node and edge positions to R^2

      • -

    • with_color (bool) – set to False to disable color cycling of edges

      • -

    • with_node_counts (bool) – set to True to label collapsed nodes with number of elements

      • -

    • with_edge_counts (bool) – set to True to label collapsed edges with number of elements

      • -

    • layout (function) – layout algorithm to compute

      • -

    • layout_kwargs (dict) – keyword arguments passed to layout function

      • -

    • ax (Axis) – matplotlib axis on which the plot is rendered

      • -

    • edges_kwargs (dict) – keyword arguments passed to matplotlib.collections.PolyCollection for edges

      • -

    • node_radius (None, int, float, or dict) – radius of all nodes, or dictionary of node:value; the default (None) calculates radius based on number of collapsed nodes; reasonable values range between 1 and 3

      • -

    • nodes_kwargs (dict) – keyword arguments passed to matplotlib.collections.PolyCollection for nodes

      • -

    • edge_labels_kwargs (dict) – keyword arguments passed to matplotlib.annotate for edge labels

      • -

    • node_labels_kwargs (dict) – keyword argumetns passed to matplotlib.annotate for node labels

      • -

    • with_edge_labels (bool) – set to False to make edge labels invisible

      • -

    • with_node_labels (bool) – set to False to make node labels invisible

      • -

    • label_alpha (float) – the transparency (alpha) of the box behind text drawn in the figure

      • -
    -
    -
    -
    - -
    -
    -drawing.rubber_band.draw_hyper_edge_labels(H, polys, labels={}, ax=None, **kwargs)[source]
    -

    Draws a label on the hyper edge boundary.

    -

    Should be passed Matplotlib PolyCollection representing the hyper-edges, see -the return value of draw_hyper_edges.

    -

    The label will be draw on the least curvy part of the polygon, and will be -aligned parallel to the orientation of the polygon where it is drawn.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • polys (PolyCollection) – collection of polygons returned by draw_hyper_edges

      • -

    • labels (dict) – mapping of node id to string label

      • -

    • ax (Axis) – matplotlib axis on which the plot is rendered

      • -

    • kwargs (dict) – Keyword arguments are passed through to Matplotlib’s annotate function.

      • -
    -
    -
    -
    - -
    -
    -drawing.rubber_band.draw_hyper_edges(H, pos, ax=None, node_radius={}, dr=None, **kwargs)[source]
    -

    Draws a convex hull around the nodes contained within each edge in H

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • pos (dict) – mapping of node and edge positions to R^2

      • -

    • node_radius (dict) – mapping of node to R^1 (radius of each node)

      • -

    • dr (float) – the spacing between concentric rings

      • -

    • ax (Axis) – matplotlib axis on which the plot is rendered

      • -

    • kwargs (dict) – keyword arguments, e.g., linewidth, facecolors, are passed through to the PolyCollection constructor

      • -
    -
    -
    Returns
    -

    a Matplotlib PolyCollection that can be further styled

    -
    -
    Return type
    -

    PolyCollection

    -
    -
    -
    - -
    -
    -drawing.rubber_band.draw_hyper_labels(H, pos, node_radius={}, ax=None, labels={}, **kwargs)[source]
    -

    Draws text labels for the hypergraph nodes.

    -

    The label is drawn to the right of the node. The node radius is needed (see -draw_hyper_nodes) so the text can be offset appropriately as the node size -changes.

    -

    The text label can be customized by passing in a dictionary, labels, mapping -a node to its custom label. By default, the label is the string -representation of the node.

    -

    Keyword arguments are passed through to Matplotlib’s annotate function.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • pos (dict) – mapping of node and edge positions to R^2

      • -

    • node_radius (dict) – mapping of node to R^1 (radius of each node)

      • -

    • ax (Axis) – matplotlib axis on which the plot is rendered

      • -

    • labels (dict) – mapping of node to text label

      • -

    • kwargs (dict) – keyword arguments passed to matplotlib.annotate

      • -
    -
    -
    -
    - -
    -
    -drawing.rubber_band.draw_hyper_nodes(H, pos, node_radius={}, r0=None, ax=None, **kwargs)[source]
    -

    Draws a circle for each node in H.

    -

    The position of each node is specified by the a dictionary/list-like, pos, -where pos[v] is the xy-coordinate for the vertex. The radius of each node -can be specified as a dictionary where node_radius[v] is the radius. If a -node is missing from this dictionary, or the node_radius is not specified at -all, a sensible default radius is chosen based on distances between nodes -given by pos.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • pos (dict) – mapping of node and edge positions to R^2

      • -

    • node_radius (dict) – mapping of node to R^1 (radius of each node)

      • -

    • r0 (float) – minimum distance that concentric rings start from the node position

      • -

    • ax (Axis) – matplotlib axis on which the plot is rendered

      • -

    • kwargs (dict) – keyword arguments, e.g., linewidth, facecolors, are passed through to the PolyCollection constructor

      • -
    -
    -
    Returns
    -

    a Matplotlib PolyCollection that can be further styled

    -
    -
    Return type
    -

    PolyCollection

    -
    -
    -
    - -
    -
    -drawing.rubber_band.get_default_radius(H, pos)[source]
    -

    Calculate a reasonable default node radius

    -

    This function iterates over the hyper edges and finds the most distant -pair of points given the positions provided. Then, the node radius is a fraction -of the median of this distance take across all hyper-edges.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • pos (dict) – mapping of node and edge positions to R^2

      • -
    -
    -
    Returns
    -

    the recommended radius

    -
    -
    Return type
    -

    float

    -
    -
    -
    - -
    -
    -drawing.rubber_band.layout_hyper_edges(H, pos, node_radius={}, dr=None)[source]
    -

    Draws a convex hull for each edge in H.

    -

    Position of the nodes in the graph is specified by the position dictionary, -pos. Convex hulls are spaced out such that if one set contains another, the -convex hull will surround the contained set. The amount of spacing added -between hulls is specified by the parameter, dr.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • pos (dict) – mapping of node and edge positions to R^2

      • -

    • node_radius (dict) – mapping of node to R^1 (radius of each node)

      • -

    • dr (float) – the spacing between concentric rings

      • -

    • ax (Axis) – matplotlib axis on which the plot is rendered

      • -
    -
    -
    Returns
    -

    A mapping from hyper edge ids to paths (Nx2 numpy matrices)

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    - -

    Helper function to use a NetwrokX-like graph layout algorithm on a Hypergraph

    -

    The hypergraph is converted to a bipartite graph, allowing the usual graph layout -techniques to be applied.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • layout (function) – the layout algorithm which accepts a NetworkX graph and keyword arguments

      • -

    • kwargs (dict) – Keyword arguments are passed through to the layout algorithm

      • -
    -
    -
    Returns
    -

    mapping of node and edge positions to R^2

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - +
    +

    drawing.two_column module

    -
    -

    drawing.two_column module

    -
    -
    -drawing.two_column.draw(H, with_node_labels=True, with_edge_labels=True, with_node_counts=False, with_edge_counts=False, with_color=True, edge_kwargs=None, ax=None)[source]
    -

    Draw a hypergraph using a two-collumn layout.

    -

    This is intended reproduce an illustrative technique for bipartite graphs -and hypergraphs that is typically used in papers and textbooks.

    -

    The left column is reserved for nodes and the right column is reserved for -edges. A line is drawn between a node an an edge

    -

    The order of nodes and edges is optimized to reduce line crossings between -the two columns. Spacing between disconnected components is adjusted to make -the diagram easier to read, by reducing the angle of the lines.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • with_node_labels (bool) – False to disable node labels

      • -

    • with_edge_labels (bool) – False to disable edge labels

      • -

    • with_node_counts (bool) – set to True to label collapsed nodes with number of elements

      • -

    • with_edge_counts (bool) – set to True to label collapsed edges with number of elements

      • -

    • with_color (bool) – set to False to disable color cycling of hyper edges

      • -

    • edge_kwargs (dict) – keyword arguments to pass to matplotlib.LineCollection

      • -

    • ax (Axis) – matplotlib axis on which the plot is rendered

      • -
    -
    -
    -
    - -
    -
    -drawing.two_column.draw_hyper_edges(H, pos, ax=None, **kwargs)[source]
    -

    Renders hyper edges for the two column layout.

    -

    Each node-hyper edge membership is rendered as a line connecting the node -in the left column to the edge in the right column.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • pos (dict) – mapping of node and edge positions to R^2

      • -

    • ax (Axis) – matplotlib axis on which the plot is rendered

      • -

    • kwargs (dict) – keyword arguments passed to matplotlib.LineCollection

      • -
    -
    -
    Returns
    -

    the hyper edges

    -
    -
    Return type
    -

    LineCollection

    -
    -
    -
    - -
    -
    -drawing.two_column.draw_hyper_labels(H, pos, labels={}, with_node_labels=True, with_edge_labels=True, ax=None)[source]
    -

    Renders hyper labels (nodes and edges) for the two column layout.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • pos (dict) – mapping of node and edge positions to R^2

      • -

    • labels (dict) – custom labels for nodes and edges can be supplied

      • -

    • with_node_labels (bool) – False to disable node labels

      • -

    • with_edge_labels (bool) – False to disable edge labels

      • -

    • ax (Axis) – matplotlib axis on which the plot is rendered

      • -

    • kwargs (dict) – keyword arguments passed to matplotlib.LineCollection

      • -
    -
    -
    -
    - -
    -
    -drawing.two_column.layout_two_column(H, spacing=2)[source]
    -

    Two column (bipartite) layout algorithm.

    -

    This algorithm first converts the hypergraph into a bipartite graph and -then computes connected components. Disonneccted components are handled -independently and then stacked together.

    -

    Within a connected component, the spectral ordering of the bipartite graph -provides a quick and dirty ordering that minimizes edge crossings in the -diagram.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • spacing (float) – amount of whitespace between disconnected components

      • -
    -
    -
    -
    - -
    -
    -

    drawing.util module

    -
    -
    -drawing.util.get_frozenset_label(S, count=False, override={})[source]
    -

    Helper function for rendering the labels of possibly collapsed nodes and edges

    -
    -
    Parameters
    -
      -

    • S (iterable) – list of entities to be labeled

      • -

    • count (bool) – True if labels should be counts of entities instead of list

      • -
    -
    -
    Returns
    -

    mapping of entity to its string representation

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -drawing.util.get_line_graph(H, collapse=True)[source]
    -

    Computes the line graph, a directed graph, where a directed edge (u, v) -exists if the edge u is a subset of the edge v in the hypergraph.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • collapse (bool) – True if edges should be added if hyper edges are identical

      • -
    -
    -
    Returns
    -

    A directed graph

    -
    -
    Return type
    -

    networkx.DiGraph

    -
    -
    -
    - -
    -
    -drawing.util.get_set_layering(H, collapse=True)[source]
    -

    Computes a layering of the edges in the hyper graph.

    -

    In this layering, each edge is assigned a level. An edge u will be above -(e.g., have a smaller level value) another edge v if v is a subset of u.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) – the entity to be drawn

      • -

    • collapse (bool) – True if edges should be added if hyper edges are identical

      • -
    -
    -
    Returns
    -

    a mapping of vertices in H to integer levels

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -drawing.util.inflate(items, v)[source]
    -
    - -
    -
    -drawing.util.inflate_kwargs(items, kwargs)[source]
    -

    Helper function to expand keyword arguments.

    -
    -
    Parameters
    -
      -

    • n (int) – length of resulting list if argument is expanded

      • -

    • kwargs (dict) – keyword arguments to be expanded

      • -
    -
    -
    Returns
    -

    dictionary with same keys as kwargs and whose values are lists of length n

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -drawing.util.transpose_inflated_kwargs(inflated)[source]
    -
    - +
    +

    drawing.util module

    -
    -

    Module contents

    +
    +

    Module contents

    diff --git a/docs/build/drawing/modules.html b/docs/build/drawing/modules.html index 6e693e5b..68658da8 100644 --- a/docs/build/drawing/modules.html +++ b/docs/build/drawing/modules.html @@ -7,7 +7,7 @@ - drawing — HyperNetX 1.0.0 documentation + drawing — HyperNetX 1.0.1 documentation @@ -189,10 +189,10 @@

    drawingdrawing package

    • diff --git a/docs/build/genindex.html b/docs/build/genindex.html index ebd20a43..1986b9ff 100644 --- a/docs/build/genindex.html +++ b/docs/build/genindex.html @@ -7,7 +7,7 @@ - Index — HyperNetX 1.0.0 documentation + Index — HyperNetX 1.0.1 documentation @@ -172,180 +172,19 @@

    Index

    - A - | B - | C + B | D | E - | F - | G | H | I - | K - | L - | M - | N - | O - | P - | R | S | T - | U
    -

    A

    - - - -
    -

    B

    - -
    - -

    C

    - - -
    @@ -353,87 +192,11 @@

    C

    D

    @@ -441,46 +204,16 @@

    D

    E

    - + -
    - -

    F

    - - - -
    - -

    G

    - - -
    @@ -535,15 +228,7 @@

    G

    H

    -
    @@ -552,245 +237,6 @@

    I

    - -
    - -

    K

    - - - -
    - -

    L

    - - - -
    - -

    M

    - - -
    - -

    N

    - - - -
    - -

    O

    - - -
    - -

    P

    - - -
    - -

    R

    - - -
    @@ -814,6 +260,8 @@

    S

  • s-edge
    • + + - @@ -891,46 +287,6 @@

    T

    - -
    - -

    U

    - - -
    diff --git a/docs/build/glossary.html b/docs/build/glossary.html index 8e761813..002f174a 100644 --- a/docs/build/glossary.html +++ b/docs/build/glossary.html @@ -7,7 +7,7 @@ - Glossary of HNX terms — HyperNetX 1.0.0 documentation + Glossary of HNX terms — HyperNetX 1.0.1 documentation @@ -180,7 +180,7 @@ elements and children of an EntitySet generate a specific partition for a bipartite graph. partition is isomorphic to a Hypergraph where the elements correspond to hyperedges and children correspond to the nodes. EntitySets are the basic objects used to construct dynamic hypergraphs -NX. See methods classes.hypergraph.Hypergraph.bipartite() and classes.hypergraph.Hypergraph.from_bipartite().

    +NX. See methods classes.hypergraph.Hypergraph.bipartite() and classes.hypergraph.Hypergraph.from_bipartite().

    degree

    Given a hypergraph (Nodes,Edges), the degree of a node in Nodes is the number of edges in Edges to which the node belongs. See also: s-degree

    diff --git a/docs/build/home.html b/docs/build/home.html index 54efa90f..4417d511 100644 --- a/docs/build/home.html +++ b/docs/build/home.html @@ -7,7 +7,7 @@ - HyperNetX (HNX) — HyperNetX 1.0.0 documentation + HyperNetX (HNX) — HyperNetX 1.0.1 documentation diff --git a/docs/build/index.html b/docs/build/index.html index 8f1e5140..c2f68ceb 100644 --- a/docs/build/index.html +++ b/docs/build/index.html @@ -7,7 +7,7 @@ - HyperNetX (HNX) — HyperNetX 1.0.0 documentation + HyperNetX (HNX) — HyperNetX 1.0.1 documentation diff --git a/docs/build/install.html b/docs/build/install.html index 2298e562..5db68008 100644 --- a/docs/build/install.html +++ b/docs/build/install.html @@ -7,7 +7,7 @@ - Installing HyperNetX — HyperNetX 1.0.0 documentation + Installing HyperNetX — HyperNetX 1.0.1 documentation diff --git a/docs/build/license.html b/docs/build/license.html index 17945953..5a6e5945 100644 --- a/docs/build/license.html +++ b/docs/build/license.html @@ -7,7 +7,7 @@ - License — HyperNetX 1.0.0 documentation + License — HyperNetX 1.0.1 documentation diff --git a/docs/build/nwhy.html b/docs/build/nwhy.html index a23e0b53..f0df4dac 100644 --- a/docs/build/nwhy.html +++ b/docs/build/nwhy.html @@ -7,7 +7,7 @@ - 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    - a
    - algorithms -
        - algorithms.homology_mod2 -
        - algorithms.s_centrality_measures -
     
    - c
    - classes -
        - classes.entity -
        - classes.hypergraph -
        - classes.staticentity -
     
    - d
    - drawing -
        - drawing.rubber_band -
        - drawing.two_column -
        - drawing.util -
     
    - r
    - reports -
        - reports.descriptive_stats -
    - - -
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    - © Copyright 2018 Battelle Memorial Institute. - -

    -
    - - - - Built with Sphinx using a - - theme - - provided by Read the Docs. - -
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    - - - - - - - - - - - \ No newline at end of file diff --git a/docs/build/reports/modules.html b/docs/build/reports/modules.html index 39710e6d..7ff9b3c5 100644 --- a/docs/build/reports/modules.html +++ b/docs/build/reports/modules.html @@ -7,7 +7,7 @@ - reports — HyperNetX 1.0.0 documentation + reports — HyperNetX 1.0.1 documentation @@ -189,8 +189,8 @@

    reportsreports package diff --git a/docs/build/reports/reports.html b/docs/build/reports/reports.html index ce30a973..edb5cc4b 100644 --- a/docs/build/reports/reports.html +++ b/docs/build/reports/reports.html @@ -7,7 +7,7 @@ - reports package — HyperNetX 1.0.0 documentation + reports package — HyperNetX 1.0.1 documentation @@ -107,8 +107,8 @@
  • Reports @@ -195,282 +195,11 @@

    reports package

    Submodules

    -
    -

    reports.descriptive_stats module

    -
    -
    This module contains methods which compute various distributions for hypergraphs:
      -

    • Edge size distribution

      • -

    • Node degree distribution

      • -

    • Component size distribution

      • -

    • Toplex size distribution

      • -

    • Diameter

      • -
    -
    -
    -

    Also computes general hypergraph information: number of nodes, edges, cells, aspect ratio, incidence matrix density

    -
    -
    -reports.descriptive_stats.centrality_stats(X)[source]
    -

    Computes basic centrality statistics for X

    -
    -
    Parameters
    -

    X – an iterable of numbers

    -
    -
    Returns
    -

    [min, max, mean, median, standard deviation] – List of centrality statistics for X

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -reports.descriptive_stats.comp_dist(H, aggregated=False)[source]
    -

    Computes component sizes, number of nodes.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) –

      • -

    • aggregated – If aggregated is True, returns a dictionary of -component sizes (number of nodes) and counts. If aggregated -is False, returns a list of components sizes in H.

      • -
    -
    -
    Returns
    -

    comp_dist – List of component sizes or dictionary of component size distribution

    -
    -
    Return type
    -

    list or dictionary

    -
    -
    -
    -

    See also

    -

    s_comp_dist

    -
    -
    - -
    -
    -reports.descriptive_stats.degree_dist(H, aggregated=False)[source]
    -

    Computes degrees of nodes of a hypergraph.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) –

      • -

    • aggregated – If aggregated is True, returns a dictionary of -degrees and counts. If aggregated is False, returns a -list of degrees in H.

      • -
    -
    -
    Returns
    -

    degree_dist – List of degrees or dictionary of degree distribution

    -
    -
    Return type
    -

    list or dict

    -
    -
    -
    - -
    -
    -reports.descriptive_stats.dist_stats(H)[source]
    -

    Computes many basic hypergraph stats and puts them all into a single dictionary object

    -
    -
      -

    • nrows = number of nodes (rows in the incidence matrix)

      • -

    • ncols = number of edges (columns in the incidence matrix)

      • -

    • aspect ratio = nrows/ncols

      • -

    • ncells = number of filled cells in incidence matrix

      • -

    • density = ncells/(nrows*ncols)

      • -

    • node degree list = degree_dist(H)

      • -

    • node degree dist = centrality_stats(degree_dist(H))

      • -

    • node degree hist = Counter(degree_dist(H))

      • -

    • max node degree = max(degree_dist(H))

      • -

    • edge size list = edge_size_dist(H)

      • -

    • edge size dist = centrality_stats(edge_size_dist(H))

      • -

    • edge size hist = Counter(edge_size_dist(H))

      • -

    • max edge size = max(edge_size_dist(H))

      • -

    • comp nodes list = s_comp_dist(H, s=1, edges=False)

      • -

    • comp nodes dist = centrality_stats(s_comp_dist(H, s=1, edges=False))

      • -

    • comp nodes hist = Counter(s_comp_dist(H, s=1, edges=False))

      • -

    • comp edges list = s_comp_dist(H, s=1, edges=True)

      • -

    • comp edges dist = centrality_stats(s_comp_dist(H, s=1, edges=True))

      • -

    • comp edges hist = Counter(s_comp_dist(H, s=1, edges=True))

      • -

    • num comps = len(s_comp_dist(H))

      • -
    -
    -
    -
    Parameters
    -

    H (Hypergraph) –

    -
    -
    Returns
    -

    dist_stats – Dictionary which keeps track of each of the above items (e.g., basic[‘nrows’] = the number of nodes in H)

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -reports.descriptive_stats.edge_size_dist(H, aggregated=False)[source]
    -

    Computes edge sizes of a hypergraph.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) –

      • -

    • aggregated – If aggregated is True, returns a dictionary of -edge sizes and counts. If aggregated is False, returns a -list of edge sizes in H.

      • -
    -
    -
    Returns
    -

    edge_size_dist – List of edge sizes or dictionary of edge size distribution.

    -
    -
    Return type
    -

    list or dict

    -
    -
    -
    - -
    -
    -reports.descriptive_stats.info(H, node=None, edge=None)[source]
    -

    Print a summary of simple statistics for H

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) –

      • -

    • obj (optional) – either a node or edge uid from the hypergraph

      • -

    • dictionary (optional) – If True then returns the info as a dictionary rather -than a string -If False (default) returns the info as a string

      • -
    -
    -
    Returns
    -

    info – Returns a string of statistics of the size, -aspect ratio, and density of the hypergraph. -Print the string to see it formatted.

    -
    -
    Return type
    -

    string

    -
    -
    -
    - -
    -
    -reports.descriptive_stats.info_dict(H, node=None, edge=None)[source]
    -

    Create a summary of simple statistics for H

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) –

      • -

    • obj (optional) – either a node or edge uid from the hypergraph

      • -
    -
    -
    Returns
    -

    info_dict – Returns a dictionary of statistics of the size, -aspect ratio, and density of the hypergraph.

    -
    -
    Return type
    -

    dict

    -
    -
    -
    - -
    -
    -reports.descriptive_stats.s_comp_dist(H, s=1, aggregated=False, edges=True, return_singletons=True)[source]
    -

    Computes s-component sizes, counting nodes or edges.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) –

      • -

    • s (positive integer, default is 1) –

      • -

    • aggregated – If aggregated is True, returns a dictionary of -s-component sizes and counts in H. If aggregated is -False, returns a list of s-component sizes in H.

      • -

    • edges – If edges is True, the component size is number of edges. -If edges is False, the component size is number of nodes.

      • -

    • return_singletons (bool, optional, default=True) –

      • -
    -
    -
    Returns
    -

    s_comp_dist – List of component sizes or dictionary of component size distribution in H

    -
    -
    Return type
    -

    list or dictionary

    -
    -
    -
    -

    See also

    -

    comp_dist

    -
    -
    - -
    -
    -reports.descriptive_stats.s_edge_diameter_dist(H)[source]
    -
    -
    Parameters
    -

    H (Hypergraph) –

    -
    -
    Returns
    -

    s_edge_diameter_dist – List of s-edge-diameters for hypergraph H starting with s=1 -and going up as long as the hypergraph is s-edge-connected

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -reports.descriptive_stats.s_node_diameter_dist(H)[source]
    -
    -
    Parameters
    -

    H (Hypergraph) –

    -
    -
    Returns
    -

    s_node_diameter_dist – List of s-node-diameters for hypergraph H starting with s=1 -and going up as long as the hypergraph is s-node-connected

    -
    -
    Return type
    -

    list

    -
    -
    -
    - -
    -
    -reports.descriptive_stats.toplex_dist(H, aggregated=False)[source]
    -

    Computes toplex sizes for hypergraph H.

    -
    -
    Parameters
    -
      -

    • H (Hypergraph) –

      • -

    • aggregated – If aggregated is True, returns a dictionary of -toplex sizes and counts in H. If aggregated -is False, returns a list of toplex sizes in H.

      • -
    -
    -
    Returns
    -

    toplex_dist – List of toplex sizes or dictionary of toplex size distribution in H

    -
    -
    Return type
    -

    list or dictionary

    -
    -
    -
    - +
    +

    reports.descriptive_stats module

    -
    -

    Module contents

    +
    +

    Module contents

    diff --git a/docs/build/search.html b/docs/build/search.html index eaeb5f89..7243c541 100644 --- a/docs/build/search.html +++ b/docs/build/search.html @@ -7,7 +7,7 @@ - Search — HyperNetX 1.0.0 documentation + Search — HyperNetX 1.0.1 documentation diff --git a/docs/build/searchindex.js b/docs/build/searchindex.js index 61908666..7f405576 100644 --- a/docs/build/searchindex.js +++ b/docs/build/searchindex.js @@ -1 +1 @@ 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a/docs/build/widget.html +++ b/docs/build/widget.html @@ -7,7 +7,7 @@ - Hypernetx-Widget — HyperNetX 1.0.0 documentation + Hypernetx-Widget — HyperNetX 1.0.1 documentation diff --git a/docs/source/conf.py b/docs/source/conf.py index e2f7b209..76582fce 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -19,7 +19,7 @@ import os import shlex -__version__ = "1.0.0" +__version__ = "1.0.1" # If extensions (or modules to document with autodoc) are in another directory, diff --git a/setup.py b/setup.py index cec73023..87c61475 100644 --- a/setup.py +++ b/setup.py @@ -1,7 +1,7 @@ from setuptools import setup import sys -__version__ = "1.0" +__version__ = "1.0.1" if sys.version_info < (3, 7): sys.exit("HyperNetX requires Python 3.7 or later.")