From 7956b10e546fe49147191a95df6c6f08dbe939a4 Mon Sep 17 00:00:00 2001
From: michielstock <michielfmstock@gmail.com>
Date: Fri, 5 Apr 2019 17:53:23 +0200
Subject: [PATCH 1/7] :tada: basics methods for network resilience

---
 src/community/resilience.jl | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)
 create mode 100644 src/community/resilience.jl

diff --git a/src/community/resilience.jl b/src/community/resilience.jl
new file mode 100644
index 000000000..24dd98c99
--- /dev/null
+++ b/src/community/resilience.jl
@@ -0,0 +1,21 @@
+#=
+Some functions from *Universal resilience patterns in complex networks*
+by Gao et al. (2016)
+=#
+
+using Statistics: mean, std
+
+# TODO : AbstractUnipartiteNetwork as type
+
+s_in(N::UnipartiteNetwork) = mean(N.A, dims=2)
+s_out(N::UnipartiteNetwork) = mean(N.A, dims=1)'
+s_mean(N::UnipartiteNetwork) = mean(N.A)
+
+σ_in(N::UnipartiteNetwork) = std(s_in(N))
+σ_out(N::UnipartiteNetwork) = std(s_out(N))
+
+symmetry(N::UnipartiteNetwork) = (mean(s_in(N) .* s_in(N)) - mean(s_in(N)) * mean(s_out(N))) / (σ_in(N)*σ_out(N))
+heterogenity(N::UnipartiteNetwork) = σ_in(N) * σ_out(N) / s_mean(N)
+
+βeff(N::UnipartiteNetwork) = mean(s_in(N) .* s_out(N)) / s_mean(N)
+resilience(N) = βeff(N)

From f296e9414f0bf851afb53dc49cdf3ce526ab4ea0 Mon Sep 17 00:00:00 2001
From: michielstock <michielfmstock@gmail.com>
Date: Wed, 10 Apr 2019 14:16:56 +0200
Subject: [PATCH 2/7] :construction: development of resilience indices.

---
 src/community/resilience.jl | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/src/community/resilience.jl b/src/community/resilience.jl
index 24dd98c99..ebff12c72 100644
--- a/src/community/resilience.jl
+++ b/src/community/resilience.jl
@@ -14,8 +14,12 @@ s_mean(N::UnipartiteNetwork) = mean(N.A)
 σ_in(N::UnipartiteNetwork) = std(s_in(N))
 σ_out(N::UnipartiteNetwork) = std(s_out(N))
 
-symmetry(N::UnipartiteNetwork) = (mean(s_in(N) .* s_in(N)) - mean(s_in(N)) * mean(s_out(N))) / (σ_in(N)*σ_out(N))
-heterogenity(N::UnipartiteNetwork) = σ_in(N) * σ_out(N) / s_mean(N)
+# symmetry computed wrongly in paper?
+symmetry(N::UnipartiteNetwork) = -(mean(s_in(N) .* s_in(N)) - mean(s_in(N)) * mean(s_out(N))) / (σ_in(N) * σ_out(N))
+heterogenity(N::UnipartiteNetwork) = (σ_in(N) * σ_out(N)) / s_mean(N)
 
 βeff(N::UnipartiteNetwork) = mean(s_in(N) .* s_out(N)) / s_mean(N)
 resilience(N) = βeff(N)
+
+# check if  βeff = sum(A *s_in) / sum(A)
+# and βeff = <s> + HS

From 93800649d25e3a04827a096a4ce632173d28ebcf Mon Sep 17 00:00:00 2001
From: michielstock <michielfmstock@gmail.com>
Date: Wed, 1 May 2019 18:41:58 +0200
Subject: [PATCH 3/7] :wrench: finishing resilience code + UT

---
 Manifest.toml               | 14 +++++++-------
 Project.toml                |  1 +
 src/EcologicalNetworks.jl   |  7 +++++++
 src/community/resilience.jl | 22 ++++++++++------------
 test/runtests.jl            |  1 +
 5 files changed, 26 insertions(+), 19 deletions(-)

diff --git a/Manifest.toml b/Manifest.toml
index 98ba49a7a..380b90763 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -16,10 +16,10 @@ uuid = "9e28174c-4ba2-5203-b857-d8d62c4213ee"
 version = "0.8.10"
 
 [[BinaryProvider]]
-deps = ["Libdl", "Pkg", "SHA", "Test"]
-git-tree-sha1 = "055eb2690182ebc31087859c3dd8598371d3ef9e"
+deps = ["Libdl", "SHA"]
+git-tree-sha1 = "c7361ce8a2129f20b0e05a89f7070820cfed6648"
 uuid = "b99e7846-7c00-51b0-8f62-c81ae34c0232"
-version = "0.5.3"
+version = "0.5.4"
 
 [[Combinatorics]]
 deps = ["LinearAlgebra", "Polynomials", "Test"]
@@ -89,15 +89,15 @@ uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
 [[OrderedCollections]]
 deps = ["Random", "Serialization", "Test"]
-git-tree-sha1 = "85619a3f3e17bb4761fe1b1fd47f0e979f964d5b"
+git-tree-sha1 = "c4c13474d23c60d20a67b217f1d7f22a40edf8f1"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
-version = "1.0.2"
+version = "1.1.0"
 
 [[PDMats]]
 deps = ["Arpack", "LinearAlgebra", "SparseArrays", "SuiteSparse", "Test"]
-git-tree-sha1 = "b6c91fc0ab970c0563cbbe69af18d741a49ce551"
+git-tree-sha1 = "8b68513175b2dc4023a564cb0e917ce90e74fd69"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.9.6"
+version = "0.9.7"
 
 [[Pkg]]
 deps = ["Dates", "LibGit2", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
diff --git a/Project.toml b/Project.toml
index 2f4a480af..cfe4c6eb6 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,6 +11,7 @@ Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/src/EcologicalNetworks.jl b/src/EcologicalNetworks.jl
index 3442b5a54..6683a9751 100644
--- a/src/EcologicalNetworks.jl
+++ b/src/EcologicalNetworks.jl
@@ -102,6 +102,13 @@ include(joinpath(".", "community/overlap.jl"))
 export overlap
 export AJS, EAJS
 
+# Overlap
+include(joinpath(".", "community/resilience.jl"))
+export βeff, resilience
+export symmetry, heterogenity
+export s_in, s_out, s_mean
+export σ_in, σ_out
+
 # Modularity
 include(joinpath(".", "modularity/utilities.jl"))
 export Q, Qr
diff --git a/src/community/resilience.jl b/src/community/resilience.jl
index ebff12c72..63034aeaa 100644
--- a/src/community/resilience.jl
+++ b/src/community/resilience.jl
@@ -3,23 +3,21 @@ Some functions from *Universal resilience patterns in complex networks*
 by Gao et al. (2016)
 =#
 
-using Statistics: mean, std
+using StatsBase: mean, std
 
-# TODO : AbstractUnipartiteNetwork as type
+s_in(N::AbstractUnipartiteNetwork) = sum(N.A, dims=2)
+s_out(N::AbstractUnipartiteNetwork) = sum(N.A, dims=1)'
+s_mean(N::AbstractUnipartiteNetwork) = sum(N.A) / size(N.A, 1)
 
-s_in(N::UnipartiteNetwork) = mean(N.A, dims=2)
-s_out(N::UnipartiteNetwork) = mean(N.A, dims=1)'
-s_mean(N::UnipartiteNetwork) = mean(N.A)
-
-σ_in(N::UnipartiteNetwork) = std(s_in(N))
-σ_out(N::UnipartiteNetwork) = std(s_out(N))
+σ_in(N::AbstractUnipartiteNetwork) = std(s_in(N), corrected=false)
+σ_out(N::AbstractUnipartiteNetwork) = std(s_out(N), corrected=false)
 
 # symmetry computed wrongly in paper?
-symmetry(N::UnipartiteNetwork) = -(mean(s_in(N) .* s_in(N)) - mean(s_in(N)) * mean(s_out(N))) / (σ_in(N) * σ_out(N))
-heterogenity(N::UnipartiteNetwork) = (σ_in(N) * σ_out(N)) / s_mean(N)
+symmetry(N::AbstractUnipartiteNetwork) = (mean(s_in(N) .* s_out(N)) - mean(s_in(N)) * mean(s_out(N))) / (σ_in(N) * σ_out(N))
+heterogenity(N::AbstractUnipartiteNetwork) = (σ_in(N) * σ_out(N)) / s_mean(N)
 
-βeff(N::UnipartiteNetwork) = mean(s_in(N) .* s_out(N)) / s_mean(N)
-resilience(N) = βeff(N)
+βeff(N::AbstractUnipartiteNetwork) = dot(s_in(N), s_out(N)) / sum(N.A)
+resilience(N::AbstractUnipartiteNetwork) = βeff(N)
 
 # check if  βeff = sum(A *s_in) / sum(A)
 # and βeff = <s> + HS
diff --git a/test/runtests.jl b/test/runtests.jl
index f40afcfd2..55922882d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -25,6 +25,7 @@ my_tests = [
    "community/centrality.jl",
    "community/motifs.jl",
    "community/foodwebs.jl",
+   "community/resilience.jl",
    "betadiversity/operations.jl",
    "betadiversity/partitions.jl",
    "modularity/utilities.jl",

From 9fabffaa1fe17e3a75d9f4394d4ffff25b0bdf5d Mon Sep 17 00:00:00 2001
From: michielstock <michielfmstock@gmail.com>
Date: Mon, 6 May 2019 18:19:08 +0200
Subject: [PATCH 4/7] :pencil2: documentation

---
 docs/make.jl                      |  3 +-
 docs/src/properties/resilience.md | 53 ++++++++++++++++++++
 src/community/resilience.jl       | 80 +++++++++++++++++++++++++++++--
 test/community/resilience.jl      | 42 ++++++++++++++++
 4 files changed, 173 insertions(+), 5 deletions(-)
 create mode 100644 docs/src/properties/resilience.md
 create mode 100644 test/community/resilience.jl

diff --git a/docs/make.jl b/docs/make.jl
index e9002ddf8..4c12ed509 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -26,7 +26,8 @@ makedocs(
             "Centrality and paths" => "properties/paths.md",
             "Overlap and similarity" => "properties/overlap.md",
             "Null models" => "properties/nullmodels.md",
-            "Beta-diversity" => "properties/betadiversity.md"
+            "Beta-diversity" => "properties/betadiversity.md",
+            "Resilience" => "properties/resilience.md"
         ]
     ]
 )
diff --git a/docs/src/properties/resilience.md b/docs/src/properties/resilience.md
new file mode 100644
index 000000000..3e032839c
--- /dev/null
+++ b/docs/src/properties/resilience.md
@@ -0,0 +1,53 @@
+# Resilience
+
+Species interaction networks provide the interactions of the individual species.
+We provide the metrics proposed by Gao et al (2016) that summarize the global
+behaviour of complex unipartite networks. The dynamics of a system of N components
+(nodes/species) can follow the coupled nonlinear differential equation
+
+$$
+\frac{\text{d}x_i}{\text{d}t} = F(x_i) + \sum_{j=1}^N A_{ij}G(x_i, x_j)
+$$
+
+where the adjacency matrix $$A$$ captures the interaction between the components.
+
+This system can be descibed in 1-D using an effective term
+
+$$
+\frac{\text{d}x_\text{eff}}{\text{d}t} = F(x_\text{eff}) + \beta_\text{eff}G(x_\text{eff}, x_\text{eff})
+$$
+
+with $$\beta_\text{eff}$$ a single resilience parameter which can capture
+the effect of perturbating the system (node/link removal, weight change...).
+This resience parameter can be computed from an `AbstractUnipartiteNetwork`
+using the functions `βeff` or `resilience`.
+
+It can be shown that
+
+$$
+\beta_\text{eff} = \langle s \rangle + \mathcal{S}  \mathcal{H}\,,
+$$
+
+with
+
+- $$\langle s \rangle$$ the average weighted degree (computed using `s_mean`),
+- $$\mathcal{S}$$ the symmetry(computed using `symmetry`),
+- $$\mathcal{H}$$ the heterogenity (computed using `heterogenity`).
+
+
+> Goa, J., Barzael, B. and Barabási 2016. Universal resilience patterns in complex networks.
+> Nature 530(7590), 307-312. doi:10.1038/nature16948
+
+## Available functions
+
+```@docs
+s_in
+s_out
+s_mean
+σ_in
+σ_out
+symmetry
+heterogenity
+βeff
+resilience
+```
diff --git a/src/community/resilience.jl b/src/community/resilience.jl
index 63034aeaa..ba30a6b6c 100644
--- a/src/community/resilience.jl
+++ b/src/community/resilience.jl
@@ -5,19 +5,91 @@ by Gao et al. (2016)
 
 using StatsBase: mean, std
 
+"""
+    s_in(N::AbstractUnipartiteNetwork)
+
+Computes the vector of incoming weighted degrees of an unipartite network.
+"""
 s_in(N::AbstractUnipartiteNetwork) = sum(N.A, dims=2)
+
+"""
+    s_out(N::AbstractUnipartiteNetwork)
+
+Computes the vector of outgoing weighted degrees of an unipartite network.
+"""
 s_out(N::AbstractUnipartiteNetwork) = sum(N.A, dims=1)'
+
+"""
+    s_mean(N::AbstractUnipartiteNetwork)
+
+Computes the average weighted degree. This is proportional to the (weighted)
+density of interactions.
+"""
 s_mean(N::AbstractUnipartiteNetwork) = sum(N.A) / size(N.A, 1)
 
+"""
+    σ_in(N::AbstractUnipartiteNetwork)
+
+Computes the standard deviation of the ingoing weighted degree of an unipartite
+network.
+"""
 σ_in(N::AbstractUnipartiteNetwork) = std(s_in(N), corrected=false)
+
+"""
+    σ_out(N::AbstractUnipartiteNetwork)
+
+Computes the standard deviation of the outgoing weighted degree of an unipartite
+network.
+"""
 σ_out(N::AbstractUnipartiteNetwork) = std(s_out(N), corrected=false)
 
-# symmetry computed wrongly in paper?
+"""
+    symmetry(N::AbstractUnipartiteNetwork)
+
+Computes the symmetry between s^in and s^out (the in- and outgoing weighted
+degree of an unipartite network). This is computed as the Pearson correlation
+between the s^in and s^out. It is hence a value between -1 and 1, where high
+positive values indicate that species with many outgoing degrees also tend to have
+many ingoing degrees and negative values mean the opposite. An undirected network
+is perfectly symmetric but, for example, a food web where predators are less likely
+to be prey would have a negative symmetry.
+
+> Goa, J., Barzael, B. and Barabási 2016. Universal resilience patterns in complex networks.
+> Nature 530(7590), 307-312. doi:10.1038/nature16948
+
+"""
 symmetry(N::AbstractUnipartiteNetwork) = (mean(s_in(N) .* s_out(N)) - mean(s_in(N)) * mean(s_out(N))) / (σ_in(N) * σ_out(N))
+
+"""
+    heterogenity(N::AbstractUnipartiteNetwork)
+
+Computes the heterogenity for an unipartite network, a topological characteristic
+which quantifies the difference in in- and outgoing degrees between species. It
+is computed as σ_in * σ_out / s_mean. A value of 0 indicates that all species
+have the same (weighted) in- and outdegrees.
+
+> Goa, J., Barzael, B. and Barabási 2016. Universal resilience patterns in complex networks.
+> Nature 530(7590), 307-312. doi:10.1038/nature16948
+
+"""
 heterogenity(N::AbstractUnipartiteNetwork) = (σ_in(N) * σ_out(N)) / s_mean(N)
 
+"""
+    βeff(N::AbstractUnipartiteNetwork)
+
+A resilience parameters described by Gao et al. (2016). It is a global parameters
+describing the dynamics of an unipartite network as an effective 1D equation of
+the form
+
+f(xeff) = F(xeff) + βeff G(xeff, xeff)
+
+i.e. describing a second-order term representing the effect of the network on the
+dynamics of the 'effective state' xeff of the system.
+
+> Goa, J., Barzael, B. and Barabási 2016. Universal resilience patterns in complex networks.
+> Nature 530(7590), 307-312. doi:10.1038/nature16948
+
+"""
 βeff(N::AbstractUnipartiteNetwork) = dot(s_in(N), s_out(N)) / sum(N.A)
-resilience(N::AbstractUnipartiteNetwork) = βeff(N)
 
-# check if  βeff = sum(A *s_in) / sum(A)
-# and βeff = <s> + HS
+resilience(N::AbstractUnipartiteNetwork) = βeff(N)
diff --git a/test/community/resilience.jl b/test/community/resilience.jl
new file mode 100644
index 000000000..b69fc6ad5
--- /dev/null
+++ b/test/community/resilience.jl
@@ -0,0 +1,42 @@
+module TestResilience
+    using Test, EcologicalNetworks
+
+    A = rand([0, 1, 0.5], 10, 10)
+    N = UnipartiteQuantitativeNetwork(A)
+
+    @assert s_mean(N) ≈ sum(A) / 10
+    @assert s_in(N) ≈ sum(A, dims=2)
+    @assert s_out(N) ≈ sum(A, dims=1)'
+
+    @assert βeff(N) ≈ s_mean(N) + symmetry(N) * heterogenity(N)
+
+    # species only interact with themselves
+    Nid = UnipartiteNetwork([true false false false;
+                              false true false false;
+                              false false true false;
+                              false false false true])
+
+    @assert heterogenity(Nid) ≈ 0.0
+    # @assert symmetry(Nid)   NAN
+
+    # symetric network
+    Nsym = UnipartiteNetwork([false true true true;
+                               true false false false;
+                               true false false false;
+                               true false false false])
+    @assert symmetry(Nsym) ≈ 1.0  # in- and out degree is same
+    @assert heterogenity(Nsym) ≈ 0.5
+
+
+    # asymetric network
+    Nasym = UnipartiteNetwork([false true true true;
+                               false false false false;
+                               false false false false;
+                               false false false false])
+    @assert symmetry(Nasym) ≈ -1.0  # in- and out degree is same
+    @assert heterogenity(Nasym) ≈ 0.75
+
+    v = ones(10) / 10
+    Nhomo = UnipartiteProbabilisticNetwork(v * v')
+    @assert isapprox(heterogenity(Nhomo), 0.0, atol=1e-10)
+end

From c9d1076061f4a9e784ea9cdb2c48618f4b4caa39 Mon Sep 17 00:00:00 2001
From: michielstock <michielfmstock@gmail.com>
Date: Mon, 6 May 2019 18:26:08 +0200
Subject: [PATCH 5/7] :pencil2: typo in docstring

---
 docs/src/properties/resilience.md |  3 +--
 src/community/resilience.jl       | 18 +++++++++++++++++-
 2 files changed, 18 insertions(+), 3 deletions(-)

diff --git a/docs/src/properties/resilience.md b/docs/src/properties/resilience.md
index 3e032839c..1ae1698de 100644
--- a/docs/src/properties/resilience.md
+++ b/docs/src/properties/resilience.md
@@ -1,7 +1,6 @@
 # Resilience
 
-Species interaction networks provide the interactions of the individual species.
-We provide the metrics proposed by Gao et al (2016) that summarize the global
+We provide the metrics proposed by Gao et al (2016) which summarize the global
 behaviour of complex unipartite networks. The dynamics of a system of N components
 (nodes/species) can follow the coupled nonlinear differential equation
 
diff --git a/src/community/resilience.jl b/src/community/resilience.jl
index ba30a6b6c..1ca513f42 100644
--- a/src/community/resilience.jl
+++ b/src/community/resilience.jl
@@ -49,7 +49,7 @@ network.
 Computes the symmetry between s^in and s^out (the in- and outgoing weighted
 degree of an unipartite network). This is computed as the Pearson correlation
 between the s^in and s^out. It is hence a value between -1 and 1, where high
-positive values indicate that species with many outgoing degrees also tend to have
+positive values indicate that species with many outgoing degrees tend to have
 many ingoing degrees and negative values mean the opposite. An undirected network
 is perfectly symmetric but, for example, a food web where predators are less likely
 to be prey would have a negative symmetry.
@@ -92,4 +92,20 @@ dynamics of the 'effective state' xeff of the system.
 """
 βeff(N::AbstractUnipartiteNetwork) = dot(s_in(N), s_out(N)) / sum(N.A)
 
+"""
+    resilience(N::AbstractUnipartiteNetwork)
+
+A resilience parameters described by Gao et al. (2016). It is a global parameters
+describing the dynamics of an unipartite network as an effective 1D equation of
+the form
+
+f(xeff) = F(xeff) + βeff G(xeff, xeff)
+
+i.e. describing a second-order term representing the effect of the network on the
+dynamics of the 'effective state' xeff of the system.
+
+> Goa, J., Barzael, B. and Barabási 2016. Universal resilience patterns in complex networks.
+> Nature 530(7590), 307-312. doi:10.1038/nature16948
+
+"""
 resilience(N::AbstractUnipartiteNetwork) = βeff(N)

From 4a121ee609104d83596d0c93354e3365bb9f5b36 Mon Sep 17 00:00:00 2001
From: michielstock <michielfmstock@gmail.com>
Date: Sun, 12 May 2019 16:47:15 +0200
Subject: [PATCH 6/7] :pencil2: typo function + general `s`

---
 docs/src/properties/resilience.md |  4 ++--
 src/EcologicalNetworks.jl         |  4 ++--
 src/community/resilience.jl       | 34 ++++++++++++++++++++-----------
 test/community/resilience.jl      | 10 ++++-----
 4 files changed, 31 insertions(+), 21 deletions(-)

diff --git a/docs/src/properties/resilience.md b/docs/src/properties/resilience.md
index 1ae1698de..564726cb2 100644
--- a/docs/src/properties/resilience.md
+++ b/docs/src/properties/resilience.md
@@ -31,7 +31,7 @@ with
 
 - $$\langle s \rangle$$ the average weighted degree (computed using `s_mean`),
 - $$\mathcal{S}$$ the symmetry(computed using `symmetry`),
-- $$\mathcal{H}$$ the heterogenity (computed using `heterogenity`).
+- $$\mathcal{H}$$ the heterogeneity (computed using `heterogeneity`).
 
 
 > Goa, J., Barzael, B. and Barabási 2016. Universal resilience patterns in complex networks.
@@ -46,7 +46,7 @@ s_mean
 σ_in
 σ_out
 symmetry
-heterogenity
+heterogeneity
 βeff
 resilience
 ```
diff --git a/src/EcologicalNetworks.jl b/src/EcologicalNetworks.jl
index 5a563c4e3..a530ecf5b 100644
--- a/src/EcologicalNetworks.jl
+++ b/src/EcologicalNetworks.jl
@@ -111,8 +111,8 @@ export AJS, EAJS
 # Overlap
 include(joinpath(".", "community/resilience.jl"))
 export βeff, resilience
-export symmetry, heterogenity
-export s_in, s_out, s_mean
+export symmetry, heterogeneity
+export s
 export σ_in, σ_out
 
 # Modularity
diff --git a/src/community/resilience.jl b/src/community/resilience.jl
index 1ca513f42..b572424fa 100644
--- a/src/community/resilience.jl
+++ b/src/community/resilience.jl
@@ -3,10 +3,26 @@ Some functions from *Universal resilience patterns in complex networks*
 by Gao et al. (2016)
 =#
 
-using StatsBase: mean, std
+using Statistics: mean, std
 
 """
-    s_in(N::AbstractUnipartiteNetwork)
+    s(N::AbstractUnipartiteNetwork; dims::Union{Nothing,Integer}=nothing)
+
+Computes the average weighted degree. This is proportional to the (weighted)
+density of interactions.
+
+If dims is provided, the incoming (`dims=1`) or outgoing (`dims=2`) is computed.
+"""
+function s(N::AbstractUnipartiteNetwork; dims::Union{Nothing,Integer}=nothing)
+    dims == 1 && return sum(N, dims=2)
+    dims == 2 && return sum(N, dims=1)'
+    if dims == nothing
+        return sum(N) / size(N)[1]
+    end
+end
+#=
+"""
+    s(N::AbstractUnipartiteNetwork; dims)
 
 Computes the vector of incoming weighted degrees of an unipartite network.
 """
@@ -19,13 +35,7 @@ Computes the vector of outgoing weighted degrees of an unipartite network.
 """
 s_out(N::AbstractUnipartiteNetwork) = sum(N.A, dims=1)'
 
-"""
-    s_mean(N::AbstractUnipartiteNetwork)
-
-Computes the average weighted degree. This is proportional to the (weighted)
-density of interactions.
-"""
-s_mean(N::AbstractUnipartiteNetwork) = sum(N.A) / size(N.A, 1)
+=#
 
 """
     σ_in(N::AbstractUnipartiteNetwork)
@@ -61,9 +71,9 @@ to be prey would have a negative symmetry.
 symmetry(N::AbstractUnipartiteNetwork) = (mean(s_in(N) .* s_out(N)) - mean(s_in(N)) * mean(s_out(N))) / (σ_in(N) * σ_out(N))
 
 """
-    heterogenity(N::AbstractUnipartiteNetwork)
+    heterogeneity(N::AbstractUnipartiteNetwork)
 
-Computes the heterogenity for an unipartite network, a topological characteristic
+Computes the heterogeneity for an unipartite network, a topological characteristic
 which quantifies the difference in in- and outgoing degrees between species. It
 is computed as σ_in * σ_out / s_mean. A value of 0 indicates that all species
 have the same (weighted) in- and outdegrees.
@@ -72,7 +82,7 @@ have the same (weighted) in- and outdegrees.
 > Nature 530(7590), 307-312. doi:10.1038/nature16948
 
 """
-heterogenity(N::AbstractUnipartiteNetwork) = (σ_in(N) * σ_out(N)) / s_mean(N)
+heterogeneity(N::AbstractUnipartiteNetwork) = (σ_in(N) * σ_out(N)) / s_mean(N)
 
 """
     βeff(N::AbstractUnipartiteNetwork)
diff --git a/test/community/resilience.jl b/test/community/resilience.jl
index b69fc6ad5..4018b40b9 100644
--- a/test/community/resilience.jl
+++ b/test/community/resilience.jl
@@ -8,7 +8,7 @@ module TestResilience
     @assert s_in(N) ≈ sum(A, dims=2)
     @assert s_out(N) ≈ sum(A, dims=1)'
 
-    @assert βeff(N) ≈ s_mean(N) + symmetry(N) * heterogenity(N)
+    @assert βeff(N) ≈ s_mean(N) + symmetry(N) * heterogeneity(N)
 
     # species only interact with themselves
     Nid = UnipartiteNetwork([true false false false;
@@ -16,7 +16,7 @@ module TestResilience
                               false false true false;
                               false false false true])
 
-    @assert heterogenity(Nid) ≈ 0.0
+    @assert heterogeneity(Nid) ≈ 0.0
     # @assert symmetry(Nid)   NAN
 
     # symetric network
@@ -25,7 +25,7 @@ module TestResilience
                                true false false false;
                                true false false false])
     @assert symmetry(Nsym) ≈ 1.0  # in- and out degree is same
-    @assert heterogenity(Nsym) ≈ 0.5
+    @assert heterogeneity(Nsym) ≈ 0.5
 
 
     # asymetric network
@@ -34,9 +34,9 @@ module TestResilience
                                false false false false;
                                false false false false])
     @assert symmetry(Nasym) ≈ -1.0  # in- and out degree is same
-    @assert heterogenity(Nasym) ≈ 0.75
+    @assert heterogeneity(Nasym) ≈ 0.75
 
     v = ones(10) / 10
     Nhomo = UnipartiteProbabilisticNetwork(v * v')
-    @assert isapprox(heterogenity(Nhomo), 0.0, atol=1e-10)
+    @assert isapprox(heterogeneity(Nhomo), 0.0, atol=1e-10)
 end

From f7cf182dedff5f9d854d7915ba48f33e5976d275 Mon Sep 17 00:00:00 2001
From: michielstock <michielfmstock@gmail.com>
Date: Sun, 12 May 2019 17:09:38 +0200
Subject: [PATCH 7/7] :wrench: dependency to `Statistics` + update tests

---
 Manifest.toml                     |  6 +++---
 Project.toml                      |  1 +
 docs/src/properties/resilience.md |  5 +----
 src/EcologicalNetworks.jl         |  2 +-
 src/community/resilience.jl       | 34 ++++++++-----------------------
 test/community/resilience.jl      |  8 ++++----
 6 files changed, 18 insertions(+), 38 deletions(-)

diff --git a/Manifest.toml b/Manifest.toml
index e43be206d..e48015ca6 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -79,10 +79,10 @@ deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
 [[Missings]]
-deps = ["Dates", "InteractiveUtils", "SparseArrays", "Test"]
-git-tree-sha1 = "d1d2585677f2bd93a97cfeb8faa7a0de0f982042"
+deps = ["SparseArrays", "Test"]
+git-tree-sha1 = "f0719736664b4358aa9ec173077d4285775f8007"
 uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
-version = "0.4.0"
+version = "0.4.1"
 
 [[Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
diff --git a/Project.toml b/Project.toml
index dea7a45d0..644ec5d63 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,6 +11,7 @@ Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
diff --git a/docs/src/properties/resilience.md b/docs/src/properties/resilience.md
index 564726cb2..9e69e3199 100644
--- a/docs/src/properties/resilience.md
+++ b/docs/src/properties/resilience.md
@@ -40,13 +40,10 @@ with
 ## Available functions
 
 ```@docs
-s_in
-s_out
-s_mean
+s
 σ_in
 σ_out
 symmetry
 heterogeneity
-βeff
 resilience
 ```
diff --git a/src/EcologicalNetworks.jl b/src/EcologicalNetworks.jl
index a530ecf5b..4d7263425 100644
--- a/src/EcologicalNetworks.jl
+++ b/src/EcologicalNetworks.jl
@@ -110,7 +110,7 @@ export AJS, EAJS
 
 # Overlap
 include(joinpath(".", "community/resilience.jl"))
-export βeff, resilience
+export resilience
 export symmetry, heterogeneity
 export s
 export σ_in, σ_out
diff --git a/src/community/resilience.jl b/src/community/resilience.jl
index b572424fa..627b5e1e7 100644
--- a/src/community/resilience.jl
+++ b/src/community/resilience.jl
@@ -14,10 +14,10 @@ density of interactions.
 If dims is provided, the incoming (`dims=1`) or outgoing (`dims=2`) is computed.
 """
 function s(N::AbstractUnipartiteNetwork; dims::Union{Nothing,Integer}=nothing)
-    dims == 1 && return sum(N, dims=2)
-    dims == 2 && return sum(N, dims=1)'
+    dims == 1 && return sum(N.A, dims=2)
+    dims == 2 && return sum(N.A, dims=1)'
     if dims == nothing
-        return sum(N) / size(N)[1]
+        return sum(N.A) / size(N)[1]
     end
 end
 #=
@@ -43,7 +43,7 @@ s_out(N::AbstractUnipartiteNetwork) = sum(N.A, dims=1)'
 Computes the standard deviation of the ingoing weighted degree of an unipartite
 network.
 """
-σ_in(N::AbstractUnipartiteNetwork) = std(s_in(N), corrected=false)
+σ_in(N::AbstractUnipartiteNetwork) = std(s(N, dims=1), corrected=false)
 
 """
     σ_out(N::AbstractUnipartiteNetwork)
@@ -51,7 +51,7 @@ network.
 Computes the standard deviation of the outgoing weighted degree of an unipartite
 network.
 """
-σ_out(N::AbstractUnipartiteNetwork) = std(s_out(N), corrected=false)
+σ_out(N::AbstractUnipartiteNetwork) = std(s(N, dims=2), corrected=false)
 
 """
     symmetry(N::AbstractUnipartiteNetwork)
@@ -68,7 +68,7 @@ to be prey would have a negative symmetry.
 > Nature 530(7590), 307-312. doi:10.1038/nature16948
 
 """
-symmetry(N::AbstractUnipartiteNetwork) = (mean(s_in(N) .* s_out(N)) - mean(s_in(N)) * mean(s_out(N))) / (σ_in(N) * σ_out(N))
+symmetry(N::AbstractUnipartiteNetwork) = (mean(s(N, dims=1) .* s(N, dims=2)) - mean(s(N, dims=1)) * mean(s(N, dims=2))) / (σ_in(N) * σ_out(N))
 
 """
     heterogeneity(N::AbstractUnipartiteNetwork)
@@ -82,25 +82,7 @@ have the same (weighted) in- and outdegrees.
 > Nature 530(7590), 307-312. doi:10.1038/nature16948
 
 """
-heterogeneity(N::AbstractUnipartiteNetwork) = (σ_in(N) * σ_out(N)) / s_mean(N)
-
-"""
-    βeff(N::AbstractUnipartiteNetwork)
-
-A resilience parameters described by Gao et al. (2016). It is a global parameters
-describing the dynamics of an unipartite network as an effective 1D equation of
-the form
-
-f(xeff) = F(xeff) + βeff G(xeff, xeff)
-
-i.e. describing a second-order term representing the effect of the network on the
-dynamics of the 'effective state' xeff of the system.
-
-> Goa, J., Barzael, B. and Barabási 2016. Universal resilience patterns in complex networks.
-> Nature 530(7590), 307-312. doi:10.1038/nature16948
-
-"""
-βeff(N::AbstractUnipartiteNetwork) = dot(s_in(N), s_out(N)) / sum(N.A)
+heterogeneity(N::AbstractUnipartiteNetwork) = (σ_in(N) * σ_out(N)) / s(N)
 
 """
     resilience(N::AbstractUnipartiteNetwork)
@@ -118,4 +100,4 @@ dynamics of the 'effective state' xeff of the system.
 > Nature 530(7590), 307-312. doi:10.1038/nature16948
 
 """
-resilience(N::AbstractUnipartiteNetwork) = βeff(N)
+resilience(N::AbstractUnipartiteNetwork) = dot(s(N, dims=1), s(N, dims=2)) / sum(N)
diff --git a/test/community/resilience.jl b/test/community/resilience.jl
index 4018b40b9..861c746d9 100644
--- a/test/community/resilience.jl
+++ b/test/community/resilience.jl
@@ -4,11 +4,11 @@ module TestResilience
     A = rand([0, 1, 0.5], 10, 10)
     N = UnipartiteQuantitativeNetwork(A)
 
-    @assert s_mean(N) ≈ sum(A) / 10
-    @assert s_in(N) ≈ sum(A, dims=2)
-    @assert s_out(N) ≈ sum(A, dims=1)'
+    @assert s(N) ≈ sum(A) / 10
+    @assert s(N, dims=1) ≈ sum(A, dims=2)
+    @assert s(N, dims=2) ≈ sum(A, dims=1)'
 
-    @assert βeff(N) ≈ s_mean(N) + symmetry(N) * heterogeneity(N)
+    @assert resilience(N) ≈ s(N) + symmetry(N) * heterogeneity(N)
 
     # species only interact with themselves
     Nid = UnipartiteNetwork([true false false false;