add scalar and tensor products

README.md

@@ -90,7 +90,8 @@ write(g,"mygraph.jgz")
 
 - **connectivity:** strongly- and weakly-connected components, bipartite checks, condensation, attracting components
 
-- **operators:** complement, reverse, reverse!, union, join, intersect, difference, symmetric difference, blkdiag, induced subgraphs
+- **operators:** complement, reverse, reverse!, union, join, intersect, difference,
+symmetric difference, blkdiag, induced subgraphs, products (cartesian/scalar)
 
 - **shortest paths:** Dijkstra, Dijkstra with predecessors, Bellman-Ford, Floyd-Warshall, A*
 

src/LightGraphs.jl

@@ -41,7 +41,7 @@ eccentricity, diameter, periphery, radius, center,
 # operators
 complement, reverse, reverse!, union, intersect,
 difference, symmetric_difference,
-induced_subgraph, join,
+induced_subgraph, join, tensor_product, cartesian_product,
 
 # graph visit
 SimpleGraphVisitor, TrivialGraphVisitor, LogGraphVisitor,

src/operators.jl

@@ -236,3 +236,43 @@ eltype(g::SimpleGraph) = Float64
 length(g::SimpleGraph) = nv(g)*nv(g)
 ndims(g::SimpleGraph) = 2
 issym(g::SimpleGraph) = !is_directed(g)
+
+"""
+Returns the (cartesian product)[https://en.wikipedia.org/wiki/Tensor_product_of_graphs] of `g` and `h`
+"""
+function cartesian_product{G<:SimpleGraph}(g::G, h::G)
+    z = G(nv(g)*nv(h))
+    id(i, j) = (i-1)*nv(h) + j
+    for e in edges(g)
+        i1, i2 = src(e), dst(e)
+        for j=1:nv(h)
+            add_edge!(z, id(i1,j), id(i2,j))
+        end
+    end
+
+    for e in edges(h)
+        j1, j2 = src(e), dst(e)
+        for i=1:nv(g)
+            add_edge!(z, id(i,j1), id(i,j2))
+        end
+    end
+
+    z
+end
+
+"""
+Returns the (tensor product)[https://en.wikipedia.org/wiki/Tensor_product_of_graphs] of `g` and `h`
+"""
+function tensor_product{G<:SimpleGraph}(g::G, h::G)
+    z = G(nv(g)*nv(h))
+    id(i, j) = (i-1)*nv(h) + j
+    for eg in edges(g)
+        i1, i2 = src(eg), dst(eg)
+        for eh in edges(h)
+            j1, j2 = src(eh), dst(eh)
+            add_edge!(z, id(i1,j1), id(i2,j2))
+        end
+    end
+
+    z
+end

test/operators.jl

@@ -83,3 +83,13 @@ x = p*ones(10)
 @test ndims(p) == 2
 @test issym(p)
 @test !issym(g5)
+
+g22 = CompleteGraph(2)
+h = cartesian_product(g22, g22)
+@test nv(h) == 4
+@test ne(h)== 4
+
+g22 = CompleteGraph(2)
+h = tensor_product(g22, g22)
+@test nv(h) == 4
+@test ne(h) == 1