New s_metric method

docs/src/community.md

@@ -19,6 +19,7 @@ Pages   = [
     "community/label_propagation.jl",
     "community/modularity.jl",
     "community/assortativity.jl"
+    "community/s_metric.jl"
 ]
 Private = false
 ```

src/LightGraphs.jl

@@ -114,7 +114,7 @@ barabasi_albert!, static_fitness_model, static_scale_free, kronecker, dorogovtse
 #community
 modularity, core_periphery_deg,
 local_clustering,local_clustering_coefficient, global_clustering_coefficient, triangles,
-label_propagation, maximal_cliques, clique_percolation, assortativity,
+label_propagation, maximal_cliques, clique_percolation, assortativity,s_metric,
 
 #generators
 complete_graph, star_graph, path_graph, wheel_graph, cycle_graph,
@@ -256,6 +256,7 @@ include("community/clustering.jl")
 include("community/cliques.jl")
 include("community/clique_percolation.jl")
 include("community/assortativity.jl")
+include("community/s_metric.jl")
 include("spanningtrees/boruvka.jl")
 include("spanningtrees/kruskal.jl")
 include("spanningtrees/prim.jl")

src/community/s_metric.jl

@@ -0,0 +1,35 @@
+"""
+    s_metric(g; norm=true)
+
+Return the normalised s-metric of `g`.
+
+The s-metric is defined as the sum of the product of degrees between pair of vertices
+for every edge in `g`. [Ref](https://arxiv.org/abs/cond-mat/0501169)
+In directed graphs, the paired values are the out-degree of source vertices
+and the in-degree of destination vertices.
+It is normalised by the maximum s_metric obtained from the family of graph
+with similar degree distribution. s_max is computed from an approximation
+formula as in https://journals.aps.org/pre/pdf/10.1103/PhysRevE.75.046102
+If `norm=false`, no normalisation is performed.
+
+# Examples
+```jldoctest
+julia> using LightGraphs
+
+julia> s_metric(star_graph(4))
+0.6
+```
+"""
+
+function s_metric(g::AbstractGraph{T}; norm=true) where T
+    s = zero(T)
+    for e in edges(g)
+        s += outdegree(g, src(e)) * indegree(g, dst(e))
+    end
+    if norm
+        sm = sum(degree(g).^3)/2
+        return s/sm
+    else
+        return s
+    end
+end

test/community/s_metric.jl

@@ -0,0 +1,22 @@
+using Random, Statistics
+
+@testset "S-metric" begin
+    @testset "Directed ($seed)" for seed in [1, 2, 3], (_n, _ne) in [(14, 18), (10, 22), (7, 16)]
+        g = erdos_renyi(_n, _ne; is_directed=true, seed=seed)
+        sm = s_metric(g, norm=false)
+        sm2 = sum([outdegree(g, src(d)) * indegree(g, dst(d)) for d in edges(g)])
+        @test @inferred sm ≈ sm2
+        sm = s_metric(g, norm=true)
+        sm2 /= sum(degree(g).^3)/2
+        @test @inferred sm ≈ sm2
+    end
+    @testset "Undirected ($seed)" for seed in [1, 2, 3], (_n, _ne) in [(14, 18), (10, 22), (7, 16)]
+        g = erdos_renyi(_n, _ne; is_directed=false, seed=seed)
+        sm = s_metric(g, norm=false)
+        sm2 = sum([degree(g, src(d)) * degree(g, dst(d)) for d in edges(g)])
+        @test @inferred sm ≈ sm2
+        sm = s_metric(g, norm=true)
+        sm2 /= sum(degree(g).^3)/2
+        @test @inferred sm ≈ sm2
+    end
+end

test/runtests.jl

@@ -11,13 +11,13 @@ using Statistics: mean
 
 const testdir = dirname(@__FILE__)
 
-testgraphs(g) = is_directed(g) ? [g, DiGraph{UInt8}(g), DiGraph{Int16}(g)] : [g, Graph{UInt8}(g), Graph{Int16}(g)] 
+testgraphs(g) = is_directed(g) ? [g, DiGraph{UInt8}(g), DiGraph{Int16}(g)] : [g, Graph{UInt8}(g), Graph{Int16}(g)]
 testgraphs(gs...) = vcat((testgraphs(g) for g in gs)...)
 testdigraphs = testgraphs
 
 # some operations will create a large graph from two smaller graphs. We
 # might error out on very small eltypes.
-testlargegraphs(g) = is_directed(g) ? [g, DiGraph{UInt16}(g), DiGraph{Int32}(g)] : [g, Graph{UInt16}(g), Graph{Int32}(g)] 
+testlargegraphs(g) = is_directed(g) ? [g, DiGraph{UInt16}(g), DiGraph{Int32}(g)] : [g, Graph{UInt16}(g), Graph{Int32}(g)]
 testlargegraphs(gs...) = vcat((testlargegraphs(g) for g in gs)...)
 
 tests = [
@@ -60,6 +60,7 @@ tests = [
     "community/clustering",
     "community/clique_percolation",
     "community/assortativity",
+    "community/s_metric",
     "centrality/betweenness",
     "centrality/closeness",
     "centrality/degree",