[Port] New rich club metric (#29)

added rich club metric with tests and support for directed graphs

Co-authored-by: Victor <[email protected]>
Co-authored-by: vboussange <[email protected]>

docs/src/community.md

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

src/Graphs.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,rich_club,
 
 #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/rich_club.jl")
 include("spanningtrees/boruvka.jl")
 include("spanningtrees/kruskal.jl")
 include("spanningtrees/prim.jl")

src/community/rich_club.jl

@@ -0,0 +1,27 @@
+"""
+    rich_club(g, k)
+
+Return the non-normalised [rich-club coefficient](https://en.wikipedia.org/wiki/Rich-club_coefficient) of graph `g`,
+with degree cut-off `k`.
+
+```jldoctest
+julia> using LightGraphs
+julia> g = star_graph(5)
+julia> rich_club(g, 1)
+0.4
+```
+"""
+function rich_club(g::AbstractGraph{T}, k::Int) where T
+    E = zero(T)
+    for e in edges(g)
+        if (outdegree(g, src(e)) >= k) && (indegree(g, dst(e)) >= k )
+            E +=1
+        end
+    end
+    N = count(degree(g) .>= k)
+    if is_directed(g)
+        return E / (N*(N-1))
+    else
+        return 2*E / (N*(N-1))
+    end
+end

test/community/rich_club.jl

@@ -0,0 +1,17 @@
+
+@testset "Rich club coefficient" begin
+    @testset "Small graphs" for _n in 5:10
+        @test @inferred rich_club(star_graph(_n), 1) ≈ 2 / _n
+        @test @inferred rich_club(DiGraph(star_graph(_n)), 1) ≈ 2 / _n
+    end
+    @testset "Directed ($seed)" for seed in [1, 2, 3], (n, ne) in [(14, 18), (10, 22), (7, 16)]
+        g = erdos_renyi(n, ne; is_directed=true, seed=seed)
+        _r = rich_club(g, 1)
+        @test @inferred rich_club(g, 1) > 0.
+    end
+    @testset "Undirected ($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)
+        _r = rich_club(g, 1)
+        @test @inferred rich_club(g, 1) > 0.
+    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/rich_club",
     "centrality/betweenness",
     "centrality/closeness",
     "centrality/degree",