Fix modularity when self loops exist (#487)

Author: ryandewolfe33

src/community/modularity.jl

@@ -48,7 +48,7 @@ julia> barbell = blockdiag(complete_graph(3), complete_graph(3));
 julia> add_edge!(barbell, 1, 4);
 
 julia> modularity(barbell, [1, 1, 1, 2, 2, 2])
-0.35714285714285715
+0.3571428571428571
 
 julia> modularity(barbell, [1, 1, 1, 2, 2, 2], γ=0.5)
 0.6071428571428571  
@@ -90,14 +90,20 @@ function modularity(
             c2 = c[v]
             if c1 == c2
                 Q += distmx[u, v]
+                if u == v && !is_directed(g)
+                    #Since we do not look at each end in outer loop
+                    Q += distmx[u, v]
+                end
             end
             kout[c1] += distmx[u, v]
             kin[c2] += distmx[u, v]
+            if u == v && !is_directed(g)
+                #Since we do not look at each end in outer loop
+                kout[c1] += distmx[u, v]
+                kin[c2] += distmx[u, v]
+            end
         end
     end
-    Q = Q * m
-    @inbounds for i in 1:nc
-        Q -= γ * kin[i] * kout[i]
-    end
-    return Q / m^2
+    Q = Q/m - γ * sum(kin .* kout) / m^2
+    return Q
 end

test/community/modularity.jl

@@ -24,6 +24,13 @@
         @test isapprox(Q2, 0.6071428571428571, atol=1e-3)
     end
 
+    # Test with self loop
+    add_edge!(barbell, 1, 1)
+    for g in test_generic_graphs(barbell)
+        Q = @inferred(modularity(g, c))
+        @test isapprox(Q, 0.3671875, atol=1e-3)
+    end
+
     # 2. directed test cases 
     triangle = SimpleDiGraph(3)
     add_edge!(triangle, 1, 2)
@@ -65,6 +72,20 @@
         Q = @inferred(modularity(g, c, distmx=d))
         @test isapprox(Q, 0.045454545454545456, atol=1e-3)
     end
+    # Add self loop with weight 5
+    add_edge!(barbell, 1, 1)
+    d = [
+        [5 1 1 0 0 0]
+        [1 0 1 0 0 0]
+        [1 1 0 1 0 0]
+        [0 0 1 0 1 1]
+        [0 0 0 1 0 1]
+        [0 0 0 1 1 0]
+    ]
+    for g in test_generic_graphs(barbell)
+        Q = @inferred(modularity(g, c, distmx=d))
+        @test isapprox(Q, 0.329861, atol=1e-3)
+    end
 
     # 3.2. directed and weighted test cases
     triangle = SimpleDiGraph(3)
@@ -73,12 +94,12 @@
     add_edge!(triangle, 3, 1)
 
     barbell = blockdiag(triangle, triangle)
-    add_edge!(barbell, 1, 4) # this edge has a weight of 5
+    add_edge!(barbell, 3, 4) # this edge has a weight of 5
     c = [1, 1, 1, 2, 2, 2]
     d = [
-        [0 1 0 5 0 0]
+        [0 1 0 0 0 0]
         [0 0 1 0 0 0]
-        [1 0 0 0 0 0]
+        [1 0 0 5 0 0]
         [0 0 0 0 1 0]
         [0 0 0 0 0 1]
         [0 0 0 1 0 0]
@@ -87,4 +108,18 @@
         Q = @inferred(modularity(g, c, distmx=d))
         @test isapprox(Q, 0.1487603305785124, atol=1e-3)
     end
+    # Add self loop with weight 5
+    add_edge!(barbell, 1, 1)
+    d = [
+        [5 1 0 0 0 0]
+        [0 0 1 0 0 0]
+        [1 0 0 1 0 0]
+        [0 0 0 0 1 0]
+        [0 0 0 0 0 1]
+        [0 0 0 1 0 0]
+    ]
+    for g in test_generic_graphs(barbell)
+        Q = @inferred(modularity(g, c, distmx=d))
+        @test isapprox(Q, 0.333333333, atol=1e-3)
+    end
 end