refactor: community_edge_betweenness() now always computes modularity

as weights represent connection strengths

Author: szhorvat

src/_igraph/graphobject.c

@@ -13076,7 +13076,7 @@ PyObject *igraphmodule_Graph_community_edge_betweenness(igraphmodule_GraphObject
         /* edge_betweenness = */ 0,
         /* merges = */ &merges,
         /* bridges = */ 0,
-        /* modularity = */ weights ? 0 : &q,
+        /* modularity = */ &q,
         /* membership = */ 0,
         PyObject_IsTrue(directed),
         weights,
@@ -13094,19 +13094,11 @@ PyObject *igraphmodule_Graph_community_edge_betweenness(igraphmodule_GraphObject
     igraph_vector_destroy(weights); free(weights);
   }
 
-  if (weights == 0) {
-    /* Calculate modularity vector only in the unweighted case as we don't
-     * calculate modularities for the weighted case */
-    qs=igraphmodule_vector_t_to_PyList(&q, IGRAPHMODULE_TYPE_FLOAT);
-    igraph_vector_destroy(&q);
-    if (!qs) {
-      igraph_matrix_int_destroy(&merges);
-      return NULL;
-    }
-  } else {
-    qs = Py_None;
-    Py_INCREF(qs);
-    igraph_vector_destroy(&q);
+  qs = igraphmodule_vector_t_to_PyList(&q, IGRAPHMODULE_TYPE_FLOAT);
+  igraph_vector_destroy(&q);
+  if (!qs) {
+    igraph_matrix_int_destroy(&merges);
+    return NULL;
   }
 
   ms=igraphmodule_matrix_int_t_to_PyList(&merges);
@@ -18531,12 +18523,18 @@ struct PyMethodDef igraphmodule_Graph_methods[] = {
   "is typically high. So we gradually remove the edge with the highest\n"
   "betweenness from the network and recalculate edge betweenness after every\n"
   "removal, as long as all edges are removed.\n\n"
+  "When edge weights are given, the ratio of betweenness and weight values\n"
+  "is used to choose which edges to remove first, as described in\n"
+  "M. E. J. Newman: Analysis of Weighted Networks (2004), Section C.\n"
+  "Thus, edges with large weights are treated as strong connections,\n"
+  "and will be removed later than weak connections having similar betweenness.\n"
+  "Weights are also used for calculating modularity.\n\n"
   "Attention: this function is wrapped in a more convenient syntax in the\n"
   "derived class L{Graph}. It is advised to use that instead of this version.\n\n"
   "@param directed: whether to take into account the directedness of the edges\n"
   "  when we calculate the betweenness values.\n"
   "@param weights: name of an edge attribute or a list containing\n"
-  "  edge weights.\n\n"
+  "  edge weights. Higher weights indicate stronger connections.\n\n"
   "@return: a tuple with the merge matrix that describes the dendrogram\n"
   "  and the modularity scores before each merge. The modularity scores\n"
   "  use the weights if the original graph was weighted.\n"

src/igraph/community.py

@@ -235,6 +235,13 @@ def _community_edge_betweenness(graph, clusters=None, directed=True, weights=Non
     separate components. The result of the clustering will be represented
     by a dendrogram.
 
+    When edge weights are given, the ratio of betweenness and weight values
+    is used to choose which edges to remove first, as described in
+    M. E. J. Newman: Analysis of Weighted Networks (2004), Section C.
+    Thus, edges with large weights are treated as strong connections,
+    and will be removed later than weak connections having similar betweenness.
+    Weights are also used for calculating modularity.
+
     @param clusters: the number of clusters we would like to see. This
       practically defines the "level" where we "cut" the dendrogram to
       get the membership vector of the vertices. If C{None}, the dendrogram
@@ -245,7 +252,7 @@ def _community_edge_betweenness(graph, clusters=None, directed=True, weights=Non
     @param directed: whether the directionality of the edges should be
       taken into account or not.
     @param weights: name of an edge attribute or a list containing
-      edge weights.
+      edge weights. Higher weights indicate stronger connections.
     @return: a L{VertexDendrogram} object, initally cut at the maximum
       modularity or at the desired number of clusters.
     """

tests/test_decomposition.py

@@ -263,11 +263,7 @@ def testEdgeBetweenness(self):
         g.es["weight"] = 1
         g[0, 1] = g[1, 2] = g[2, 0] = g[3, 4] = 10
 
-        # We need to specify the desired cluster count explicitly; this is
-        # because edge betweenness-based detection does not play well with
-        # modularity-based cluster count selection (the edge weights have
-        # different semantics) so we need to give igraph a hint
-        cl = g.community_edge_betweenness(weights="weight").as_clustering(n=2)
+        cl = g.community_edge_betweenness(weights="weight").as_clustering()
         self.assertMembershipsEqual(cl, [0, 0, 0, 1, 1])
         self.assertAlmostEqual(cl.q, 0.2750, places=3)