Implement edge_reciprocity()

Ressurect old edge_reciprocity code.

src/graph/topology/Makefile.am

@@ -25,6 +25,7 @@ libgraph_tool_topology_la_SOURCES = \
     graph_minimum_spanning_tree.cc \
     graph_planar.cc \
     graph_random_matching.cc \
+    graph_reciprocity.cc \
     graph_similarity.cc \
     graph_subgraph_isomorphism.cc \
     graph_topological_sort.cc \

src/graph/topology/graph_reciprocity.cc

@@ -28,11 +28,9 @@ using namespace graph_tool;
 struct get_reciprocity
 {
     template <class Graph>
-    void operator()(const Graph* gp, double& reciprocity) const
+    void operator()(const Graph& g, double& reciprocity) const
     {
-        const Graph& g = *gp;
-        size_t L = 0;
-        double Lbd = 0.0;
+        size_t L = 0, Lbd = 0;
 
         int i, NV = num_vertices(g);
         #pragma omp parallel for default(shared) private(i) reduction(+:L,Lbd) \
@@ -47,44 +45,28 @@ struct get_reciprocity
             tie(e_begin,e_end) = out_edges(v,g);
             for(e = e_begin; e != e_end; ++e)
             {
-                typename graph_traits<Graph>::vertex_descriptor s,t;
-                s = v;
-                t = target(*e,g);
+                typename graph_traits<Graph>::vertex_descriptor t;
+                t = target(*e, g);
 
-                size_t o = 0;
                 typename graph_traits<Graph>::adjacency_iterator a, a_end;
-                for (tie(a,a_end) = adjacent_vertices(s, g); a != a_end; ++a)
-                    if (*a == t)
-                        o++;
-
-                size_t j = 0;
                 for (tie(a, a_end) = adjacent_vertices(t, g); a != a_end; ++a)
-                    if (*a == s)
-                        j++;
-
-                Lbd += min(j/double(o),1.0);
+                    if (*a == v)
+                    {
+                        Lbd += 1;
+                        break;
+                    }
                 L++;
             }
         }
 
-        if(is_convertible<typename graph_traits<Graph>::directed_category,
-                          undirected_tag>::value)
-        {
-            L /= 2;
-            Lbd /= 2;
-        }
-
-        size_t N = HardNumVertices()(&g);
-        double a = L/double(N*(N-1));
-
-        reciprocity = (Lbd/L - a)/(1-a);
+        reciprocity = Lbd / double(L);
     }
 };
 
-double GraphInterface::GetReciprocity() const
+double reciprocity(GraphInterface& gi)
 {
     double reciprocity;
-    run_action<>()(*this, bind<void>(get_reciprocity(), _1,
-                                     var(reciprocity)))();
+    run_action<>()(gi, bind<void>(get_reciprocity(), _1,
+                                  ref(reciprocity)))();
     return reciprocity;
 }

src/graph/topology/graph_topology.cc

@@ -37,6 +37,7 @@ void subgraph_isomorphism(GraphInterface& gi1, GraphInterface& gi2,
                           boost::any edge_label1, boost::any edge_label2,
                           python::list vmapping, python::list emapping,
                           size_t n_max, size_t seed);
+double reciprocity(GraphInterface& gi);
 
 void export_components();
 void export_similarity();
@@ -57,6 +58,7 @@ BOOST_PYTHON_MODULE(libgraph_tool_topology)
     def("dominator_tree", &dominator_tree);
     def("transitive_closure", &transitive_closure);
     def("is_planar", &is_planar);
+    def("reciprocity", &reciprocity);
     export_components();
     export_similarity();
     export_dists();

src/graph_tool/topology/__init__.py

@@ -45,6 +45,7 @@ Summary
    label_biconnected_components
    label_largest_component
    is_planar
+   edge_reciprocity
 
 Contents
 ++++++++
@@ -63,7 +64,7 @@ __all__ = ["isomorphism", "subgraph_isomorphism", "mark_subgraph",
            "min_spanning_tree", "dominator_tree", "topological_sort",
            "transitive_closure", "label_components", "label_largest_component",
            "label_biconnected_components", "shortest_distance", "shortest_path",
-           "pseudo_diameter", "is_planar", "similarity"]
+           "pseudo_diameter", "is_planar", "similarity", "edge_reciprocity"]
 
 
 def similarity(g1, g2, label1=None, label2=None, norm=True):
@@ -1249,3 +1250,56 @@ def max_independent_vertex_set(g, high_deg=False, mivs=None):
                            seed)
     mivs = g.own_property(mivs)
     return mivs
+
+
+def edge_reciprocity(g):
+    r"""Calculate the edge reciprocity of the graph.
+
+    Parameters
+    ----------
+    g : :class:`~graph_tool.Graph`
+        Graph to be used
+        edges.
+
+    Returns
+    -------
+    reciprocity : float
+        The reciprocity value.
+
+    Notes
+    -----
+
+    The edge [reciprocity]_ is defined as :math:`E^\leftrightarrow/E`, where
+    :math:`E^\leftrightarrow` and :math:`E` are the number of bidirectional and
+    all edges in the graph, respectively.
+
+    The algorithm runs with complexity :math:`O(E + V)`.
+
+    Examples
+    --------
+
+    >>> g = gt.Graph()
+    >>> g.add_vertex(2)
+    [<Vertex object with index '0' at 0x1254dd0>,
+     <Vertex object with index '1' at 0x1254bd0>]
+    >>> g.add_edge(g.vertex(0), g.vertex(1))
+    <Edge object with source '0' and target '1' at 0x33bc710>
+    >>> gt.edge_reciprocity(g)
+    0.0
+    >>> g.add_edge(g.vertex(1), g.vertex(0))
+    <Edge object with source '1' and target '0' at 0x33bc7a0>
+    >>> gt.edge_reciprocity(g)
+    1.0
+
+    References
+    ----------
+    .. [reciprocity] S. Wasserman and K. Faust, "Social Network Analysis".
+       (Cambridge University Press, Cambridge, 1994)
+    .. [lopez_reciprocity_2007] Gorka Zamora-López, Vinko Zlatić, Changsong Zhou, Hrvoje Štefančić, and Jürgen Kurths
+       "Reciprocity of networks with degree correlations and arbitrary degree sequences", Phys. Rev. E 77, 016106 (2008)
+       :doi:`10.1103/PhysRevE.77.016106`, :arxiv:`0706.3372`
+
+    """
+
+    r = libgraph_tool_topology.reciprocity(g._Graph__graph)
+    return r