sl@0: // Copyright 2004 The Trustees of Indiana University.
sl@0: 
sl@0: // Distributed under the Boost Software License, Version 1.0.
sl@0: // (See accompanying file LICENSE_1_0.txt or copy at
sl@0: // http://www.boost.org/LICENSE_1_0.txt)
sl@0: 
sl@0: //  Authors: Douglas Gregor
sl@0: //           Andrew Lumsdaine
sl@0: #ifndef BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP
sl@0: #define BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP
sl@0: 
sl@0: #include <stack>
sl@0: #include <vector>
sl@0: #include <boost/graph/dijkstra_shortest_paths.hpp>
sl@0: #include <boost/graph/breadth_first_search.hpp>
sl@0: #include <boost/graph/relax.hpp>
sl@0: #include <boost/graph/graph_traits.hpp>
sl@0: #include <boost/tuple/tuple.hpp>
sl@0: #include <boost/type_traits/is_convertible.hpp>
sl@0: #include <boost/type_traits/is_same.hpp>
sl@0: #include <boost/mpl/if.hpp>
sl@0: #include <boost/property_map.hpp>
sl@0: #include <boost/graph/named_function_params.hpp>
sl@0: #include <algorithm>
sl@0: 
sl@0: namespace boost {
sl@0: 
sl@0: namespace detail { namespace graph {
sl@0: 
sl@0:   /**
sl@0:    * Customized visitor passed to Dijkstra's algorithm by Brandes'
sl@0:    * betweenness centrality algorithm. This visitor is responsible for
sl@0:    * keeping track of the order in which vertices are discovered, the
sl@0:    * predecessors on the shortest path(s) to a vertex, and the number
sl@0:    * of shortest paths.
sl@0:    */
sl@0:   template<typename Graph, typename WeightMap, typename IncomingMap,
sl@0:            typename DistanceMap, typename PathCountMap>
sl@0:   struct brandes_dijkstra_visitor : public bfs_visitor<>
sl@0:   {
sl@0:     typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
sl@0:     typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
sl@0: 
sl@0:     brandes_dijkstra_visitor(std::stack<vertex_descriptor>& ordered_vertices,
sl@0:                              WeightMap weight,
sl@0:                              IncomingMap incoming,
sl@0:                              DistanceMap distance,
sl@0:                              PathCountMap path_count)
sl@0:       : ordered_vertices(ordered_vertices), weight(weight), 
sl@0:         incoming(incoming), distance(distance),
sl@0:         path_count(path_count)
sl@0:     { }
sl@0: 
sl@0:     /**
sl@0:      * Whenever an edge e = (v, w) is relaxed, the incoming edge list
sl@0:      * for w is set to {(v, w)} and the shortest path count of w is set to
sl@0:      * the number of paths that reach {v}.
sl@0:      */
sl@0:     void edge_relaxed(edge_descriptor e, const Graph& g) 
sl@0:     { 
sl@0:       vertex_descriptor v = source(e, g), w = target(e, g);
sl@0:       incoming[w].clear();
sl@0:       incoming[w].push_back(e);
sl@0:       put(path_count, w, get(path_count, v));
sl@0:     }
sl@0: 
sl@0:     /**
sl@0:      * If an edge e = (v, w) was not relaxed, it may still be the case
sl@0:      * that we've found more equally-short paths, so include {(v, w)} in the
sl@0:      * incoming edges of w and add all of the shortest paths to v to the
sl@0:      * shortest path count of w.
sl@0:      */
sl@0:     void edge_not_relaxed(edge_descriptor e, const Graph& g) 
sl@0:     {
sl@0:       typedef typename property_traits<WeightMap>::value_type weight_type;
sl@0:       typedef typename property_traits<DistanceMap>::value_type distance_type;
sl@0:       vertex_descriptor v = source(e, g), w = target(e, g);
sl@0:       distance_type d_v = get(distance, v), d_w = get(distance, w);
sl@0:       weight_type w_e = get(weight, e);
sl@0: 
sl@0:       closed_plus<distance_type> combine;
sl@0:       if (d_w == combine(d_v, w_e)) {
sl@0:         put(path_count, w, get(path_count, w) + get(path_count, v));
sl@0:         incoming[w].push_back(e);
sl@0:       }
sl@0:     }
sl@0: 
sl@0:     /// Keep track of vertices as they are reached
sl@0:     void examine_vertex(vertex_descriptor w, const Graph&) 
sl@0:     { 
sl@0:       ordered_vertices.push(w);
sl@0:     }
sl@0: 
sl@0:   private:
sl@0:     std::stack<vertex_descriptor>& ordered_vertices;
sl@0:     WeightMap weight;
sl@0:     IncomingMap incoming;
sl@0:     DistanceMap distance;
sl@0:     PathCountMap path_count;
sl@0:   };
sl@0: 
sl@0:   /**
sl@0:    * Function object that calls Dijkstra's shortest paths algorithm
sl@0:    * using the Dijkstra visitor for the Brandes betweenness centrality
sl@0:    * algorithm.
sl@0:    */
sl@0:   template<typename WeightMap>
sl@0:   struct brandes_dijkstra_shortest_paths
sl@0:   {
sl@0:     brandes_dijkstra_shortest_paths(WeightMap weight_map) 
sl@0:       : weight_map(weight_map) { }
sl@0: 
sl@0:     template<typename Graph, typename IncomingMap, typename DistanceMap, 
sl@0:              typename PathCountMap, typename VertexIndexMap>
sl@0:     void 
sl@0:     operator()(Graph& g, 
sl@0:                typename graph_traits<Graph>::vertex_descriptor s,
sl@0:                std::stack<typename graph_traits<Graph>::vertex_descriptor>& ov,
sl@0:                IncomingMap incoming,
sl@0:                DistanceMap distance,
sl@0:                PathCountMap path_count,
sl@0:                VertexIndexMap vertex_index)
sl@0:     {
sl@0:       typedef brandes_dijkstra_visitor<Graph, WeightMap, IncomingMap, 
sl@0:                                        DistanceMap, PathCountMap> visitor_type;
sl@0:       visitor_type visitor(ov, weight_map, incoming, distance, path_count);
sl@0: 
sl@0:       dijkstra_shortest_paths(g, s, 
sl@0:                               boost::weight_map(weight_map)
sl@0:                               .vertex_index_map(vertex_index)
sl@0:                               .distance_map(distance)
sl@0:                               .visitor(visitor));
sl@0:     }
sl@0: 
sl@0:   private:
sl@0:     WeightMap weight_map;
sl@0:   };
sl@0: 
sl@0:   /**
sl@0:    * Function object that invokes breadth-first search for the
sl@0:    * unweighted form of the Brandes betweenness centrality algorithm.
sl@0:    */
sl@0:   struct brandes_unweighted_shortest_paths
sl@0:   {
sl@0:     /**
sl@0:      * Customized visitor passed to breadth-first search, which
sl@0:      * records predecessor and the number of shortest paths to each
sl@0:      * vertex.
sl@0:      */
sl@0:     template<typename Graph, typename IncomingMap, typename DistanceMap, 
sl@0:              typename PathCountMap>
sl@0:     struct visitor_type : public bfs_visitor<>
sl@0:     {
sl@0:       typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
sl@0:       typedef typename graph_traits<Graph>::vertex_descriptor 
sl@0:         vertex_descriptor;
sl@0:       
sl@0:       visitor_type(IncomingMap incoming, DistanceMap distance, 
sl@0:                    PathCountMap path_count, 
sl@0:                    std::stack<vertex_descriptor>& ordered_vertices)
sl@0:         : incoming(incoming), distance(distance), 
sl@0:           path_count(path_count), ordered_vertices(ordered_vertices) { }
sl@0: 
sl@0:       /// Keep track of vertices as they are reached
sl@0:       void examine_vertex(vertex_descriptor v, Graph&)
sl@0:       {
sl@0:         ordered_vertices.push(v);
sl@0:       }
sl@0: 
sl@0:       /**
sl@0:        * Whenever an edge e = (v, w) is labelled a tree edge, the
sl@0:        * incoming edge list for w is set to {(v, w)} and the shortest
sl@0:        * path count of w is set to the number of paths that reach {v}.
sl@0:        */
sl@0:       void tree_edge(edge_descriptor e, Graph& g)
sl@0:       {
sl@0:         vertex_descriptor v = source(e, g);
sl@0:         vertex_descriptor w = target(e, g);
sl@0:         put(distance, w, get(distance, v) + 1);
sl@0:         
sl@0:         put(path_count, w, get(path_count, v));
sl@0:         incoming[w].push_back(e);
sl@0:       }
sl@0: 
sl@0:       /**
sl@0:        * If an edge e = (v, w) is not a tree edge, it may still be the
sl@0:        * case that we've found more equally-short paths, so include (v, w)
sl@0:        * in the incoming edge list of w and add all of the shortest
sl@0:        * paths to v to the shortest path count of w.
sl@0:        */
sl@0:       void non_tree_edge(edge_descriptor e, Graph& g)
sl@0:       {
sl@0:         vertex_descriptor v = source(e, g);
sl@0:         vertex_descriptor w = target(e, g);
sl@0:         if (get(distance, w) == get(distance, v) + 1) {
sl@0:           put(path_count, w, get(path_count, w) + get(path_count, v));
sl@0:           incoming[w].push_back(e);
sl@0:         }
sl@0:       }
sl@0: 
sl@0:     private:
sl@0:       IncomingMap incoming;
sl@0:       DistanceMap distance;
sl@0:       PathCountMap path_count;
sl@0:       std::stack<vertex_descriptor>& ordered_vertices;
sl@0:     };
sl@0: 
sl@0:     template<typename Graph, typename IncomingMap, typename DistanceMap, 
sl@0:              typename PathCountMap, typename VertexIndexMap>
sl@0:     void 
sl@0:     operator()(Graph& g, 
sl@0:                typename graph_traits<Graph>::vertex_descriptor s,
sl@0:                std::stack<typename graph_traits<Graph>::vertex_descriptor>& ov,
sl@0:                IncomingMap incoming,
sl@0:                DistanceMap distance,
sl@0:                PathCountMap path_count,
sl@0:                VertexIndexMap vertex_index)
sl@0:     {
sl@0:       typedef typename graph_traits<Graph>::vertex_descriptor
sl@0:         vertex_descriptor;
sl@0: 
sl@0:       visitor_type<Graph, IncomingMap, DistanceMap, PathCountMap>
sl@0:         visitor(incoming, distance, path_count, ov);
sl@0:       
sl@0:       std::vector<default_color_type> 
sl@0:         colors(num_vertices(g), color_traits<default_color_type>::white());
sl@0:       boost::queue<vertex_descriptor> Q;
sl@0:       breadth_first_visit(g, s, Q, visitor, 
sl@0:                           make_iterator_property_map(colors.begin(), 
sl@0:                                                      vertex_index));
sl@0:     }
sl@0:   };
sl@0: 
sl@0:   // When the edge centrality map is a dummy property map, no
sl@0:   // initialization is needed.
sl@0:   template<typename Iter>
sl@0:   inline void 
sl@0:   init_centrality_map(std::pair<Iter, Iter>, dummy_property_map) { }
sl@0: 
sl@0:   // When we have a real edge centrality map, initialize all of the
sl@0:   // centralities to zero.
sl@0:   template<typename Iter, typename Centrality>
sl@0:   void 
sl@0:   init_centrality_map(std::pair<Iter, Iter> keys, Centrality centrality_map)
sl@0:   {
sl@0:     typedef typename property_traits<Centrality>::value_type 
sl@0:       centrality_type;
sl@0:     while (keys.first != keys.second) {
sl@0:       put(centrality_map, *keys.first, centrality_type(0));
sl@0:       ++keys.first;
sl@0:     }
sl@0:   }
sl@0: 
sl@0:   // When the edge centrality map is a dummy property map, no update
sl@0:   // is performed.
sl@0:   template<typename Key, typename T>
sl@0:   inline void 
sl@0:   update_centrality(dummy_property_map, const Key&, const T&) { }
sl@0: 
sl@0:   // When we have a real edge centrality map, add the value to the map
sl@0:   template<typename CentralityMap, typename Key, typename T>
sl@0:   inline void 
sl@0:   update_centrality(CentralityMap centrality_map, Key k, const T& x)
sl@0:   { put(centrality_map, k, get(centrality_map, k) + x); }
sl@0: 
sl@0:   template<typename Iter>
sl@0:   inline void 
sl@0:   divide_centrality_by_two(std::pair<Iter, Iter>, dummy_property_map) {}
sl@0: 
sl@0:   template<typename Iter, typename CentralityMap>
sl@0:   inline void
sl@0:   divide_centrality_by_two(std::pair<Iter, Iter> keys, 
sl@0:                            CentralityMap centrality_map)
sl@0:   {
sl@0:     typename property_traits<CentralityMap>::value_type two(2);
sl@0:     while (keys.first != keys.second) {
sl@0:       put(centrality_map, *keys.first, get(centrality_map, *keys.first) / two);
sl@0:       ++keys.first;
sl@0:     }
sl@0:   }
sl@0: 
sl@0:   template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
sl@0:            typename IncomingMap, typename DistanceMap, 
sl@0:            typename DependencyMap, typename PathCountMap,
sl@0:            typename VertexIndexMap, typename ShortestPaths>
sl@0:   void 
sl@0:   brandes_betweenness_centrality_impl(const Graph& g, 
sl@0:                                       CentralityMap centrality,     // C_B
sl@0:                                       EdgeCentralityMap edge_centrality_map,
sl@0:                                       IncomingMap incoming, // P
sl@0:                                       DistanceMap distance,         // d
sl@0:                                       DependencyMap dependency,     // delta
sl@0:                                       PathCountMap path_count,      // sigma
sl@0:                                       VertexIndexMap vertex_index,
sl@0:                                       ShortestPaths shortest_paths)
sl@0:   {
sl@0:     typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
sl@0:     typedef typename graph_traits<Graph>::edge_iterator edge_iterator;
sl@0:     typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
sl@0: 
sl@0:     // Initialize centrality
sl@0:     init_centrality_map(vertices(g), centrality);
sl@0:     init_centrality_map(edges(g), edge_centrality_map);
sl@0: 
sl@0:     std::stack<vertex_descriptor> ordered_vertices;
sl@0:     vertex_iterator s, s_end;
sl@0:     for (tie(s, s_end) = vertices(g); s != s_end; ++s) {
sl@0:       // Initialize for this iteration
sl@0:       vertex_iterator w, w_end;
sl@0:       for (tie(w, w_end) = vertices(g); w != w_end; ++w) {
sl@0:         incoming[*w].clear();
sl@0:         put(path_count, *w, 0);
sl@0:         put(dependency, *w, 0);
sl@0:       }
sl@0:       put(path_count, *s, 1);
sl@0:       
sl@0:       // Execute the shortest paths algorithm. This will be either
sl@0:       // Dijkstra's algorithm or a customized breadth-first search,
sl@0:       // depending on whether the graph is weighted or unweighted.
sl@0:       shortest_paths(g, *s, ordered_vertices, incoming, distance,
sl@0:                      path_count, vertex_index);
sl@0:       
sl@0:       while (!ordered_vertices.empty()) {
sl@0:         vertex_descriptor w = ordered_vertices.top();
sl@0:         ordered_vertices.pop();
sl@0:         
sl@0:         typedef typename property_traits<IncomingMap>::value_type
sl@0:           incoming_type;
sl@0:         typedef typename incoming_type::iterator incoming_iterator;
sl@0:         typedef typename property_traits<DependencyMap>::value_type 
sl@0:           dependency_type;
sl@0:         
sl@0:         for (incoming_iterator vw = incoming[w].begin();
sl@0:              vw != incoming[w].end(); ++vw) {
sl@0:           vertex_descriptor v = source(*vw, g);
sl@0:           dependency_type factor = dependency_type(get(path_count, v))
sl@0:             / dependency_type(get(path_count, w));
sl@0:           factor *= (dependency_type(1) + get(dependency, w));
sl@0:           put(dependency, v, get(dependency, v) + factor);
sl@0:           update_centrality(edge_centrality_map, *vw, factor);
sl@0:         }
sl@0:         
sl@0:         if (w != *s) {
sl@0:           update_centrality(centrality, w, get(dependency, w));
sl@0:         }
sl@0:       }
sl@0:     }
sl@0: 
sl@0:     typedef typename graph_traits<Graph>::directed_category directed_category;
sl@0:     const bool is_undirected = 
sl@0:       is_convertible<directed_category*, undirected_tag*>::value;
sl@0:     if (is_undirected) {
sl@0:       divide_centrality_by_two(vertices(g), centrality);
sl@0:       divide_centrality_by_two(edges(g), edge_centrality_map);
sl@0:     }
sl@0:   }
sl@0: 
sl@0: } } // end namespace detail::graph
sl@0: 
sl@0: template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
sl@0:          typename IncomingMap, typename DistanceMap, 
sl@0:          typename DependencyMap, typename PathCountMap, 
sl@0:          typename VertexIndexMap>
sl@0: void 
sl@0: brandes_betweenness_centrality(const Graph& g, 
sl@0:                                CentralityMap centrality,     // C_B
sl@0:                                EdgeCentralityMap edge_centrality_map,
sl@0:                                IncomingMap incoming, // P
sl@0:                                DistanceMap distance,         // d
sl@0:                                DependencyMap dependency,     // delta
sl@0:                                PathCountMap path_count,      // sigma
sl@0:                                VertexIndexMap vertex_index)
sl@0: {
sl@0:   detail::graph::brandes_unweighted_shortest_paths shortest_paths;
sl@0: 
sl@0:   detail::graph::brandes_betweenness_centrality_impl(g, centrality, 
sl@0:                                                      edge_centrality_map,
sl@0:                                                      incoming, distance,
sl@0:                                                      dependency, path_count,
sl@0:                                                      vertex_index, 
sl@0:                                                      shortest_paths);
sl@0: }
sl@0: 
sl@0: template<typename Graph, typename CentralityMap, typename EdgeCentralityMap, 
sl@0:          typename IncomingMap, typename DistanceMap, 
sl@0:          typename DependencyMap, typename PathCountMap, 
sl@0:          typename VertexIndexMap, typename WeightMap>    
sl@0: void 
sl@0: brandes_betweenness_centrality(const Graph& g, 
sl@0:                                CentralityMap centrality,     // C_B
sl@0:                                EdgeCentralityMap edge_centrality_map,
sl@0:                                IncomingMap incoming, // P
sl@0:                                DistanceMap distance,         // d
sl@0:                                DependencyMap dependency,     // delta
sl@0:                                PathCountMap path_count,      // sigma
sl@0:                                VertexIndexMap vertex_index,
sl@0:                                WeightMap weight_map)
sl@0: {
sl@0:   detail::graph::brandes_dijkstra_shortest_paths<WeightMap>
sl@0:     shortest_paths(weight_map);
sl@0: 
sl@0:   detail::graph::brandes_betweenness_centrality_impl(g, centrality, 
sl@0:                                                      edge_centrality_map,
sl@0:                                                      incoming, distance,
sl@0:                                                      dependency, path_count,
sl@0:                                                      vertex_index, 
sl@0:                                                      shortest_paths);
sl@0: }
sl@0: 
sl@0: namespace detail { namespace graph {
sl@0:   template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
sl@0:            typename WeightMap, typename VertexIndexMap>
sl@0:   void 
sl@0:   brandes_betweenness_centrality_dispatch2(const Graph& g,
sl@0:                                            CentralityMap centrality,
sl@0:                                            EdgeCentralityMap edge_centrality_map,
sl@0:                                            WeightMap weight_map,
sl@0:                                            VertexIndexMap vertex_index)
sl@0:   {
sl@0:     typedef typename graph_traits<Graph>::degree_size_type degree_size_type;
sl@0:     typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
sl@0:     typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
sl@0:     typedef typename mpl::if_c<(is_same<CentralityMap, 
sl@0:                                         dummy_property_map>::value),
sl@0:                                          EdgeCentralityMap, 
sl@0:                                CentralityMap>::type a_centrality_map;
sl@0:     typedef typename property_traits<a_centrality_map>::value_type 
sl@0:       centrality_type;
sl@0: 
sl@0:     typename graph_traits<Graph>::vertices_size_type V = num_vertices(g);
sl@0:     
sl@0:     std::vector<std::vector<edge_descriptor> > incoming(V);
sl@0:     std::vector<centrality_type> distance(V);
sl@0:     std::vector<centrality_type> dependency(V);
sl@0:     std::vector<degree_size_type> path_count(V);
sl@0: 
sl@0:     brandes_betweenness_centrality(
sl@0:       g, centrality, edge_centrality_map,
sl@0:       make_iterator_property_map(incoming.begin(), vertex_index),
sl@0:       make_iterator_property_map(distance.begin(), vertex_index),
sl@0:       make_iterator_property_map(dependency.begin(), vertex_index),
sl@0:       make_iterator_property_map(path_count.begin(), vertex_index),
sl@0:       vertex_index,
sl@0:       weight_map);
sl@0:   }
sl@0:   
sl@0: 
sl@0:   template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
sl@0:            typename VertexIndexMap>
sl@0:   void 
sl@0:   brandes_betweenness_centrality_dispatch2(const Graph& g,
sl@0:                                            CentralityMap centrality,
sl@0:                                            EdgeCentralityMap edge_centrality_map,
sl@0:                                            VertexIndexMap vertex_index)
sl@0:   {
sl@0:     typedef typename graph_traits<Graph>::degree_size_type degree_size_type;
sl@0:     typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
sl@0:     typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
sl@0:     typedef typename mpl::if_c<(is_same<CentralityMap, 
sl@0:                                         dummy_property_map>::value),
sl@0:                                          EdgeCentralityMap, 
sl@0:                                CentralityMap>::type a_centrality_map;
sl@0:     typedef typename property_traits<a_centrality_map>::value_type 
sl@0:       centrality_type;
sl@0: 
sl@0:     typename graph_traits<Graph>::vertices_size_type V = num_vertices(g);
sl@0:     
sl@0:     std::vector<std::vector<edge_descriptor> > incoming(V);
sl@0:     std::vector<centrality_type> distance(V);
sl@0:     std::vector<centrality_type> dependency(V);
sl@0:     std::vector<degree_size_type> path_count(V);
sl@0: 
sl@0:     brandes_betweenness_centrality(
sl@0:       g, centrality, edge_centrality_map,
sl@0:       make_iterator_property_map(incoming.begin(), vertex_index),
sl@0:       make_iterator_property_map(distance.begin(), vertex_index),
sl@0:       make_iterator_property_map(dependency.begin(), vertex_index),
sl@0:       make_iterator_property_map(path_count.begin(), vertex_index),
sl@0:       vertex_index);
sl@0:   }
sl@0: 
sl@0:   template<typename WeightMap>
sl@0:   struct brandes_betweenness_centrality_dispatch1
sl@0:   {
sl@0:     template<typename Graph, typename CentralityMap, 
sl@0:              typename EdgeCentralityMap, typename VertexIndexMap>
sl@0:     static void 
sl@0:     run(const Graph& g, CentralityMap centrality, 
sl@0:         EdgeCentralityMap edge_centrality_map, VertexIndexMap vertex_index,
sl@0:         WeightMap weight_map)
sl@0:     {
sl@0:       brandes_betweenness_centrality_dispatch2(g, centrality, edge_centrality_map,
sl@0:                                                weight_map, vertex_index);
sl@0:     }
sl@0:   };
sl@0: 
sl@0:   template<>
sl@0:   struct brandes_betweenness_centrality_dispatch1<error_property_not_found>
sl@0:   {
sl@0:     template<typename Graph, typename CentralityMap, 
sl@0:              typename EdgeCentralityMap, typename VertexIndexMap>
sl@0:     static void 
sl@0:     run(const Graph& g, CentralityMap centrality, 
sl@0:         EdgeCentralityMap edge_centrality_map, VertexIndexMap vertex_index,
sl@0:         error_property_not_found)
sl@0:     {
sl@0:       brandes_betweenness_centrality_dispatch2(g, centrality, edge_centrality_map,
sl@0:                                                vertex_index);
sl@0:     }
sl@0:   };
sl@0: 
sl@0: } } // end namespace detail::graph
sl@0: 
sl@0: template<typename Graph, typename Param, typename Tag, typename Rest>
sl@0: void 
sl@0: brandes_betweenness_centrality(const Graph& g, 
sl@0:                                const bgl_named_params<Param,Tag,Rest>& params)
sl@0: {
sl@0:   typedef bgl_named_params<Param,Tag,Rest> named_params;
sl@0: 
sl@0:   typedef typename property_value<named_params, edge_weight_t>::type ew;
sl@0:   detail::graph::brandes_betweenness_centrality_dispatch1<ew>::run(
sl@0:     g, 
sl@0:     choose_param(get_param(params, vertex_centrality), 
sl@0:                  dummy_property_map()),
sl@0:     choose_param(get_param(params, edge_centrality), 
sl@0:                  dummy_property_map()),
sl@0:     choose_const_pmap(get_param(params, vertex_index), g, vertex_index),
sl@0:     get_param(params, edge_weight));
sl@0: }
sl@0: 
sl@0: template<typename Graph, typename CentralityMap>
sl@0: void 
sl@0: brandes_betweenness_centrality(const Graph& g, CentralityMap centrality)
sl@0: {
sl@0:   detail::graph::brandes_betweenness_centrality_dispatch2(
sl@0:     g, centrality, dummy_property_map(), get(vertex_index, g));
sl@0: }
sl@0: 
sl@0: template<typename Graph, typename CentralityMap, typename EdgeCentralityMap>
sl@0: void 
sl@0: brandes_betweenness_centrality(const Graph& g, CentralityMap centrality,
sl@0:                                EdgeCentralityMap edge_centrality_map)
sl@0: {
sl@0:   detail::graph::brandes_betweenness_centrality_dispatch2(
sl@0:     g, centrality, edge_centrality_map, get(vertex_index, g));
sl@0: }
sl@0: 
sl@0: /**
sl@0:  * Converts "absolute" betweenness centrality (as computed by the
sl@0:  * brandes_betweenness_centrality algorithm) in the centrality map
sl@0:  * into "relative" centrality. The result is placed back into the
sl@0:  * given centrality map.
sl@0:  */
sl@0: template<typename Graph, typename CentralityMap>
sl@0: void 
sl@0: relative_betweenness_centrality(const Graph& g, CentralityMap centrality)
sl@0: {
sl@0:   typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
sl@0:   typedef typename property_traits<CentralityMap>::value_type centrality_type;
sl@0: 
sl@0:   typename graph_traits<Graph>::vertices_size_type n = num_vertices(g);
sl@0:   centrality_type factor = centrality_type(2)/centrality_type(n*n - 3*n + 2);
sl@0:   vertex_iterator v, v_end;
sl@0:   for (tie(v, v_end) = vertices(g); v != v_end; ++v) {
sl@0:     put(centrality, *v, factor * get(centrality, *v));
sl@0:   }
sl@0: }
sl@0: 
sl@0: // Compute the central point dominance of a graph.
sl@0: template<typename Graph, typename CentralityMap>
sl@0: typename property_traits<CentralityMap>::value_type
sl@0: central_point_dominance(const Graph& g, CentralityMap centrality)
sl@0: {
sl@0:   using std::max;
sl@0: 
sl@0:   typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
sl@0:   typedef typename property_traits<CentralityMap>::value_type centrality_type;
sl@0: 
sl@0:   typename graph_traits<Graph>::vertices_size_type n = num_vertices(g);
sl@0: 
sl@0:   // Find max centrality
sl@0:   centrality_type max_centrality(0);
sl@0:   vertex_iterator v, v_end;
sl@0:   for (tie(v, v_end) = vertices(g); v != v_end; ++v) {
sl@0:     max_centrality = (max)(max_centrality, get(centrality, *v));
sl@0:   }
sl@0: 
sl@0:   // Compute central point dominance
sl@0:   centrality_type sum(0);
sl@0:   for (tie(v, v_end) = vertices(g); v != v_end; ++v) {
sl@0:     sum += (max_centrality - get(centrality, *v));
sl@0:   }
sl@0:   return sum/(n-1);
sl@0: }
sl@0: 
sl@0: } // end namespace boost
sl@0: 
sl@0: #endif // BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP