betweenness_centrality.hpp

CGAL is a collaborative effort of several sites in Europe and Israel. The goal is to make the most i

    // Initialize centrality
    init_centrality_map(vertices(g), centrality);
    init_centrality_map(edges(g), edge_centrality_map);

    std::stack<vertex_descriptor> ordered_vertices;
    vertex_iterator s, s_end;
    for (tie(s, s_end) = vertices(g); s != s_end; ++s) {
      // Initialize for this iteration
      vertex_iterator w, w_end;
      for (tie(w, w_end) = vertices(g); w != w_end; ++w) {
        incoming[*w].clear();
        put(path_count, *w, 0);
        put(dependency, *w, 0);
      }
      put(path_count, *s, 1);
      
      // Execute the shortest paths algorithm. This will be either
      // Dijkstra's algorithm or a customized breadth-first search,
      // depending on whether the graph is weighted or unweighted.
      shortest_paths(g, *s, ordered_vertices, incoming, distance,
                     path_count, vertex_index);
      
      while (!ordered_vertices.empty()) {
        vertex_descriptor w = ordered_vertices.top();
        ordered_vertices.pop();
        
        typedef typename property_traits<IncomingMap>::value_type
          incoming_type;
        typedef typename incoming_type::iterator incoming_iterator;
        typedef typename property_traits<DependencyMap>::value_type 
          dependency_type;
        
        for (incoming_iterator vw = incoming[w].begin();
             vw != incoming[w].end(); ++vw) {
          vertex_descriptor v = source(*vw, g);
          dependency_type factor = dependency_type(get(path_count, v))
            / dependency_type(get(path_count, w));
          factor *= (dependency_type(1) + get(dependency, w));
          put(dependency, v, get(dependency, v) + factor);
          update_centrality(edge_centrality_map, *vw, factor);
        }
        
        if (w != *s) {
          update_centrality(centrality, w, get(dependency, w));
        }
      }
    }

    typedef typename graph_traits<Graph>::directed_category directed_category;
    const bool is_undirected = 
      is_convertible<directed_category*, undirected_tag*>::value;
    if (is_undirected) {
      divide_centrality_by_two(vertices(g), centrality);
      divide_centrality_by_two(edges(g), edge_centrality_map);
    }
  }

} } // end namespace detail::graph

template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
         typename IncomingMap, typename DistanceMap, 
         typename DependencyMap, typename PathCountMap, 
         typename VertexIndexMap>
void 
brandes_betweenness_centrality(const Graph& g, 
                               CentralityMap centrality,     // C_B
                               EdgeCentralityMap edge_centrality_map,
                               IncomingMap incoming, // P
                               DistanceMap distance,         // d
                               DependencyMap dependency,     // delta
                               PathCountMap path_count,      // sigma
                               VertexIndexMap vertex_index)
{
  detail::graph::brandes_unweighted_shortest_paths shortest_paths;

  detail::graph::brandes_betweenness_centrality_impl(g, centrality, 
                                                     edge_centrality_map,
                                                     incoming, distance,
                                                     dependency, path_count,
                                                     vertex_index, 
                                                     shortest_paths);
}

template<typename Graph, typename CentralityMap, typename EdgeCentralityMap, 
         typename IncomingMap, typename DistanceMap, 
         typename DependencyMap, typename PathCountMap, 
         typename VertexIndexMap, typename WeightMap>    
void 
brandes_betweenness_centrality(const Graph& g, 
                               CentralityMap centrality,     // C_B
                               EdgeCentralityMap edge_centrality_map,
                               IncomingMap incoming, // P
                               DistanceMap distance,         // d
                               DependencyMap dependency,     // delta
                               PathCountMap path_count,      // sigma
                               VertexIndexMap vertex_index,
                               WeightMap weight_map)
{
  detail::graph::brandes_dijkstra_shortest_paths<WeightMap>
    shortest_paths(weight_map);

  detail::graph::brandes_betweenness_centrality_impl(g, centrality, 
                                                     edge_centrality_map,
                                                     incoming, distance,
                                                     dependency, path_count,
                                                     vertex_index, 
                                                     shortest_paths);
}

namespace detail { namespace graph {
  template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
           typename WeightMap, typename VertexIndexMap>
  void 
  brandes_betweenness_centrality_dispatch2(const Graph& g,
                                           CentralityMap centrality,
                                           EdgeCentralityMap edge_centrality_map,
                                           WeightMap weight_map,
                                           VertexIndexMap vertex_index)
  {
    typedef typename graph_traits<Graph>::degree_size_type degree_size_type;
    typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
    typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
    typedef typename mpl::if_c<(is_same<CentralityMap, 
                                        dummy_property_map>::value),
                                         EdgeCentralityMap, 
                               CentralityMap>::type a_centrality_map;
    typedef typename property_traits<a_centrality_map>::value_type 
      centrality_type;

    typename graph_traits<Graph>::vertices_size_type V = num_vertices(g);
    
    std::vector<std::vector<edge_descriptor> > incoming(V);
    std::vector<centrality_type> distance(V);
    std::vector<centrality_type> dependency(V);
    std::vector<degree_size_type> path_count(V);

    brandes_betweenness_centrality(
      g, centrality, edge_centrality_map,
      make_iterator_property_map(incoming.begin(), vertex_index),
      make_iterator_property_map(distance.begin(), vertex_index),
      make_iterator_property_map(dependency.begin(), vertex_index),
      make_iterator_property_map(path_count.begin(), vertex_index),
      vertex_index,
      weight_map);
  }
  

  template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
           typename VertexIndexMap>
  void 
  brandes_betweenness_centrality_dispatch2(const Graph& g,
                                           CentralityMap centrality,
                                           EdgeCentralityMap edge_centrality_map,
                                           VertexIndexMap vertex_index)
  {
    typedef typename graph_traits<Graph>::degree_size_type degree_size_type;
    typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
    typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
    typedef typename mpl::if_c<(is_same<CentralityMap, 
                                        dummy_property_map>::value),
                                         EdgeCentralityMap, 
                               CentralityMap>::type a_centrality_map;
    typedef typename property_traits<a_centrality_map>::value_type 
      centrality_type;

    typename graph_traits<Graph>::vertices_size_type V = num_vertices(g);
    
    std::vector<std::vector<edge_descriptor> > incoming(V);
    std::vector<centrality_type> distance(V);
    std::vector<centrality_type> dependency(V);
    std::vector<degree_size_type> path_count(V);

    brandes_betweenness_centrality(
      g, centrality, edge_centrality_map,
      make_iterator_property_map(incoming.begin(), vertex_index),
      make_iterator_property_map(distance.begin(), vertex_index),
      make_iterator_property_map(dependency.begin(), vertex_index),
      make_iterator_property_map(path_count.begin(), vertex_index),
      vertex_index);
  }

  template<typename WeightMap>
  struct brandes_betweenness_centrality_dispatch1
  {
    template<typename Graph, typename CentralityMap, 
             typename EdgeCentralityMap, typename VertexIndexMap>
    static void 
    run(const Graph& g, CentralityMap centrality, 
        EdgeCentralityMap edge_centrality_map, VertexIndexMap vertex_index,
        WeightMap weight_map)
    {
      brandes_betweenness_centrality_dispatch2(g, centrality, edge_centrality_map,
                                               weight_map, vertex_index);
    }
  };

  template<>
  struct brandes_betweenness_centrality_dispatch1<error_property_not_found>
  {
    template<typename Graph, typename CentralityMap, 
             typename EdgeCentralityMap, typename VertexIndexMap>
    static void 
    run(const Graph& g, CentralityMap centrality, 
        EdgeCentralityMap edge_centrality_map, VertexIndexMap vertex_index,
        error_property_not_found)
    {
      brandes_betweenness_centrality_dispatch2(g, centrality, edge_centrality_map,
                                               vertex_index);
    }
  };

} } // end namespace detail::graph

template<typename Graph, typename Param, typename Tag, typename Rest>
void 
brandes_betweenness_centrality(const Graph& g, 
                               const bgl_named_params<Param,Tag,Rest>& params)
{
  typedef bgl_named_params<Param,Tag,Rest> named_params;

  typedef typename property_value<named_params, edge_weight_t>::type ew;
  detail::graph::brandes_betweenness_centrality_dispatch1<ew>::run(
    g, 
    choose_param(get_param(params, vertex_centrality), 
                 dummy_property_map()),
    choose_param(get_param(params, edge_centrality), 
                 dummy_property_map()),
    choose_const_pmap(get_param(params, vertex_index), g, vertex_index),
    get_param(params, edge_weight));
}

template<typename Graph, typename CentralityMap>
void 
brandes_betweenness_centrality(const Graph& g, CentralityMap centrality)
{
  detail::graph::brandes_betweenness_centrality_dispatch2(
    g, centrality, dummy_property_map(), get(vertex_index, g));
}

template<typename Graph, typename CentralityMap, typename EdgeCentralityMap>
void 
brandes_betweenness_centrality(const Graph& g, CentralityMap centrality,
                               EdgeCentralityMap edge_centrality_map)
{
  detail::graph::brandes_betweenness_centrality_dispatch2(
    g, centrality, edge_centrality_map, get(vertex_index, g));
}

/**
 * Converts "absolute" betweenness centrality (as computed by the
 * brandes_betweenness_centrality algorithm) in the centrality map
 * into "relative" centrality. The result is placed back into the
 * given centrality map.
 */
template<typename Graph, typename CentralityMap>
void 
relative_betweenness_centrality(const Graph& g, CentralityMap centrality)
{
  typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
  typedef typename property_traits<CentralityMap>::value_type centrality_type;

  typename graph_traits<Graph>::vertices_size_type n = num_vertices(g);
  centrality_type factor = centrality_type(2)/centrality_type(n*n - 3*n + 2);
  vertex_iterator v, v_end;
  for (tie(v, v_end) = vertices(g); v != v_end; ++v) {
    put(centrality, *v, factor * get(centrality, *v));
  }
}

// Compute the central point dominance of a graph.
template<typename Graph, typename CentralityMap>
typename property_traits<CentralityMap>::value_type
central_point_dominance(const Graph& g, CentralityMap centrality)
{
  using std::max;

  typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
  typedef typename property_traits<CentralityMap>::value_type centrality_type;

  typename graph_traits<Graph>::vertices_size_type n = num_vertices(g);

  // Find max centrality
  centrality_type max_centrality(0);
  vertex_iterator v, v_end;
  for (tie(v, v_end) = vertices(g); v != v_end; ++v) {
    max_centrality = max(max_centrality, get(centrality, *v));
  }

  // Compute central point dominance
  centrality_type sum(0);
  for (tie(v, v_end) = vertices(g); v != v_end; ++v) {
    sum += (max_centrality - get(centrality, *v));
  }
  return sum/(n-1);
}

} // end namespace boost

#endif // BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP