epoc32/include/stdapis/boost/graph/betweenness_centrality.hpp
branchSymbian2
changeset 2 2fe1408b6811
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/epoc32/include/stdapis/boost/graph/betweenness_centrality.hpp	Tue Mar 16 16:12:26 2010 +0000
     1.3 @@ -0,0 +1,599 @@
     1.4 +// Copyright 2004 The Trustees of Indiana University.
     1.5 +
     1.6 +// Distributed under the Boost Software License, Version 1.0.
     1.7 +// (See accompanying file LICENSE_1_0.txt or copy at
     1.8 +// http://www.boost.org/LICENSE_1_0.txt)
     1.9 +
    1.10 +//  Authors: Douglas Gregor
    1.11 +//           Andrew Lumsdaine
    1.12 +#ifndef BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP
    1.13 +#define BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP
    1.14 +
    1.15 +#include <stack>
    1.16 +#include <vector>
    1.17 +#include <boost/graph/dijkstra_shortest_paths.hpp>
    1.18 +#include <boost/graph/breadth_first_search.hpp>
    1.19 +#include <boost/graph/relax.hpp>
    1.20 +#include <boost/graph/graph_traits.hpp>
    1.21 +#include <boost/tuple/tuple.hpp>
    1.22 +#include <boost/type_traits/is_convertible.hpp>
    1.23 +#include <boost/type_traits/is_same.hpp>
    1.24 +#include <boost/mpl/if.hpp>
    1.25 +#include <boost/property_map.hpp>
    1.26 +#include <boost/graph/named_function_params.hpp>
    1.27 +#include <algorithm>
    1.28 +
    1.29 +namespace boost {
    1.30 +
    1.31 +namespace detail { namespace graph {
    1.32 +
    1.33 +  /**
    1.34 +   * Customized visitor passed to Dijkstra's algorithm by Brandes'
    1.35 +   * betweenness centrality algorithm. This visitor is responsible for
    1.36 +   * keeping track of the order in which vertices are discovered, the
    1.37 +   * predecessors on the shortest path(s) to a vertex, and the number
    1.38 +   * of shortest paths.
    1.39 +   */
    1.40 +  template<typename Graph, typename WeightMap, typename IncomingMap,
    1.41 +           typename DistanceMap, typename PathCountMap>
    1.42 +  struct brandes_dijkstra_visitor : public bfs_visitor<>
    1.43 +  {
    1.44 +    typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
    1.45 +    typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
    1.46 +
    1.47 +    brandes_dijkstra_visitor(std::stack<vertex_descriptor>& ordered_vertices,
    1.48 +                             WeightMap weight,
    1.49 +                             IncomingMap incoming,
    1.50 +                             DistanceMap distance,
    1.51 +                             PathCountMap path_count)
    1.52 +      : ordered_vertices(ordered_vertices), weight(weight), 
    1.53 +        incoming(incoming), distance(distance),
    1.54 +        path_count(path_count)
    1.55 +    { }
    1.56 +
    1.57 +    /**
    1.58 +     * Whenever an edge e = (v, w) is relaxed, the incoming edge list
    1.59 +     * for w is set to {(v, w)} and the shortest path count of w is set to
    1.60 +     * the number of paths that reach {v}.
    1.61 +     */
    1.62 +    void edge_relaxed(edge_descriptor e, const Graph& g) 
    1.63 +    { 
    1.64 +      vertex_descriptor v = source(e, g), w = target(e, g);
    1.65 +      incoming[w].clear();
    1.66 +      incoming[w].push_back(e);
    1.67 +      put(path_count, w, get(path_count, v));
    1.68 +    }
    1.69 +
    1.70 +    /**
    1.71 +     * If an edge e = (v, w) was not relaxed, it may still be the case
    1.72 +     * that we've found more equally-short paths, so include {(v, w)} in the
    1.73 +     * incoming edges of w and add all of the shortest paths to v to the
    1.74 +     * shortest path count of w.
    1.75 +     */
    1.76 +    void edge_not_relaxed(edge_descriptor e, const Graph& g) 
    1.77 +    {
    1.78 +      typedef typename property_traits<WeightMap>::value_type weight_type;
    1.79 +      typedef typename property_traits<DistanceMap>::value_type distance_type;
    1.80 +      vertex_descriptor v = source(e, g), w = target(e, g);
    1.81 +      distance_type d_v = get(distance, v), d_w = get(distance, w);
    1.82 +      weight_type w_e = get(weight, e);
    1.83 +
    1.84 +      closed_plus<distance_type> combine;
    1.85 +      if (d_w == combine(d_v, w_e)) {
    1.86 +        put(path_count, w, get(path_count, w) + get(path_count, v));
    1.87 +        incoming[w].push_back(e);
    1.88 +      }
    1.89 +    }
    1.90 +
    1.91 +    /// Keep track of vertices as they are reached
    1.92 +    void examine_vertex(vertex_descriptor w, const Graph&) 
    1.93 +    { 
    1.94 +      ordered_vertices.push(w);
    1.95 +    }
    1.96 +
    1.97 +  private:
    1.98 +    std::stack<vertex_descriptor>& ordered_vertices;
    1.99 +    WeightMap weight;
   1.100 +    IncomingMap incoming;
   1.101 +    DistanceMap distance;
   1.102 +    PathCountMap path_count;
   1.103 +  };
   1.104 +
   1.105 +  /**
   1.106 +   * Function object that calls Dijkstra's shortest paths algorithm
   1.107 +   * using the Dijkstra visitor for the Brandes betweenness centrality
   1.108 +   * algorithm.
   1.109 +   */
   1.110 +  template<typename WeightMap>
   1.111 +  struct brandes_dijkstra_shortest_paths
   1.112 +  {
   1.113 +    brandes_dijkstra_shortest_paths(WeightMap weight_map) 
   1.114 +      : weight_map(weight_map) { }
   1.115 +
   1.116 +    template<typename Graph, typename IncomingMap, typename DistanceMap, 
   1.117 +             typename PathCountMap, typename VertexIndexMap>
   1.118 +    void 
   1.119 +    operator()(Graph& g, 
   1.120 +               typename graph_traits<Graph>::vertex_descriptor s,
   1.121 +               std::stack<typename graph_traits<Graph>::vertex_descriptor>& ov,
   1.122 +               IncomingMap incoming,
   1.123 +               DistanceMap distance,
   1.124 +               PathCountMap path_count,
   1.125 +               VertexIndexMap vertex_index)
   1.126 +    {
   1.127 +      typedef brandes_dijkstra_visitor<Graph, WeightMap, IncomingMap, 
   1.128 +                                       DistanceMap, PathCountMap> visitor_type;
   1.129 +      visitor_type visitor(ov, weight_map, incoming, distance, path_count);
   1.130 +
   1.131 +      dijkstra_shortest_paths(g, s, 
   1.132 +                              boost::weight_map(weight_map)
   1.133 +                              .vertex_index_map(vertex_index)
   1.134 +                              .distance_map(distance)
   1.135 +                              .visitor(visitor));
   1.136 +    }
   1.137 +
   1.138 +  private:
   1.139 +    WeightMap weight_map;
   1.140 +  };
   1.141 +
   1.142 +  /**
   1.143 +   * Function object that invokes breadth-first search for the
   1.144 +   * unweighted form of the Brandes betweenness centrality algorithm.
   1.145 +   */
   1.146 +  struct brandes_unweighted_shortest_paths
   1.147 +  {
   1.148 +    /**
   1.149 +     * Customized visitor passed to breadth-first search, which
   1.150 +     * records predecessor and the number of shortest paths to each
   1.151 +     * vertex.
   1.152 +     */
   1.153 +    template<typename Graph, typename IncomingMap, typename DistanceMap, 
   1.154 +             typename PathCountMap>
   1.155 +    struct visitor_type : public bfs_visitor<>
   1.156 +    {
   1.157 +      typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
   1.158 +      typedef typename graph_traits<Graph>::vertex_descriptor 
   1.159 +        vertex_descriptor;
   1.160 +      
   1.161 +      visitor_type(IncomingMap incoming, DistanceMap distance, 
   1.162 +                   PathCountMap path_count, 
   1.163 +                   std::stack<vertex_descriptor>& ordered_vertices)
   1.164 +        : incoming(incoming), distance(distance), 
   1.165 +          path_count(path_count), ordered_vertices(ordered_vertices) { }
   1.166 +
   1.167 +      /// Keep track of vertices as they are reached
   1.168 +      void examine_vertex(vertex_descriptor v, Graph&)
   1.169 +      {
   1.170 +        ordered_vertices.push(v);
   1.171 +      }
   1.172 +
   1.173 +      /**
   1.174 +       * Whenever an edge e = (v, w) is labelled a tree edge, the
   1.175 +       * incoming edge list for w is set to {(v, w)} and the shortest
   1.176 +       * path count of w is set to the number of paths that reach {v}.
   1.177 +       */
   1.178 +      void tree_edge(edge_descriptor e, Graph& g)
   1.179 +      {
   1.180 +        vertex_descriptor v = source(e, g);
   1.181 +        vertex_descriptor w = target(e, g);
   1.182 +        put(distance, w, get(distance, v) + 1);
   1.183 +        
   1.184 +        put(path_count, w, get(path_count, v));
   1.185 +        incoming[w].push_back(e);
   1.186 +      }
   1.187 +
   1.188 +      /**
   1.189 +       * If an edge e = (v, w) is not a tree edge, it may still be the
   1.190 +       * case that we've found more equally-short paths, so include (v, w)
   1.191 +       * in the incoming edge list of w and add all of the shortest
   1.192 +       * paths to v to the shortest path count of w.
   1.193 +       */
   1.194 +      void non_tree_edge(edge_descriptor e, Graph& g)
   1.195 +      {
   1.196 +        vertex_descriptor v = source(e, g);
   1.197 +        vertex_descriptor w = target(e, g);
   1.198 +        if (get(distance, w) == get(distance, v) + 1) {
   1.199 +          put(path_count, w, get(path_count, w) + get(path_count, v));
   1.200 +          incoming[w].push_back(e);
   1.201 +        }
   1.202 +      }
   1.203 +
   1.204 +    private:
   1.205 +      IncomingMap incoming;
   1.206 +      DistanceMap distance;
   1.207 +      PathCountMap path_count;
   1.208 +      std::stack<vertex_descriptor>& ordered_vertices;
   1.209 +    };
   1.210 +
   1.211 +    template<typename Graph, typename IncomingMap, typename DistanceMap, 
   1.212 +             typename PathCountMap, typename VertexIndexMap>
   1.213 +    void 
   1.214 +    operator()(Graph& g, 
   1.215 +               typename graph_traits<Graph>::vertex_descriptor s,
   1.216 +               std::stack<typename graph_traits<Graph>::vertex_descriptor>& ov,
   1.217 +               IncomingMap incoming,
   1.218 +               DistanceMap distance,
   1.219 +               PathCountMap path_count,
   1.220 +               VertexIndexMap vertex_index)
   1.221 +    {
   1.222 +      typedef typename graph_traits<Graph>::vertex_descriptor
   1.223 +        vertex_descriptor;
   1.224 +
   1.225 +      visitor_type<Graph, IncomingMap, DistanceMap, PathCountMap>
   1.226 +        visitor(incoming, distance, path_count, ov);
   1.227 +      
   1.228 +      std::vector<default_color_type> 
   1.229 +        colors(num_vertices(g), color_traits<default_color_type>::white());
   1.230 +      boost::queue<vertex_descriptor> Q;
   1.231 +      breadth_first_visit(g, s, Q, visitor, 
   1.232 +                          make_iterator_property_map(colors.begin(), 
   1.233 +                                                     vertex_index));
   1.234 +    }
   1.235 +  };
   1.236 +
   1.237 +  // When the edge centrality map is a dummy property map, no
   1.238 +  // initialization is needed.
   1.239 +  template<typename Iter>
   1.240 +  inline void 
   1.241 +  init_centrality_map(std::pair<Iter, Iter>, dummy_property_map) { }
   1.242 +
   1.243 +  // When we have a real edge centrality map, initialize all of the
   1.244 +  // centralities to zero.
   1.245 +  template<typename Iter, typename Centrality>
   1.246 +  void 
   1.247 +  init_centrality_map(std::pair<Iter, Iter> keys, Centrality centrality_map)
   1.248 +  {
   1.249 +    typedef typename property_traits<Centrality>::value_type 
   1.250 +      centrality_type;
   1.251 +    while (keys.first != keys.second) {
   1.252 +      put(centrality_map, *keys.first, centrality_type(0));
   1.253 +      ++keys.first;
   1.254 +    }
   1.255 +  }
   1.256 +
   1.257 +  // When the edge centrality map is a dummy property map, no update
   1.258 +  // is performed.
   1.259 +  template<typename Key, typename T>
   1.260 +  inline void 
   1.261 +  update_centrality(dummy_property_map, const Key&, const T&) { }
   1.262 +
   1.263 +  // When we have a real edge centrality map, add the value to the map
   1.264 +  template<typename CentralityMap, typename Key, typename T>
   1.265 +  inline void 
   1.266 +  update_centrality(CentralityMap centrality_map, Key k, const T& x)
   1.267 +  { put(centrality_map, k, get(centrality_map, k) + x); }
   1.268 +
   1.269 +  template<typename Iter>
   1.270 +  inline void 
   1.271 +  divide_centrality_by_two(std::pair<Iter, Iter>, dummy_property_map) {}
   1.272 +
   1.273 +  template<typename Iter, typename CentralityMap>
   1.274 +  inline void
   1.275 +  divide_centrality_by_two(std::pair<Iter, Iter> keys, 
   1.276 +                           CentralityMap centrality_map)
   1.277 +  {
   1.278 +    typename property_traits<CentralityMap>::value_type two(2);
   1.279 +    while (keys.first != keys.second) {
   1.280 +      put(centrality_map, *keys.first, get(centrality_map, *keys.first) / two);
   1.281 +      ++keys.first;
   1.282 +    }
   1.283 +  }
   1.284 +
   1.285 +  template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
   1.286 +           typename IncomingMap, typename DistanceMap, 
   1.287 +           typename DependencyMap, typename PathCountMap,
   1.288 +           typename VertexIndexMap, typename ShortestPaths>
   1.289 +  void 
   1.290 +  brandes_betweenness_centrality_impl(const Graph& g, 
   1.291 +                                      CentralityMap centrality,     // C_B
   1.292 +                                      EdgeCentralityMap edge_centrality_map,
   1.293 +                                      IncomingMap incoming, // P
   1.294 +                                      DistanceMap distance,         // d
   1.295 +                                      DependencyMap dependency,     // delta
   1.296 +                                      PathCountMap path_count,      // sigma
   1.297 +                                      VertexIndexMap vertex_index,
   1.298 +                                      ShortestPaths shortest_paths)
   1.299 +  {
   1.300 +    typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
   1.301 +    typedef typename graph_traits<Graph>::edge_iterator edge_iterator;
   1.302 +    typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
   1.303 +
   1.304 +    // Initialize centrality
   1.305 +    init_centrality_map(vertices(g), centrality);
   1.306 +    init_centrality_map(edges(g), edge_centrality_map);
   1.307 +
   1.308 +    std::stack<vertex_descriptor> ordered_vertices;
   1.309 +    vertex_iterator s, s_end;
   1.310 +    for (tie(s, s_end) = vertices(g); s != s_end; ++s) {
   1.311 +      // Initialize for this iteration
   1.312 +      vertex_iterator w, w_end;
   1.313 +      for (tie(w, w_end) = vertices(g); w != w_end; ++w) {
   1.314 +        incoming[*w].clear();
   1.315 +        put(path_count, *w, 0);
   1.316 +        put(dependency, *w, 0);
   1.317 +      }
   1.318 +      put(path_count, *s, 1);
   1.319 +      
   1.320 +      // Execute the shortest paths algorithm. This will be either
   1.321 +      // Dijkstra's algorithm or a customized breadth-first search,
   1.322 +      // depending on whether the graph is weighted or unweighted.
   1.323 +      shortest_paths(g, *s, ordered_vertices, incoming, distance,
   1.324 +                     path_count, vertex_index);
   1.325 +      
   1.326 +      while (!ordered_vertices.empty()) {
   1.327 +        vertex_descriptor w = ordered_vertices.top();
   1.328 +        ordered_vertices.pop();
   1.329 +        
   1.330 +        typedef typename property_traits<IncomingMap>::value_type
   1.331 +          incoming_type;
   1.332 +        typedef typename incoming_type::iterator incoming_iterator;
   1.333 +        typedef typename property_traits<DependencyMap>::value_type 
   1.334 +          dependency_type;
   1.335 +        
   1.336 +        for (incoming_iterator vw = incoming[w].begin();
   1.337 +             vw != incoming[w].end(); ++vw) {
   1.338 +          vertex_descriptor v = source(*vw, g);
   1.339 +          dependency_type factor = dependency_type(get(path_count, v))
   1.340 +            / dependency_type(get(path_count, w));
   1.341 +          factor *= (dependency_type(1) + get(dependency, w));
   1.342 +          put(dependency, v, get(dependency, v) + factor);
   1.343 +          update_centrality(edge_centrality_map, *vw, factor);
   1.344 +        }
   1.345 +        
   1.346 +        if (w != *s) {
   1.347 +          update_centrality(centrality, w, get(dependency, w));
   1.348 +        }
   1.349 +      }
   1.350 +    }
   1.351 +
   1.352 +    typedef typename graph_traits<Graph>::directed_category directed_category;
   1.353 +    const bool is_undirected = 
   1.354 +      is_convertible<directed_category*, undirected_tag*>::value;
   1.355 +    if (is_undirected) {
   1.356 +      divide_centrality_by_two(vertices(g), centrality);
   1.357 +      divide_centrality_by_two(edges(g), edge_centrality_map);
   1.358 +    }
   1.359 +  }
   1.360 +
   1.361 +} } // end namespace detail::graph
   1.362 +
   1.363 +template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
   1.364 +         typename IncomingMap, typename DistanceMap, 
   1.365 +         typename DependencyMap, typename PathCountMap, 
   1.366 +         typename VertexIndexMap>
   1.367 +void 
   1.368 +brandes_betweenness_centrality(const Graph& g, 
   1.369 +                               CentralityMap centrality,     // C_B
   1.370 +                               EdgeCentralityMap edge_centrality_map,
   1.371 +                               IncomingMap incoming, // P
   1.372 +                               DistanceMap distance,         // d
   1.373 +                               DependencyMap dependency,     // delta
   1.374 +                               PathCountMap path_count,      // sigma
   1.375 +                               VertexIndexMap vertex_index)
   1.376 +{
   1.377 +  detail::graph::brandes_unweighted_shortest_paths shortest_paths;
   1.378 +
   1.379 +  detail::graph::brandes_betweenness_centrality_impl(g, centrality, 
   1.380 +                                                     edge_centrality_map,
   1.381 +                                                     incoming, distance,
   1.382 +                                                     dependency, path_count,
   1.383 +                                                     vertex_index, 
   1.384 +                                                     shortest_paths);
   1.385 +}
   1.386 +
   1.387 +template<typename Graph, typename CentralityMap, typename EdgeCentralityMap, 
   1.388 +         typename IncomingMap, typename DistanceMap, 
   1.389 +         typename DependencyMap, typename PathCountMap, 
   1.390 +         typename VertexIndexMap, typename WeightMap>    
   1.391 +void 
   1.392 +brandes_betweenness_centrality(const Graph& g, 
   1.393 +                               CentralityMap centrality,     // C_B
   1.394 +                               EdgeCentralityMap edge_centrality_map,
   1.395 +                               IncomingMap incoming, // P
   1.396 +                               DistanceMap distance,         // d
   1.397 +                               DependencyMap dependency,     // delta
   1.398 +                               PathCountMap path_count,      // sigma
   1.399 +                               VertexIndexMap vertex_index,
   1.400 +                               WeightMap weight_map)
   1.401 +{
   1.402 +  detail::graph::brandes_dijkstra_shortest_paths<WeightMap>
   1.403 +    shortest_paths(weight_map);
   1.404 +
   1.405 +  detail::graph::brandes_betweenness_centrality_impl(g, centrality, 
   1.406 +                                                     edge_centrality_map,
   1.407 +                                                     incoming, distance,
   1.408 +                                                     dependency, path_count,
   1.409 +                                                     vertex_index, 
   1.410 +                                                     shortest_paths);
   1.411 +}
   1.412 +
   1.413 +namespace detail { namespace graph {
   1.414 +  template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
   1.415 +           typename WeightMap, typename VertexIndexMap>
   1.416 +  void 
   1.417 +  brandes_betweenness_centrality_dispatch2(const Graph& g,
   1.418 +                                           CentralityMap centrality,
   1.419 +                                           EdgeCentralityMap edge_centrality_map,
   1.420 +                                           WeightMap weight_map,
   1.421 +                                           VertexIndexMap vertex_index)
   1.422 +  {
   1.423 +    typedef typename graph_traits<Graph>::degree_size_type degree_size_type;
   1.424 +    typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
   1.425 +    typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
   1.426 +    typedef typename mpl::if_c<(is_same<CentralityMap, 
   1.427 +                                        dummy_property_map>::value),
   1.428 +                                         EdgeCentralityMap, 
   1.429 +                               CentralityMap>::type a_centrality_map;
   1.430 +    typedef typename property_traits<a_centrality_map>::value_type 
   1.431 +      centrality_type;
   1.432 +
   1.433 +    typename graph_traits<Graph>::vertices_size_type V = num_vertices(g);
   1.434 +    
   1.435 +    std::vector<std::vector<edge_descriptor> > incoming(V);
   1.436 +    std::vector<centrality_type> distance(V);
   1.437 +    std::vector<centrality_type> dependency(V);
   1.438 +    std::vector<degree_size_type> path_count(V);
   1.439 +
   1.440 +    brandes_betweenness_centrality(
   1.441 +      g, centrality, edge_centrality_map,
   1.442 +      make_iterator_property_map(incoming.begin(), vertex_index),
   1.443 +      make_iterator_property_map(distance.begin(), vertex_index),
   1.444 +      make_iterator_property_map(dependency.begin(), vertex_index),
   1.445 +      make_iterator_property_map(path_count.begin(), vertex_index),
   1.446 +      vertex_index,
   1.447 +      weight_map);
   1.448 +  }
   1.449 +  
   1.450 +
   1.451 +  template<typename Graph, typename CentralityMap, typename EdgeCentralityMap,
   1.452 +           typename VertexIndexMap>
   1.453 +  void 
   1.454 +  brandes_betweenness_centrality_dispatch2(const Graph& g,
   1.455 +                                           CentralityMap centrality,
   1.456 +                                           EdgeCentralityMap edge_centrality_map,
   1.457 +                                           VertexIndexMap vertex_index)
   1.458 +  {
   1.459 +    typedef typename graph_traits<Graph>::degree_size_type degree_size_type;
   1.460 +    typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
   1.461 +    typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
   1.462 +    typedef typename mpl::if_c<(is_same<CentralityMap, 
   1.463 +                                        dummy_property_map>::value),
   1.464 +                                         EdgeCentralityMap, 
   1.465 +                               CentralityMap>::type a_centrality_map;
   1.466 +    typedef typename property_traits<a_centrality_map>::value_type 
   1.467 +      centrality_type;
   1.468 +
   1.469 +    typename graph_traits<Graph>::vertices_size_type V = num_vertices(g);
   1.470 +    
   1.471 +    std::vector<std::vector<edge_descriptor> > incoming(V);
   1.472 +    std::vector<centrality_type> distance(V);
   1.473 +    std::vector<centrality_type> dependency(V);
   1.474 +    std::vector<degree_size_type> path_count(V);
   1.475 +
   1.476 +    brandes_betweenness_centrality(
   1.477 +      g, centrality, edge_centrality_map,
   1.478 +      make_iterator_property_map(incoming.begin(), vertex_index),
   1.479 +      make_iterator_property_map(distance.begin(), vertex_index),
   1.480 +      make_iterator_property_map(dependency.begin(), vertex_index),
   1.481 +      make_iterator_property_map(path_count.begin(), vertex_index),
   1.482 +      vertex_index);
   1.483 +  }
   1.484 +
   1.485 +  template<typename WeightMap>
   1.486 +  struct brandes_betweenness_centrality_dispatch1
   1.487 +  {
   1.488 +    template<typename Graph, typename CentralityMap, 
   1.489 +             typename EdgeCentralityMap, typename VertexIndexMap>
   1.490 +    static void 
   1.491 +    run(const Graph& g, CentralityMap centrality, 
   1.492 +        EdgeCentralityMap edge_centrality_map, VertexIndexMap vertex_index,
   1.493 +        WeightMap weight_map)
   1.494 +    {
   1.495 +      brandes_betweenness_centrality_dispatch2(g, centrality, edge_centrality_map,
   1.496 +                                               weight_map, vertex_index);
   1.497 +    }
   1.498 +  };
   1.499 +
   1.500 +  template<>
   1.501 +  struct brandes_betweenness_centrality_dispatch1<error_property_not_found>
   1.502 +  {
   1.503 +    template<typename Graph, typename CentralityMap, 
   1.504 +             typename EdgeCentralityMap, typename VertexIndexMap>
   1.505 +    static void 
   1.506 +    run(const Graph& g, CentralityMap centrality, 
   1.507 +        EdgeCentralityMap edge_centrality_map, VertexIndexMap vertex_index,
   1.508 +        error_property_not_found)
   1.509 +    {
   1.510 +      brandes_betweenness_centrality_dispatch2(g, centrality, edge_centrality_map,
   1.511 +                                               vertex_index);
   1.512 +    }
   1.513 +  };
   1.514 +
   1.515 +} } // end namespace detail::graph
   1.516 +
   1.517 +template<typename Graph, typename Param, typename Tag, typename Rest>
   1.518 +void 
   1.519 +brandes_betweenness_centrality(const Graph& g, 
   1.520 +                               const bgl_named_params<Param,Tag,Rest>& params)
   1.521 +{
   1.522 +  typedef bgl_named_params<Param,Tag,Rest> named_params;
   1.523 +
   1.524 +  typedef typename property_value<named_params, edge_weight_t>::type ew;
   1.525 +  detail::graph::brandes_betweenness_centrality_dispatch1<ew>::run(
   1.526 +    g, 
   1.527 +    choose_param(get_param(params, vertex_centrality), 
   1.528 +                 dummy_property_map()),
   1.529 +    choose_param(get_param(params, edge_centrality), 
   1.530 +                 dummy_property_map()),
   1.531 +    choose_const_pmap(get_param(params, vertex_index), g, vertex_index),
   1.532 +    get_param(params, edge_weight));
   1.533 +}
   1.534 +
   1.535 +template<typename Graph, typename CentralityMap>
   1.536 +void 
   1.537 +brandes_betweenness_centrality(const Graph& g, CentralityMap centrality)
   1.538 +{
   1.539 +  detail::graph::brandes_betweenness_centrality_dispatch2(
   1.540 +    g, centrality, dummy_property_map(), get(vertex_index, g));
   1.541 +}
   1.542 +
   1.543 +template<typename Graph, typename CentralityMap, typename EdgeCentralityMap>
   1.544 +void 
   1.545 +brandes_betweenness_centrality(const Graph& g, CentralityMap centrality,
   1.546 +                               EdgeCentralityMap edge_centrality_map)
   1.547 +{
   1.548 +  detail::graph::brandes_betweenness_centrality_dispatch2(
   1.549 +    g, centrality, edge_centrality_map, get(vertex_index, g));
   1.550 +}
   1.551 +
   1.552 +/**
   1.553 + * Converts "absolute" betweenness centrality (as computed by the
   1.554 + * brandes_betweenness_centrality algorithm) in the centrality map
   1.555 + * into "relative" centrality. The result is placed back into the
   1.556 + * given centrality map.
   1.557 + */
   1.558 +template<typename Graph, typename CentralityMap>
   1.559 +void 
   1.560 +relative_betweenness_centrality(const Graph& g, CentralityMap centrality)
   1.561 +{
   1.562 +  typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
   1.563 +  typedef typename property_traits<CentralityMap>::value_type centrality_type;
   1.564 +
   1.565 +  typename graph_traits<Graph>::vertices_size_type n = num_vertices(g);
   1.566 +  centrality_type factor = centrality_type(2)/centrality_type(n*n - 3*n + 2);
   1.567 +  vertex_iterator v, v_end;
   1.568 +  for (tie(v, v_end) = vertices(g); v != v_end; ++v) {
   1.569 +    put(centrality, *v, factor * get(centrality, *v));
   1.570 +  }
   1.571 +}
   1.572 +
   1.573 +// Compute the central point dominance of a graph.
   1.574 +template<typename Graph, typename CentralityMap>
   1.575 +typename property_traits<CentralityMap>::value_type
   1.576 +central_point_dominance(const Graph& g, CentralityMap centrality)
   1.577 +{
   1.578 +  using std::max;
   1.579 +
   1.580 +  typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
   1.581 +  typedef typename property_traits<CentralityMap>::value_type centrality_type;
   1.582 +
   1.583 +  typename graph_traits<Graph>::vertices_size_type n = num_vertices(g);
   1.584 +
   1.585 +  // Find max centrality
   1.586 +  centrality_type max_centrality(0);
   1.587 +  vertex_iterator v, v_end;
   1.588 +  for (tie(v, v_end) = vertices(g); v != v_end; ++v) {
   1.589 +    max_centrality = (max)(max_centrality, get(centrality, *v));
   1.590 +  }
   1.591 +
   1.592 +  // Compute central point dominance
   1.593 +  centrality_type sum(0);
   1.594 +  for (tie(v, v_end) = vertices(g); v != v_end; ++v) {
   1.595 +    sum += (max_centrality - get(centrality, *v));
   1.596 +  }
   1.597 +  return sum/(n-1);
   1.598 +}
   1.599 +
   1.600 +} // end namespace boost
   1.601 +
   1.602 +#endif // BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP