FM / graph

/usr/include/boost/graph

Name	Size	Mode	Actions
detail/	-	0755	rm
distributed/	-	0755	rm
parallel/	-	0755	rm
planar_detail/	-	0755	rm
property_maps/	-	0755	rm
accounting.hpp	876	0644	edit dl rm
adjacency_iterator.hpp	2899	0644	edit dl rm
adjacency_list.hpp	13692	0644	edit dl rm
adjacency_list_io.hpp	11849	0644	edit dl rm
adjacency_matrix.hpp	45743	0644	edit dl rm
adj_list_serialize.hpp	4523	0644	edit dl rm
astar_search.hpp	26736	0644	edit dl rm
bandwidth.hpp	2992	0644	edit dl rm
bc_clustering.hpp	5937	0644	edit dl rm
bellman_ford_shortest_paths.hpp	8229	0644	edit dl rm
betweenness_centrality.hpp	26290	0644	edit dl rm
biconnected_components.hpp	16701	0644	edit dl rm
bipartite.hpp	13492	0644	edit dl rm
boyer_myrvold_planar_test.hpp	9849	0644	edit dl rm
boykov_kolmogorov_max_flow.hpp	47342	0644	edit dl rm
breadth_first_search.hpp	14751	0644	edit dl rm
bron_kerbosch_all_cliques.hpp	11736	0644	edit dl rm
buffer_concepts.hpp	2429	0644	edit dl rm
chrobak_payne_drawing.hpp	8641	0644	edit dl rm
circle_layout.hpp	1924	0644	edit dl rm
closeness_centrality.hpp	6057	0644	edit dl rm
clustering_coefficient.hpp	5726	0644	edit dl rm
compressed_sparse_row_graph.hpp	69887	0644	edit dl rm
connected_components.hpp	4134	0644	edit dl rm
copy.hpp	21225	0644	edit dl rm
core_numbers.hpp	13663	0644	edit dl rm
create_condensation_graph.hpp	3159	0644	edit dl rm
cuthill_mckee_ordering.hpp	5992	0644	edit dl rm
cycle_canceling.hpp	6645	0644	edit dl rm
dag_shortest_paths.hpp	6064	0644	edit dl rm
degree_centrality.hpp	4236	0644	edit dl rm
depth_first_search.hpp	15430	0644	edit dl rm
dijkstra_shortest_paths.hpp	23687	0644	edit dl rm
dijkstra_shortest_paths_no_color_map.hpp	9620	0644	edit dl rm
dimacs.hpp	10448	0644	edit dl rm
directed_graph.hpp	24214	0644	edit dl rm
dll_import_export.hpp	892	0644	edit dl rm
dominator_tree.hpp	17553	0644	edit dl rm
eccentricity.hpp	4611	0644	edit dl rm
edge_coloring.hpp	6809	0644	edit dl rm
edge_connectivity.hpp	6796	0644	edit dl rm
edge_list.hpp	9948	0644	edit dl rm
edmonds_karp_max_flow.hpp	10177	0644	edit dl rm
edmunds_karp_max_flow.hpp	982	0644	edit dl rm
erdos_renyi_generator.hpp	7257	0644	edit dl rm
exception.hpp	1466	0644	edit dl rm
exterior_property.hpp	4289	0644	edit dl rm
filtered_graph.hpp	20098	0644	edit dl rm
find_flow_cost.hpp	1859	0644	edit dl rm
floyd_warshall_shortest.hpp	8510	0644	edit dl rm
fruchterman_reingold.hpp	17325	0644	edit dl rm
geodesic_distance.hpp	8015	0644	edit dl rm
graphml.hpp	13460	0644	edit dl rm
graphviz.hpp	33503	0644	edit dl rm
graph_archetypes.hpp	11008	0644	edit dl rm
graph_as_tree.hpp	4532	0644	edit dl rm
graph_concepts.hpp	19785	0644	edit dl rm
graph_mutability_traits.hpp	4995	0644	edit dl rm
graph_selectors.hpp	1274	0644	edit dl rm
graph_stats.hpp	4394	0644	edit dl rm
graph_traits.hpp	13065	0644	edit dl rm
graph_utility.hpp	16182	0644	edit dl rm
grid_graph.hpp	33830	0644	edit dl rm
gursoy_atun_layout.hpp	13248	0644	edit dl rm
hawick_circuits.hpp	14593	0644	edit dl rm
howard_cycle_ratio.hpp	23107	0644	edit dl rm
incremental_components.hpp	8224	0644	edit dl rm
isomorphism.hpp	26308	0644	edit dl rm
is_kuratowski_subgraph.hpp	10260	0644	edit dl rm
is_straight_line_drawing.hpp	7230	0644	edit dl rm
iteration_macros.hpp	11659	0644	edit dl rm
iteration_macros_undef.hpp	673	0644	edit dl rm
johnson_all_pairs_shortest.hpp	7646	0644	edit dl rm
kamada_kawai_spring_layout.hpp	28048	0644	edit dl rm
king_ordering.hpp	12101	0644	edit dl rm
kruskal_min_spanning_tree.hpp	5743	0644	edit dl rm
labeled_graph.hpp	30914	0644	edit dl rm
leda_graph.hpp	28789	0644	edit dl rm
lookup_edge.hpp	1894	0644	edit dl rm
loop_erased_random_walk.hpp	4436	0644	edit dl rm
make_biconnected_planar.hpp	3513	0644	edit dl rm
make_connected.hpp	2645	0644	edit dl rm
make_maximal_planar.hpp	7578	0644	edit dl rm
matrix_as_graph.hpp	7227	0644	edit dl rm
maximum_adjacency_search.hpp	15125	0644	edit dl rm
maximum_weighted_matching.hpp	49722	0644	edit dl rm
max_cardinality_matching.hpp	31000	0644	edit dl rm
mcgregor_common_subgraphs.hpp	43470	0644	edit dl rm
mesh_graph_generator.hpp	5616	0644	edit dl rm
metis.hpp	10982	0644	edit dl rm
metric_tsp_approx.hpp	10809	0644	edit dl rm
minimum_degree_ordering.hpp	27087	0644	edit dl rm
named_function_params.hpp	39639	0644	edit dl rm
named_graph.hpp	20614	0644	edit dl rm
neighbor_bfs.hpp	11763	0644	edit dl rm
numeric_values.hpp	1814	0644	edit dl rm
one_bit_color_map.hpp	3277	0644	edit dl rm
overloading.hpp	1584	0644	edit dl rm
page_rank.hpp	6164	0644	edit dl rm
planar_canonical_ordering.hpp	7203	0644	edit dl rm
planar_face_traversal.hpp	6020	0644	edit dl rm
plod_generator.hpp	7708	0644	edit dl rm
point_traits.hpp	782	0644	edit dl rm
prim_minimum_spanning_tree.hpp	2960	0644	edit dl rm
profile.hpp	1327	0644	edit dl rm
properties.hpp	12417	0644	edit dl rm
property_iter_range.hpp	4345	0644	edit dl rm
push_relabel_max_flow.hpp	34737	0644	edit dl rm
random.hpp	9672	0644	edit dl rm
random_layout.hpp	988	0644	edit dl rm
random_spanning_tree.hpp	5775	0644	edit dl rm
read_dimacs.hpp	12080	0644	edit dl rm
relax.hpp	4400	0644	edit dl rm
reverse_graph.hpp	22402	0644	edit dl rm
rmat_graph_generator.hpp	19291	0644	edit dl rm
r_c_shortest_paths.hpp	30673	0644	edit dl rm
sequential_vertex_coloring.hpp	4562	0644	edit dl rm
simple_point.hpp	628	0644	edit dl rm
sloan_ordering.hpp	15540	0644	edit dl rm
smallest_last_ordering.hpp	5458	0644	edit dl rm
small_world_generator.hpp	3670	0644	edit dl rm
ssca_graph_generator.hpp	6564	0644	edit dl rm
stanford_graph.hpp	20126	0644	edit dl rm
stoer_wagner_min_cut.hpp	12415	0644	edit dl rm
strong_components.hpp	13009	0644	edit dl rm
st_connected.hpp	2852	0644	edit dl rm
subgraph.hpp	39996	0644	edit dl rm
successive_shortest_path_nonnegative_weights.hpp	10413	0644	edit dl rm
tiernan_all_cycles.hpp	12547	0644	edit dl rm
topological_sort.hpp	2611	0644	edit dl rm
topology.hpp	20389	0644	edit dl rm
transitive_closure.hpp	14260	0644	edit dl rm
transitive_reduction.hpp	5326	0644	edit dl rm
transpose_graph.hpp	1198	0644	edit dl rm
tree_traits.hpp	1338	0644	edit dl rm
two_bit_color_map.hpp	3510	0644	edit dl rm
two_graphs_common_spanning_trees.hpp	34996	0644	edit dl rm
undirected_dfs.hpp	10672	0644	edit dl rm
undirected_graph.hpp	25276	0644	edit dl rm
use_mpi.hpp	437	0644	edit dl rm
vector_as_graph.hpp	10474	0644	edit dl rm
vertex_and_edge_range.hpp	5528	0644	edit dl rm
vf2_sub_graph_iso.hpp	48585	0644	edit dl rm
visitors.hpp	11318	0644	edit dl rm
wavefront.hpp	3932	0644	edit dl rm
write_dimacs.hpp	2889	0644	edit dl rm

Edit: /usr/include/boost/graph/betweenness_centrality.hpp (26290B)

// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)

//  Authors: Douglas Gregor
//           Andrew Lumsdaine
#ifndef BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP
#define BOOST_GRAPH_BRANDES_BETWEENNESS_CENTRALITY_HPP

#include <stack>
#include <vector>
#include <boost/graph/overloading.hpp>
#include <boost/graph/dijkstra_shortest_paths.hpp>
#include <boost/graph/breadth_first_search.hpp>
#include <boost/graph/relax.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/type_traits/is_convertible.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/mpl/if.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/named_function_params.hpp>
#include <algorithm>

namespace boost
{

namespace detail
{
    namespace graph
    {

/**
         * Customized visitor passed to Dijkstra's algorithm by Brandes'
         * betweenness centrality algorithm. This visitor is responsible for
         * keeping track of the order in which vertices are discovered, the
         * predecessors on the shortest path(s) to a vertex, and the number
         * of shortest paths.
         */
        template < typename Graph, typename WeightMap, typename IncomingMap,
            typename DistanceMap, typename PathCountMap >
        struct brandes_dijkstra_visitor : public bfs_visitor<>
        {
            typedef typename graph_traits< Graph >::vertex_descriptor
                vertex_descriptor;
            typedef
                typename graph_traits< Graph >::edge_descriptor edge_descriptor;

brandes_dijkstra_visitor(
                std::stack< vertex_descriptor >& ordered_vertices,
                WeightMap weight, IncomingMap incoming, DistanceMap distance,
                PathCountMap path_count)
            : ordered_vertices(ordered_vertices)
            , weight(weight)
            , incoming(incoming)
            , distance(distance)
            , path_count(path_count)
            {
            }

/**
             * Whenever an edge e = (v, w) is relaxed, the incoming edge list
             * for w is set to {(v, w)} and the shortest path count of w is set
             * to the number of paths that reach {v}.
             */
            void edge_relaxed(edge_descriptor e, const Graph& g)
            {
                vertex_descriptor v = source(e, g), w = target(e, g);
                incoming[w].clear();
                incoming[w].push_back(e);
                put(path_count, w, get(path_count, v));
            }

/**
             * If an edge e = (v, w) was not relaxed, it may still be the case
             * that we've found more equally-short paths, so include {(v, w)} in
             * the incoming edges of w and add all of the shortest paths to v to
             * the shortest path count of w.
             */
            void edge_not_relaxed(edge_descriptor e, const Graph& g)
            {
                typedef typename property_traits< WeightMap >::value_type
                    weight_type;
                typedef typename property_traits< DistanceMap >::value_type
                    distance_type;
                vertex_descriptor v = source(e, g), w = target(e, g);
                distance_type d_v = get(distance, v), d_w = get(distance, w);
                weight_type w_e = get(weight, e);

closed_plus< distance_type > combine;
                if (d_w == combine(d_v, w_e))
                {
                    put(path_count, w, get(path_count, w) + get(path_count, v));
                    incoming[w].push_back(e);
                }
            }

/// Keep track of vertices as they are reached
            void examine_vertex(vertex_descriptor w, const Graph&)
            {
                ordered_vertices.push(w);
            }

private:
            std::stack< vertex_descriptor >& ordered_vertices;
            WeightMap weight;
            IncomingMap incoming;
            DistanceMap distance;
            PathCountMap path_count;
        };

/**
         * Function object that calls Dijkstra's shortest paths algorithm
         * using the Dijkstra visitor for the Brandes betweenness centrality
         * algorithm.
         */
        template < typename WeightMap > struct brandes_dijkstra_shortest_paths
        {
            brandes_dijkstra_shortest_paths(WeightMap weight_map)
            : weight_map(weight_map)
            {
            }

template < typename Graph, typename IncomingMap,
                typename DistanceMap, typename PathCountMap,
                typename VertexIndexMap >
            void operator()(Graph& g,
                typename graph_traits< Graph >::vertex_descriptor s,
                std::stack< typename graph_traits< Graph >::vertex_descriptor >&
                    ov,
                IncomingMap incoming, DistanceMap distance,
                PathCountMap path_count, VertexIndexMap vertex_index)
            {
                typedef brandes_dijkstra_visitor< Graph, WeightMap, IncomingMap,
                    DistanceMap, PathCountMap >
                    visitor_type;
                visitor_type visitor(
                    ov, weight_map, incoming, distance, path_count);

dijkstra_shortest_paths(g, s,
                    boost::weight_map(weight_map)
                        .vertex_index_map(vertex_index)
                        .distance_map(distance)
                        .visitor(visitor));
            }

private:
            WeightMap weight_map;
        };

/**
         * Function object that invokes breadth-first search for the
         * unweighted form of the Brandes betweenness centrality algorithm.
         */
        struct brandes_unweighted_shortest_paths
        {
            /**
             * Customized visitor passed to breadth-first search, which
             * records predecessor and the number of shortest paths to each
             * vertex.
             */
            template < typename Graph, typename IncomingMap,
                typename DistanceMap, typename PathCountMap >
            struct visitor_type : public bfs_visitor<>
            {
                typedef typename graph_traits< Graph >::edge_descriptor
                    edge_descriptor;
                typedef typename graph_traits< Graph >::vertex_descriptor
                    vertex_descriptor;

visitor_type(IncomingMap incoming, DistanceMap distance,
                    PathCountMap path_count,
                    std::stack< vertex_descriptor >& ordered_vertices)
                : incoming(incoming)
                , distance(distance)
                , path_count(path_count)
                , ordered_vertices(ordered_vertices)
                {
                }

/// Keep track of vertices as they are reached
                void examine_vertex(vertex_descriptor v, Graph&)
                {
                    ordered_vertices.push(v);
                }

/**
                 * Whenever an edge e = (v, w) is labelled a tree edge, the
                 * incoming edge list for w is set to {(v, w)} and the shortest
                 * path count of w is set to the number of paths that reach {v}.
                 */
                void tree_edge(edge_descriptor e, Graph& g)
                {
                    vertex_descriptor v = source(e, g);
                    vertex_descriptor w = target(e, g);
                    put(distance, w, get(distance, v) + 1);

put(path_count, w, get(path_count, v));
                    incoming[w].push_back(e);
                }

/**
                 * If an edge e = (v, w) is not a tree edge, it may still be the
                 * case that we've found more equally-short paths, so include
                 * (v, w) in the incoming edge list of w and add all of the
                 * shortest paths to v to the shortest path count of w.
                 */
                void non_tree_edge(edge_descriptor e, Graph& g)
                {
                    vertex_descriptor v = source(e, g);
                    vertex_descriptor w = target(e, g);
                    if (get(distance, w) == get(distance, v) + 1)
                    {
                        put(path_count, w,
                            get(path_count, w) + get(path_count, v));
                        incoming[w].push_back(e);
                    }
                }

private:
                IncomingMap incoming;
                DistanceMap distance;
                PathCountMap path_count;
                std::stack< vertex_descriptor >& ordered_vertices;
            };

template < typename Graph, typename IncomingMap,
                typename DistanceMap, typename PathCountMap,
                typename VertexIndexMap >
            void operator()(Graph& g,
                typename graph_traits< Graph >::vertex_descriptor s,
                std::stack< typename graph_traits< Graph >::vertex_descriptor >&
                    ov,
                IncomingMap incoming, DistanceMap distance,
                PathCountMap path_count, VertexIndexMap vertex_index)
            {
                typedef typename graph_traits< Graph >::vertex_descriptor
                    vertex_descriptor;

visitor_type< Graph, IncomingMap, DistanceMap, PathCountMap >
                    visitor(incoming, distance, path_count, ov);

std::vector< default_color_type > colors(num_vertices(g),
                    color_traits< default_color_type >::white());
                boost::queue< vertex_descriptor > Q;
                breadth_first_visit(g, s, Q, visitor,
                    make_iterator_property_map(colors.begin(), vertex_index));
            }
        };

// When the edge centrality map is a dummy property map, no
        // initialization is needed.
        template < typename Iter >
        inline void init_centrality_map(
            std::pair< Iter, Iter >, dummy_property_map)
        {
        }

// When we have a real edge centrality map, initialize all of the
        // centralities to zero.
        template < typename Iter, typename Centrality >
        void init_centrality_map(
            std::pair< Iter, Iter > keys, Centrality centrality_map)
        {
            typedef typename property_traits< Centrality >::value_type
                centrality_type;
            while (keys.first != keys.second)
            {
                put(centrality_map, *keys.first, centrality_type(0));
                ++keys.first;
            }
        }

// When the edge centrality map is a dummy property map, no update
        // is performed.
        template < typename Key, typename T >
        inline void update_centrality(dummy_property_map, const Key&, const T&)
        {
        }

// When we have a real edge centrality map, add the value to the map
        template < typename CentralityMap, typename Key, typename T >
        inline void update_centrality(
            CentralityMap centrality_map, Key k, const T& x)
        {
            put(centrality_map, k, get(centrality_map, k) + x);
        }

template < typename Iter >
        inline void divide_centrality_by_two(
            std::pair< Iter, Iter >, dummy_property_map)
        {
        }

template < typename Iter, typename CentralityMap >
        inline void divide_centrality_by_two(
            std::pair< Iter, Iter > keys, CentralityMap centrality_map)
        {
            typename property_traits< CentralityMap >::value_type two(2);
            while (keys.first != keys.second)
            {
                put(centrality_map, *keys.first,
                    get(centrality_map, *keys.first) / two);
                ++keys.first;
            }
        }

template < typename Graph, typename CentralityMap,
            typename EdgeCentralityMap, typename IncomingMap,
            typename DistanceMap, typename DependencyMap, typename PathCountMap,
            typename VertexIndexMap, typename ShortestPaths >
        void brandes_betweenness_centrality_impl(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, ShortestPaths shortest_paths)
        {
            typedef
                typename graph_traits< Graph >::vertex_iterator vertex_iterator;
            typedef typename graph_traits< Graph >::vertex_descriptor
                vertex_descriptor;

// 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 (boost::tie(s, s_end) = vertices(g); s != s_end; ++s)
            {
                // Initialize for this iteration
                vertex_iterator w, w_end;
                for (boost::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 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(
        Graph, vertex_list_graph_tag))
{
    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 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(
        Graph, vertex_list_graph_tag))
{
    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 >::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 >::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);

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< param_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, param_not_found)
            {
                brandes_betweenness_centrality_dispatch2(
                    g, centrality, edge_centrality_map, vertex_index);
            }
        };

template < typename T > struct is_bgl_named_params
        {
            BOOST_STATIC_CONSTANT(bool, value = false);
        };

template < typename Param, typename Tag, typename Rest >
        struct is_bgl_named_params< bgl_named_params< Param, Tag, Rest > >
        {
            BOOST_STATIC_CONSTANT(bool, value = true);
        };

}
} // 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
        BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag))
{
    typedef bgl_named_params< Param, Tag, Rest > named_params;

typedef typename get_param_type< edge_weight_t, named_params >::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));
}

// disable_if is required to work around problem with MSVC 7.1 (it seems to not
// get partial ordering getween this overload and the previous one correct)
template < typename Graph, typename CentralityMap >
typename disable_if< detail::graph::is_bgl_named_params< CentralityMap >,
    void >::type
brandes_betweenness_centrality(const Graph& g,
    CentralityMap centrality BOOST_GRAPH_ENABLE_IF_MODELS_PARM(
        Graph, vertex_list_graph_tag))
{
    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 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(
        Graph, vertex_list_graph_tag))
{
    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 (boost::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 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(
        Graph, vertex_list_graph_tag))
{
    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 (boost::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 (boost::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

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