// Copyright 2004 The Trustees of Indiana University.

 // 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_BETWEENNESS_CENTRALITY_CLUSTERING_HPP

 #define BOOST_GRAPH_BETWEENNESS_CENTRALITY_CLUSTERING_HPP

 #include <boost/graph/betweenness_centrality.hpp>

 #include <boost/graph/graph_traits.hpp>

 #include <boost/pending/indirect_cmp.hpp>

 #include <algorithm>

 #include <vector>

 #include <boost/property_map.hpp>

 namespace boost {

 /** Threshold termination function for the betweenness centrality

  * clustering algorithm.

  */

 template<typename T>

 struct bc_clustering_threshold

 {

   typedef T centrality_type;

   /// Terminate clustering when maximum absolute edge centrality is

   /// below the given threshold.

   explicit bc_clustering_threshold(T threshold) 

     : threshold(threshold), dividend(1.0) {}

   /**

    * Terminate clustering when the maximum edge centrality is below

    * the given threshold.

    *

    * @param threshold the threshold value

    *

    * @param g the graph on which the threshold will be calculated

    *

    * @param normalize when true, the threshold is compared against the

    * normalized edge centrality based on the input graph; otherwise,

    * the threshold is compared against the absolute edge centrality.

    */

   template<typename Graph>

   bc_clustering_threshold(T threshold, const Graph& g, bool normalize = true)

     : threshold(threshold), dividend(1.0)

   {

     if (normalize) {

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

       dividend = T((n - 1) * (n - 2)) / T(2);

     }

   }

   /** Returns true when the given maximum edge centrality (potentially

    * normalized) falls below the threshold.

    */

   template<typename Graph, typename Edge>

   bool operator()(T max_centrality, Edge, const Graph&)

   {

     return (max_centrality / dividend) < threshold;

   }

  protected:

   T threshold;

   T dividend;

 };

 /** Graph clustering based on edge betweenness centrality.

  * 

  * This algorithm implements graph clustering based on edge

  * betweenness centrality. It is an iterative algorithm, where in each

  * step it compute the edge betweenness centrality (via @ref

  * brandes_betweenness_centrality) and removes the edge with the

  * maximum betweenness centrality. The @p done function object

  * determines when the algorithm terminates (the edge found when the

  * algorithm terminates will not be removed).

  *

  * @param g The graph on which clustering will be performed. The type

  * of this parameter (@c MutableGraph) must be a model of the

  * VertexListGraph, IncidenceGraph, EdgeListGraph, and Mutable Graph

  * concepts.

  *

  * @param done The function object that indicates termination of the

  * algorithm. It must be a ternary function object thats accepts the

  * maximum centrality, the descriptor of the edge that will be

  * removed, and the graph @p g.

  *

  * @param edge_centrality (UTIL/OUT) The property map that will store

  * the betweenness centrality for each edge. When the algorithm

  * terminates, it will contain the edge centralities for the

  * graph. The type of this property map must model the

  * ReadWritePropertyMap concept. Defaults to an @c

  * iterator_property_map whose value type is 

  * @c Done::centrality_type and using @c get(edge_index, g) for the 

  * index map.

  *

  * @param vertex_index (IN) The property map that maps vertices to

  * indices in the range @c [0, num_vertices(g)). This type of this

  * property map must model the ReadablePropertyMap concept and its

  * value type must be an integral type. Defaults to 

  * @c get(vertex_index, g).

  */

 template<typename MutableGraph, typename Done, typename EdgeCentralityMap,

          typename VertexIndexMap>

 void 

 betweenness_centrality_clustering(MutableGraph& g, Done done,

                                   EdgeCentralityMap edge_centrality,

                                   VertexIndexMap vertex_index)

 {

   typedef typename property_traits<EdgeCentralityMap>::value_type

     centrality_type;

   typedef typename graph_traits<MutableGraph>::edge_iterator edge_iterator;

   typedef typename graph_traits<MutableGraph>::edge_descriptor edge_descriptor;

   typedef typename graph_traits<MutableGraph>::vertices_size_type

     vertices_size_type;

   if (edges(g).first == edges(g).second) return;

   // Function object that compares the centrality of edges

   indirect_cmp<EdgeCentralityMap, std::less<centrality_type> > 

     cmp(edge_centrality);

   bool is_done;

   do {

     brandes_betweenness_centrality(g, 

                                    edge_centrality_map(edge_centrality)

                                    .vertex_index_map(vertex_index));

     edge_descriptor e = *max_element(edges(g).first, edges(g).second, cmp);

     is_done = done(get(edge_centrality, e), e, g);

     if (!is_done) remove_edge(e, g);

   } while (!is_done && edges(g).first != edges(g).second);

 }

 /**

  * \overload

  */ 

 template<typename MutableGraph, typename Done, typename EdgeCentralityMap>

 void 

 betweenness_centrality_clustering(MutableGraph& g, Done done,

                                   EdgeCentralityMap edge_centrality)

 {

   betweenness_centrality_clustering(g, done, edge_centrality,

                                     get(vertex_index, g));

 }

 /**

  * \overload

  */ 

 template<typename MutableGraph, typename Done>

 void

 betweenness_centrality_clustering(MutableGraph& g, Done done)

 {

   typedef typename Done::centrality_type centrality_type;

   std::vector<centrality_type> edge_centrality(num_edges(g));

   betweenness_centrality_clustering(g, done, 

     make_iterator_property_map(edge_centrality.begin(), get(edge_index, g)),

     get(vertex_index, g));

 }

 } // end namespace boost

 #endif // BOOST_GRAPH_BETWEENNESS_CENTRALITY_CLUSTERING_HPP