Chris@16: //
Chris@16: //=======================================================================
Chris@16: // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
Chris@16: // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
Chris@16: //
Chris@16: // Distributed under the Boost Software License, Version 1.0. (See
Chris@16: // accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: //=======================================================================
Chris@16: //
Chris@16: #ifndef BOOST_GRAPH_UTILITY_HPP
Chris@16: #define BOOST_GRAPH_UTILITY_HPP
Chris@16: 
Chris@16: #include <stdlib.h>
Chris@16: #include <iostream>
Chris@16: #include <algorithm>
Chris@16: #include <assert.h>
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/tuple/tuple.hpp>
Chris@16: 
Chris@16: #if !defined BOOST_NO_SLIST
Chris@16: #  ifdef BOOST_SLIST_HEADER
Chris@16: #    include BOOST_SLIST_HEADER
Chris@16: #  else
Chris@16: #    include <slist>
Chris@16: #  endif
Chris@16: #endif
Chris@16: 
Chris@16: #include <boost/graph/graph_traits.hpp>
Chris@16: #include <boost/graph/properties.hpp>
Chris@16: #include <boost/pending/container_traits.hpp>
Chris@16: #include <boost/graph/depth_first_search.hpp>
Chris@16: // iota moved to detail/algorithm.hpp
Chris@16: #include <boost/detail/algorithm.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16:   // Provide an undirected graph interface alternative to the
Chris@16:   // the source() and target() edge functions.
Chris@16:   template <class UndirectedGraph>
Chris@16:   inline 
Chris@16:   std::pair<typename graph_traits<UndirectedGraph>::vertex_descriptor,
Chris@16:             typename graph_traits<UndirectedGraph>::vertex_descriptor>
Chris@16:   incident(typename graph_traits<UndirectedGraph>::edge_descriptor e,
Chris@16:            UndirectedGraph& g)
Chris@16:   {
Chris@16:     return std::make_pair(source(e,g), target(e,g));
Chris@16:   }
Chris@16: 
Chris@16:   // Provide an undirected graph interface alternative
Chris@16:   // to the out_edges() function.
Chris@16:   template <class Graph>
Chris@16:   inline 
Chris@16:   std::pair<typename graph_traits<Graph>::out_edge_iterator,
Chris@16:             typename graph_traits<Graph>::out_edge_iterator>
Chris@16:   incident_edges(typename graph_traits<Graph>::vertex_descriptor u,
Chris@16:                  Graph& g)
Chris@16:   {
Chris@16:     return out_edges(u, g);
Chris@16:   }
Chris@16: 
Chris@16:   template <class Graph>
Chris@16:   inline typename graph_traits<Graph>::vertex_descriptor
Chris@16:   opposite(typename graph_traits<Graph>::edge_descriptor e,
Chris@16:            typename graph_traits<Graph>::vertex_descriptor v,
Chris@16:            const Graph& g)
Chris@16:   {
Chris@16:     typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
Chris@16:     if (v == source(e, g))
Chris@16:       return target(e, g);
Chris@16:     else if (v == target(e, g))
Chris@16:       return source(e, g);
Chris@16:     else
Chris@16:       return vertex_descriptor();
Chris@16:   }
Chris@16: 
Chris@16:   //===========================================================================
Chris@16:   // Some handy predicates
Chris@16: 
Chris@16:   template <typename Vertex, typename Graph>
Chris@16:   struct incident_from_predicate {
Chris@16:     incident_from_predicate(Vertex u, const Graph& g)
Chris@16:       : m_u(u), m_g(g) { }
Chris@16:     template <class Edge>
Chris@16:     bool operator()(const Edge& e) const {
Chris@16:       return source(e, m_g) == m_u;
Chris@16:     }
Chris@16:     Vertex m_u;
Chris@16:     const Graph& m_g;
Chris@16:   };
Chris@16:   template <typename Vertex, typename Graph>
Chris@16:   inline incident_from_predicate<Vertex, Graph>
Chris@16:   incident_from(Vertex u, const Graph& g) {
Chris@16:     return incident_from_predicate<Vertex, Graph>(u, g);
Chris@16:   }
Chris@16:   
Chris@16:   template <typename Vertex, typename Graph>
Chris@16:   struct incident_to_predicate {
Chris@16:     incident_to_predicate(Vertex u, const Graph& g)
Chris@16:       : m_u(u), m_g(g) { }
Chris@16:     template <class Edge>
Chris@16:     bool operator()(const Edge& e) const {
Chris@16:       return target(e, m_g) == m_u;
Chris@16:     }
Chris@16:     Vertex m_u;
Chris@16:     const Graph& m_g;
Chris@16:   };
Chris@16:   template <typename Vertex, typename Graph>
Chris@16:   inline incident_to_predicate<Vertex, Graph>
Chris@16:   incident_to(Vertex u, const Graph& g) {
Chris@16:     return incident_to_predicate<Vertex, Graph>(u, g);
Chris@16:   }
Chris@16: 
Chris@16:   template <typename Vertex, typename Graph>
Chris@16:   struct incident_on_predicate {
Chris@16:     incident_on_predicate(Vertex u, const Graph& g)
Chris@16:       : m_u(u), m_g(g) { }
Chris@16:     template <class Edge>
Chris@16:     bool operator()(const Edge& e) const {
Chris@16:       return source(e, m_g) == m_u || target(e, m_g) == m_u;
Chris@16:     }
Chris@16:     Vertex m_u;
Chris@16:     const Graph& m_g;
Chris@16:   };
Chris@16:   template <typename Vertex, typename Graph>
Chris@16:   inline incident_on_predicate<Vertex, Graph>
Chris@16:   incident_on(Vertex u, const Graph& g) {
Chris@16:     return incident_on_predicate<Vertex, Graph>(u, g);
Chris@16:   }
Chris@16:   
Chris@16:   template <typename Vertex, typename Graph>
Chris@16:   struct connects_predicate {
Chris@16:     connects_predicate(Vertex u, Vertex v, const Graph& g)
Chris@16:       : m_u(u), m_v(v), m_g(g) { }
Chris@16:     template <class Edge>
Chris@16:     bool operator()(const Edge& e) const {
Chris@16:       if (is_directed(m_g))
Chris@16:         return source(e, m_g) == m_u && target(e, m_g) == m_v;
Chris@16:       else
Chris@16:         return (source(e, m_g) == m_u && target(e, m_g) == m_v)
Chris@16:           || (source(e, m_g) == m_v && target(e, m_g) == m_u);
Chris@16:     }
Chris@16:     Vertex m_u, m_v;
Chris@16:     const Graph& m_g;
Chris@16:   };
Chris@16:   template <typename Vertex, typename Graph>
Chris@16:   inline connects_predicate<Vertex, Graph>
Chris@16:   connects(Vertex u, Vertex v, const Graph& g) {
Chris@16:           return connects_predicate<Vertex, Graph>(u, v, g);
Chris@16:   }
Chris@16: 
Chris@16: 
Chris@16:   // Need to convert all of these printing functions to take an ostream object
Chris@16:   // -JGS
Chris@16: 
Chris@16:   template <class IncidenceGraph, class Name>
Chris@16:   void print_in_edges(const IncidenceGraph& G, Name name)
Chris@16:   {
Chris@16:     typename graph_traits<IncidenceGraph>::vertex_iterator ui,ui_end;
Chris@16:     for (boost::tie(ui,ui_end) = vertices(G); ui != ui_end; ++ui) {
Chris@16:       std::cout << get(name,*ui) << " <-- ";
Chris@16:       typename graph_traits<IncidenceGraph>
Chris@16:         ::in_edge_iterator ei, ei_end;
Chris@16:       for(boost::tie(ei,ei_end) = in_edges(*ui,G); ei != ei_end; ++ei)
Chris@16:         std::cout << get(name,source(*ei,G)) << " ";
Chris@16:       std::cout << std::endl;
Chris@16:     }
Chris@16:   }
Chris@16: 
Chris@16:   template <class IncidenceGraph, class Name>
Chris@16:   void print_graph_dispatch(const IncidenceGraph& G, Name name, directed_tag)
Chris@16:   {
Chris@16:     typename graph_traits<IncidenceGraph>::vertex_iterator ui,ui_end;
Chris@16:     for (boost::tie(ui,ui_end) = vertices(G); ui != ui_end; ++ui) {
Chris@16:       std::cout << get(name,*ui) << " --> ";
Chris@16:       typename graph_traits<IncidenceGraph>
Chris@16:         ::out_edge_iterator ei, ei_end;
Chris@16:       for(boost::tie(ei,ei_end) = out_edges(*ui,G); ei != ei_end; ++ei)
Chris@16:         std::cout << get(name,target(*ei,G)) << " ";
Chris@16:       std::cout << std::endl;
Chris@16:     }
Chris@16:   }
Chris@16:   template <class IncidenceGraph, class Name>
Chris@16:   void print_graph_dispatch(const IncidenceGraph& G, Name name, undirected_tag)
Chris@16:   {
Chris@16:     typename graph_traits<IncidenceGraph>::vertex_iterator ui,ui_end;
Chris@16:     for (boost::tie(ui,ui_end) = vertices(G); ui != ui_end; ++ui) {
Chris@16:       std::cout << get(name,*ui) << " <--> ";
Chris@16:       typename graph_traits<IncidenceGraph>
Chris@16:         ::out_edge_iterator ei, ei_end;
Chris@16:       for(boost::tie(ei,ei_end) = out_edges(*ui,G); ei != ei_end; ++ei)
Chris@16:         std::cout << get(name,target(*ei,G)) << " ";
Chris@16:       std::cout << std::endl;
Chris@16:     }
Chris@16:   }
Chris@16:   template <class IncidenceGraph, class Name>
Chris@16:   void print_graph(const IncidenceGraph& G, Name name)
Chris@16:   {
Chris@16:     typedef typename graph_traits<IncidenceGraph>
Chris@16:       ::directed_category Cat;
Chris@16:     print_graph_dispatch(G, name, Cat());
Chris@16:   }
Chris@16:   template <class IncidenceGraph>
Chris@16:   void print_graph(const IncidenceGraph& G) {
Chris@16:     print_graph(G, get(vertex_index, G));
Chris@16:   }
Chris@16: 
Chris@16:   template <class EdgeListGraph, class Name>
Chris@16:   void print_edges(const EdgeListGraph& G, Name name)
Chris@16:   {
Chris@16:     typename graph_traits<EdgeListGraph>::edge_iterator ei, ei_end;
Chris@16:     for (boost::tie(ei, ei_end) = edges(G); ei != ei_end; ++ei)
Chris@16:       std::cout << "(" << get(name, source(*ei, G))
Chris@16:                 << "," << get(name, target(*ei, G)) << ") ";
Chris@16:     std::cout << std::endl;
Chris@16:   }
Chris@16: 
Chris@16:   template <class EdgeListGraph, class VertexName, class EdgeName>
Chris@16:   void print_edges2(const EdgeListGraph& G, VertexName vname, EdgeName ename)
Chris@16:   {
Chris@16:     typename graph_traits<EdgeListGraph>::edge_iterator ei, ei_end;
Chris@16:     for (boost::tie(ei, ei_end) = edges(G); ei != ei_end; ++ei)
Chris@16:       std::cout << get(ename, *ei) << "(" << get(vname, source(*ei, G))
Chris@16:                 << "," << get(vname, target(*ei, G)) << ") ";
Chris@16:     std::cout << std::endl;
Chris@16:   }
Chris@16: 
Chris@16:   template <class VertexListGraph, class Name>
Chris@16:   void print_vertices(const VertexListGraph& G, Name name)
Chris@16:   {
Chris@16:     typename graph_traits<VertexListGraph>::vertex_iterator vi,vi_end;
Chris@16:     for (boost::tie(vi,vi_end) = vertices(G); vi != vi_end; ++vi)
Chris@16:       std::cout << get(name,*vi) << " ";
Chris@16:     std::cout << std::endl;
Chris@16:   }
Chris@16: 
Chris@16:   template <class Graph, class Vertex>
Chris@16:   bool is_adj_dispatch(Graph& g, Vertex a, Vertex b, bidirectional_tag)
Chris@16:   {
Chris@16:     typename graph_traits<Graph>::adjacency_iterator vi, viend, 
Chris@16:       adj_found;
Chris@16:     boost::tie(vi, viend) = adjacent_vertices(a, g);
Chris@16:     adj_found = std::find(vi, viend, b);
Chris@16:     if (adj_found == viend)
Chris@16:       return false;  
Chris@16: 
Chris@16:     typename graph_traits<Graph>::out_edge_iterator oi, oiend, 
Chris@16:       out_found;
Chris@16:     boost::tie(oi, oiend) = out_edges(a, g);
Chris@16:     out_found = std::find_if(oi, oiend, incident_to(b, g));
Chris@16:     if (out_found == oiend)
Chris@16:       return false;
Chris@16: 
Chris@16:     typename graph_traits<Graph>::in_edge_iterator ii, iiend, 
Chris@16:       in_found;
Chris@16:     boost::tie(ii, iiend) = in_edges(b, g);
Chris@16:     in_found = std::find_if(ii, iiend, incident_from(a, g));
Chris@16:     if (in_found == iiend)
Chris@16:       return false;
Chris@16: 
Chris@16:     return true;
Chris@16:   }
Chris@16:   template <class Graph, class Vertex>
Chris@16:   bool is_adj_dispatch(Graph& g, Vertex a, Vertex b, directed_tag)
Chris@16:   {
Chris@16:     typename graph_traits<Graph>::adjacency_iterator vi, viend, found;
Chris@16:     boost::tie(vi, viend) = adjacent_vertices(a, g);
Chris@16:     found = std::find(vi, viend, b);
Chris@16:     if ( found == viend )
Chris@16:       return false;
Chris@16: 
Chris@16:     typename graph_traits<Graph>::out_edge_iterator oi, oiend, 
Chris@16:       out_found;
Chris@16:     boost::tie(oi, oiend) = out_edges(a, g);
Chris@16: 
Chris@16:     out_found = std::find_if(oi, oiend, incident_to(b, g));
Chris@16:     if (out_found == oiend)
Chris@16:       return false;
Chris@16:     return true;
Chris@16:   }
Chris@16:   template <class Graph, class Vertex>
Chris@16:   bool is_adj_dispatch(Graph& g, Vertex a, Vertex b, undirected_tag)
Chris@16:   {
Chris@16:     return is_adj_dispatch(g, a, b, directed_tag());
Chris@16:   }
Chris@16: 
Chris@16:   template <class Graph, class Vertex>
Chris@16:   bool is_adjacent(Graph& g, Vertex a, Vertex b) {
Chris@16:     typedef typename graph_traits<Graph>::directed_category Cat;
Chris@16:     return is_adj_dispatch(g, a, b, Cat());
Chris@16:   }
Chris@16: 
Chris@16:   template <class Graph, class Edge>
Chris@16:   bool in_edge_set(Graph& g, Edge e)
Chris@16:   {
Chris@16:     typename Graph::edge_iterator ei, ei_end, found;
Chris@16:     boost::tie(ei, ei_end) = edges(g);
Chris@16:     found = std::find(ei, ei_end, e);
Chris@16:     return found != ei_end;
Chris@16:   }
Chris@16: 
Chris@16:   template <class Graph, class Vertex>
Chris@16:   bool in_vertex_set(Graph& g, Vertex v)
Chris@16:   {
Chris@16:     typename Graph::vertex_iterator vi, vi_end, found;
Chris@16:     boost::tie(vi, vi_end) = vertices(g);
Chris@16:     found = std::find(vi, vi_end, v);
Chris@16:     return found != vi_end;
Chris@16:   }
Chris@16: 
Chris@16:   template <class Graph, class Vertex>
Chris@16:   bool in_edge_set(Graph& g, Vertex u, Vertex v)
Chris@16:   {
Chris@16:     typename Graph::edge_iterator ei, ei_end;
Chris@16:     for (boost::tie(ei,ei_end) = edges(g); ei != ei_end; ++ei)
Chris@16:       if (source(*ei,g) == u && target(*ei,g) == v)
Chris@16:         return true;
Chris@16:     return false;
Chris@16:   }
Chris@16: 
Chris@16:   // is x a descendant of y?
Chris@16:   template <typename ParentMap>
Chris@16:   inline bool is_descendant
Chris@16:   (typename property_traits<ParentMap>::value_type x,
Chris@16:    typename property_traits<ParentMap>::value_type y,
Chris@16:    ParentMap parent) 
Chris@16:   {
Chris@16:     if (get(parent, x) == x) // x is the root of the tree
Chris@16:       return false;
Chris@16:     else if (get(parent, x) == y)
Chris@16:       return true;
Chris@16:     else
Chris@16:       return is_descendant(get(parent, x), y, parent);
Chris@16:   }
Chris@16: 
Chris@16:   // is y reachable from x?
Chris@16:   template <typename IncidenceGraph, typename VertexColorMap>
Chris@16:   inline bool is_reachable
Chris@16:     (typename graph_traits<IncidenceGraph>::vertex_descriptor x,
Chris@16:      typename graph_traits<IncidenceGraph>::vertex_descriptor y,
Chris@16:      const IncidenceGraph& g,
Chris@16:      VertexColorMap color) // should start out white for every vertex
Chris@16:   {
Chris@16:     typedef typename property_traits<VertexColorMap>::value_type ColorValue;
Chris@16:     dfs_visitor<> vis;
Chris@16:     depth_first_visit(g, x, vis, color);
Chris@16:     return get(color, y) != color_traits<ColorValue>::white();
Chris@16:   }
Chris@16: 
Chris@16:   // Is the undirected graph connected?
Chris@16:   // Is the directed graph strongly connected?
Chris@16:   template <typename VertexListGraph, typename VertexColorMap>
Chris@16:   inline bool is_connected(const VertexListGraph& g, VertexColorMap color)
Chris@16:   {
Chris@16:     typedef typename property_traits<VertexColorMap>::value_type ColorValue;
Chris@16:     typedef color_traits<ColorValue> Color;
Chris@16:     typename graph_traits<VertexListGraph>::vertex_iterator 
Chris@16:       ui, ui_end, vi, vi_end, ci, ci_end;
Chris@16:     for (boost::tie(ui, ui_end) = vertices(g); ui != ui_end; ++ui)
Chris@16:       for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
Chris@16:         if (*ui != *vi) {
Chris@16:           for (boost::tie(ci, ci_end) = vertices(g); ci != ci_end; ++ci) 
Chris@16:             put(color, *ci, Color::white());
Chris@16:           if (! is_reachable(*ui, *vi, g, color))
Chris@16:             return false;
Chris@16:         }
Chris@16:     return true;
Chris@16:   }
Chris@16: 
Chris@16:   template <typename Graph>
Chris@16:   bool is_self_loop
Chris@16:     (typename graph_traits<Graph>::edge_descriptor e,
Chris@16:      const Graph& g)
Chris@16:   {
Chris@16:     return source(e, g) == target(e, g);
Chris@16:   }
Chris@16: 
Chris@16: 
Chris@16:   template <class T1, class T2>
Chris@16:   std::pair<T1,T2> 
Chris@16:   make_list(const T1& t1, const T2& t2) 
Chris@16:     { return std::make_pair(t1, t2); }
Chris@16: 
Chris@16:   template <class T1, class T2, class T3>
Chris@16:   std::pair<T1,std::pair<T2,T3> > 
Chris@16:   make_list(const T1& t1, const T2& t2, const T3& t3)
Chris@16:     { return std::make_pair(t1, std::make_pair(t2, t3)); }
Chris@16: 
Chris@16:   template <class T1, class T2, class T3, class T4>
Chris@16:   std::pair<T1,std::pair<T2,std::pair<T3,T4> > > 
Chris@16:   make_list(const T1& t1, const T2& t2, const T3& t3, const T4& t4)
Chris@16:     { return std::make_pair(t1, std::make_pair(t2, std::make_pair(t3, t4))); }
Chris@16: 
Chris@16:   template <class T1, class T2, class T3, class T4, class T5>
Chris@16:   std::pair<T1,std::pair<T2,std::pair<T3,std::pair<T4,T5> > > > 
Chris@16:   make_list(const T1& t1, const T2& t2, const T3& t3, const T4& t4, const T5& t5)
Chris@16:     { return std::make_pair(t1, std::make_pair(t2, std::make_pair(t3, std::make_pair(t4, t5)))); }
Chris@16: 
Chris@16:   namespace graph {
Chris@16:     
Chris@16:     // Functor for remove_parallel_edges: edge property of the removed edge is added to the remaining
Chris@16:     template <typename EdgeProperty>
Chris@16:     struct add_removed_edge_property
Chris@16:     {
Chris@16:       add_removed_edge_property(EdgeProperty ep) : ep(ep) {}
Chris@16:       
Chris@16:       template <typename Edge>
Chris@16:       void operator() (Edge stay, Edge away)
Chris@16:       {
Chris@16:         put(ep, stay, get(ep, stay) + get(ep, away));
Chris@16:       }
Chris@16:       EdgeProperty  ep;
Chris@16:     };
Chris@16: 
Chris@16:     // Same as above: edge property is capacity here
Chris@16:     template <typename Graph>
Chris@16:     struct add_removed_edge_capacity
Chris@16:       : add_removed_edge_property<typename property_map<Graph, edge_capacity_t>::type>
Chris@16:     {
Chris@16:       typedef add_removed_edge_property<typename property_map<Graph, edge_capacity_t>::type> base;
Chris@16:       add_removed_edge_capacity(Graph& g) : base(get(edge_capacity, g)) {}
Chris@16:     };    
Chris@16: 
Chris@16:     template <typename Graph>
Chris@16:     bool has_no_vertices(const Graph& g) {
Chris@16:       typedef typename boost::graph_traits<Graph>::vertex_iterator vi;
Chris@16:       std::pair<vi, vi> p = vertices(g);
Chris@16:       return (p.first == p.second);
Chris@16:     }
Chris@16: 
Chris@16:     template <typename Graph>
Chris@16:     bool has_no_edges(const Graph& g) {
Chris@16:       typedef typename boost::graph_traits<Graph>::edge_iterator ei;
Chris@16:       std::pair<ei, ei> p = edges(g);
Chris@16:       return (p.first == p.second);
Chris@16:     }
Chris@16: 
Chris@16:     template <typename Graph>
Chris@16:     bool has_no_out_edges(const typename boost::graph_traits<Graph>::vertex_descriptor& v, const Graph& g) {
Chris@16:       typedef typename boost::graph_traits<Graph>::out_edge_iterator ei;
Chris@16:       std::pair<ei, ei> p = out_edges(v, g);
Chris@16:       return (p.first == p.second);
Chris@16:     }
Chris@16: 
Chris@16:   } // namespace graph
Chris@16: 
Chris@16:   #include <boost/graph/iteration_macros.hpp>
Chris@16: 
Chris@16:   template <class PropertyIn, class PropertyOut, class Graph>
Chris@16:   void copy_vertex_property(PropertyIn p_in, PropertyOut p_out, Graph& g)
Chris@16:   {
Chris@16:     BGL_FORALL_VERTICES_T(u, g, Graph)
Chris@16:       put(p_out, u, get(p_in, g));
Chris@16:   }
Chris@16: 
Chris@16:   template <class PropertyIn, class PropertyOut, class Graph>
Chris@16:   void copy_edge_property(PropertyIn p_in, PropertyOut p_out, Graph& g)
Chris@16:   {
Chris@16:     BGL_FORALL_EDGES_T(e, g, Graph)
Chris@16:       put(p_out, e, get(p_in, g));
Chris@16:   }
Chris@16: 
Chris@16:   // Return true if property_map1 and property_map2 differ
Chris@16:   // for any of the vertices in graph.
Chris@16:   template <typename PropertyMapFirst,
Chris@16:             typename PropertyMapSecond,
Chris@16:             typename Graph>
Chris@16:   bool are_property_maps_different
Chris@16:   (const PropertyMapFirst property_map1,
Chris@16:    const PropertyMapSecond property_map2,
Chris@16:    const Graph& graph) {
Chris@16:   
Chris@16:     BGL_FORALL_VERTICES_T(vertex, graph, Graph) {
Chris@16:       if (get(property_map1, vertex) !=
Chris@16:           get(property_map2, vertex)) {
Chris@16: 
Chris@16:         return (true);
Chris@16:       }
Chris@16:     }
Chris@16: 
Chris@16:     return (false);
Chris@16:   }
Chris@16: 
Chris@16: } /* namespace boost */
Chris@16: 
Chris@16: #endif /* BOOST_GRAPH_UTILITY_HPP*/