//=======================================================================

 // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.

 // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek

 //

 // 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)

 //=======================================================================

 #ifndef BOOST_GRAPH_TRAITS_HPP

 #define BOOST_GRAPH_TRAITS_HPP

 #include <boost/config.hpp>

 #include <iterator>

 #include <boost/tuple/tuple.hpp>

 #include <boost/mpl/if.hpp>

 #include <boost/type_traits/is_same.hpp>

 #include <boost/iterator/iterator_categories.hpp>

 #include <boost/iterator/iterator_adaptor.hpp>

 #include <boost/detail/workaround.hpp>

 namespace boost {

   template <typename G>

   struct graph_traits {

     typedef typename G::vertex_descriptor      vertex_descriptor;

     typedef typename G::edge_descriptor        edge_descriptor;

     typedef typename G::adjacency_iterator     adjacency_iterator;

     typedef typename G::out_edge_iterator      out_edge_iterator;

     typedef typename G::in_edge_iterator       in_edge_iterator;

     typedef typename G::vertex_iterator        vertex_iterator;

     typedef typename G::edge_iterator          edge_iterator;

     typedef typename G::directed_category      directed_category;

     typedef typename G::edge_parallel_category edge_parallel_category;

     typedef typename G::traversal_category     traversal_category;

     typedef typename G::vertices_size_type     vertices_size_type;

     typedef typename G::edges_size_type        edges_size_type;

     typedef typename G::degree_size_type       degree_size_type;

     static inline vertex_descriptor null_vertex();

   };

   template <typename G>

   inline typename graph_traits<G>::vertex_descriptor

   graph_traits<G>::null_vertex()

   {

     return G::null_vertex();

   }

   // directed_category tags

   struct directed_tag { };

   struct undirected_tag { };

   struct bidirectional_tag : public directed_tag { };

   namespace detail {

     inline bool is_directed(directed_tag) { return true; }

     inline bool is_directed(undirected_tag) { return false; }

   }

   template <typename Graph>

   bool is_directed(const Graph&) { 

     typedef typename graph_traits<Graph>::directed_category Cat;

     return detail::is_directed(Cat());

   }

   template <typename Graph>

   bool is_undirected(const Graph& g) { 

     return ! is_directed(g);

   }

   // edge_parallel_category tags

   struct allow_parallel_edge_tag {};

   struct disallow_parallel_edge_tag {};

   namespace detail {

     inline bool allows_parallel(allow_parallel_edge_tag) { return true; }

     inline bool allows_parallel(disallow_parallel_edge_tag) { return false; }

   }

   template <typename Graph>

   bool allows_parallel_edges(const Graph&) { 

     typedef typename graph_traits<Graph>::edge_parallel_category Cat;

     return detail::allows_parallel(Cat());

   }

   // traversal_category tags

   struct incidence_graph_tag { };

   struct adjacency_graph_tag { };

   struct bidirectional_graph_tag : 

     public virtual incidence_graph_tag { };

   struct vertex_list_graph_tag { };

   struct edge_list_graph_tag { };

   struct adjacency_matrix_tag { };

   //?? not the right place ?? Lee

   typedef boost::forward_traversal_tag multi_pass_input_iterator_tag;

   template <typename G>

   struct edge_property_type {

     typedef typename G::edge_property_type type;

   };

   template <typename G>

   struct vertex_property_type {

     typedef typename G::vertex_property_type type;

   };

   template <typename G>

   struct graph_property_type {

     typedef typename G::graph_property_type type;

   };

   struct no_vertex_bundle {};

   struct no_edge_bundle {};

   template<typename G>

   struct vertex_bundle_type

   {

     typedef typename G::vertex_bundled type;

   };

   template<typename G>

   struct edge_bundle_type

   {

     typedef typename G::edge_bundled type;

   };

   namespace graph { namespace detail {

     template<typename Graph, typename Descriptor>

     class bundled_result

     {

       typedef typename graph_traits<Graph>::vertex_descriptor Vertex;

       typedef typename mpl::if_c<(is_same<Descriptor, Vertex>::value),

                                  vertex_bundle_type<Graph>,

                                  edge_bundle_type<Graph> >::type bundler;

     public:

       typedef typename bundler::type type;

     };

   } } // end namespace graph::detail

 } // namespace boost

 // Since pair is in namespace std, Koenig lookup will find source and

 // target if they are also defined in namespace std.  This is illegal,

 // but the alternative is to put source and target in the global

 // namespace which causes name conflicts with other libraries (like

 // SUIF).

 namespace std {

   /* Some helper functions for dealing with pairs as edges */

   template <class T, class G>

   T source(pair<T,T> p, const G&) { return p.first; }

   template <class T, class G>

   T target(pair<T,T> p, const G&) { return p.second; }

 }

 #if defined(__GNUC__) && defined(__SGI_STL_PORT)

 // For some reason g++ with STLport does not see the above definition

 // of source() and target() unless we bring them into the boost

 // namespace.

 namespace boost {

   using std::source;

   using std::target;

 }

 #endif

 #endif // BOOST_GRAPH_TRAITS_HPP