text: //=======================================================================
  // Copyright 2001 University of Notre Dame.
  // Author: Jeremy G. Siek
  //
  // This file is part of the Boost Graph Library
  //
  // You should have received a copy of the License Agreement for the
  // Boost Graph Library along with the software; see the file LICENSE.
  // If not, contact Office of Research, University of Notre Dame, Notre
  // Dame, IN 46556.
  //
  // Permission to modify the code and to distribute modified code is
  // granted, provided the text of this NOTICE is retained, a notice that
  // the code was modified is included with the above COPYRIGHT NOTICE and
  // with the COPYRIGHT NOTICE in the LICENSE file, and that the LICENSE
  // file is distributed with the modified code.
  //
  // LICENSOR MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED.
  // By way of example, but not limitation, Licensor MAKES NO
  // REPRESENTATIONS OR WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY
  // PARTICULAR PURPOSE OR THAT THE USE OF THE LICENSED SOFTWARE COMPONENTS
  // OR DOCUMENTATION WILL NOT INFRINGE ANY PATENTS, COPYRIGHTS, TRADEMARKS
  // OR OTHER RIGHTS.
  //=======================================================================
  
  #ifndef BOOST_ADJACENCY_MATRIX_HPP
  #define BOOST_ADJACENCY_MATRIX_HPP
  
  #include <boost/config.hpp>
  #include <vector>
  #include <memory>
  #include <cassert>
  #include <boost/iterator.hpp>
  #include <boost/graph/graph_traits.hpp>
  #include <boost/graph/graph_selectors.hpp>
  #include <boost/pending/ct_if.hpp>
  #include <boost/graph/adjacency_iterator.hpp>
  #include <boost/graph/detail/edge.hpp>
  #include <boost/iterator_adaptors.hpp>
  #include <boost/pending/integer_range.hpp>
  #include <boost/graph/properties.hpp>
  #include <boost/tuple/tuple.hpp>
  
  namespace boost {
    
    namespace detail {
  
      template <class Directed, class Vertex>
      class matrix_edge_desc_impl : public edge_desc_impl<Directed,Vertex>
      {
        typedef edge_desc_impl<Directed,Vertex> Base;
      public:
        matrix_edge_desc_impl() { }
        matrix_edge_desc_impl(bool exists, Vertex s, Vertex d, 
                              const void* ep = 0)
          : Base(s, d, ep), m_exists(exists) { }
        bool exists() const { return m_exists; }
      private:
        bool m_exists;
      };
  
      struct does_edge_exist {
        template <class Edge>
        bool operator()(const Edge& e) const { return e.exists(); }
      };
  
      template <typename EdgeProperty>
      bool get_edge_exists(const std::pair<bool, EdgeProperty>& stored_edge) {
        return stored_edge.first;
      }
      template <typename EdgeProperty>
      void set_edge_exists(std::pair<bool, EdgeProperty>& stored_edge, 
                           bool flag) {
        stored_edge.first = flag;
      }
  
      template <typename EdgeProxy>
      bool get_edge_exists(const EdgeProxy& edge_proxy) {
        return edge_proxy;
      }
      template <typename EdgeProxy>
      EdgeProxy& set_edge_exists(EdgeProxy& edge_proxy, bool flag) {
        edge_proxy = flag;
        return edge_proxy; // just to avoid never used warning
      }
  
  
  
      template <typename EdgeProperty>
      const EdgeProperty&
      get_property(const std::pair<bool, EdgeProperty>& stored_edge) {
        return stored_edge.second;
      }
      template <typename EdgeProperty>
      EdgeProperty&
      get_property(std::pair<bool, EdgeProperty>& stored_edge) {
        return stored_edge.second;
      }
  
      template <typename EdgeProperty>
      inline void
      set_property(std::pair<bool, EdgeProperty>& stored_edge, 
                   const EdgeProperty& ep) {
        stored_edge.second = ep;
      }
  
      inline const no_property& get_property(const char&) {
        static no_property s_prop;
        return s_prop;
      }
      inline no_property& get_property(char&) {
        static no_property s_prop;
        return s_prop;
      }
      template <typename EdgeProxy, typename EdgeProperty>
      inline void
      set_property(EdgeProxy, const EdgeProperty&) { }
      
      //=======================================================================
      // Directed Out Edge Iterator
  
      template <typename VertexDescriptor, typename MatrixIter, 
                typename VerticesSizeType>
      struct dir_adj_matrix_out_edge_iter_policies 
        : public default_iterator_policies 
      {
        dir_adj_matrix_out_edge_iter_policies() { }
        dir_adj_matrix_out_edge_iter_policies(const VertexDescriptor& src,
                                              const VerticesSizeType& n)
          : m_src(src), m_targ(0), m_n(n) { }
  
        template <typename Iter>
        void increment(Iter& i) {
          ++i.base();
          ++m_targ;
        }
        template <typename Iter>
        inline typename Iter::value_type
        dereference(const Iter& i) const 
        {
          typedef typename Iter::value_type EdgeDescriptor;
          return EdgeDescriptor(get_edge_exists(*i.base()), m_src, m_targ, 
                                &get_property(*i.base()));
        }
        VertexDescriptor m_src, m_targ;
        VerticesSizeType m_n;
      };
  
      //=======================================================================
      // Undirected Out Edge Iterator
  
      template <typename VertexDescriptor, typename MatrixIter, 
                typename VerticesSizeType>
      struct undir_adj_matrix_out_edge_iter_policies 
      {
        undir_adj_matrix_out_edge_iter_policies() { }
        undir_adj_matrix_out_edge_iter_policies(const VertexDescriptor& src,
                                                const VerticesSizeType& n)
          : m_src(src), m_inc(src), m_targ(0), m_n(n) { }
  
        void initialize(MatrixIter&) const{ }
  
        template <typename Iter>
        void increment(Iter& i) {
          if (m_targ < m_src)     // first half
            ++i.base();
          else {                  // second half
            ++m_inc;
            i.base() += m_inc;
          }
          ++m_targ;
        }
        template <typename Iter>
        inline typename Iter::value_type
        dereference(const Iter& i) const 
        {
          typedef typename Iter::value_type EdgeDescriptor;
          return EdgeDescriptor(get_edge_exists(*i.base()), m_src, m_targ,
                                &get_property(*i.base()));
        }
        template <typename Iter>
        bool equal(const Iter& x, const Iter& y) const
        { return x.base() == y.base(); }
  
        VertexDescriptor m_src, m_inc, m_targ;
        VerticesSizeType m_n;
      };
  
      //=======================================================================
      // Edge Iterator
  
      template <typename Directed, typename MatrixIter, 
                typename VerticesSizeType>
      struct adj_matrix_edge_iter_policies
        : public default_iterator_policies 
      {
        adj_matrix_edge_iter_policies() { }
        adj_matrix_edge_iter_policies(const MatrixIter& start,
                                      const VerticesSizeType& n) 
          : m_start(start), m_src(0), m_targ(0), m_n(n) { }
  
        void initialize(MatrixIter&) const{ }
  
        template <typename Iter>
        void increment(Iter& i) {
          increment_dispatch(i.base(), Directed());
        }
        void increment_dispatch(MatrixIter& i, directedS) {
          ++i;
          if (m_targ == m_n - 1) {
            m_targ = 0;
            ++m_src;
          } else
            ++m_targ;
        }
        void increment_dispatch(MatrixIter& i, undirectedS) {
          ++i;
          if (m_targ == m_src) {
            m_targ = 0;
            ++m_src;
          } else
            ++m_targ;
        }
  
        template <typename Iter>
        inline typename Iter::value_type
        dereference(const Iter& i) const 
        {
          typedef typename Iter::value_type EdgeDescriptor;
          return EdgeDescriptor(get_edge_exists(*i.base()), m_src, m_targ,
                                &get_property(*i.base()));
        }
        
        MatrixIter m_start;
        VerticesSizeType m_src, m_targ, m_n;
      };
  
    } // namespace detail
  
    //=========================================================================
    // Adjacency Matrix Traits
    template <typename Directed = directedS>
    class adjacency_matrix_traits {
      typedef typename Directed::is_bidir_t is_bidir;
      typedef typename Directed::is_directed_t is_directed;
    public:
      typedef typename boost::ct_if_t<is_bidir,
        bidirectional_tag,
        typename boost::ct_if_t<is_directed,
          directed_tag, undirected_tag
        >::type
      >::type directed_category;
      
      typedef disallow_parallel_edge_tag edge_parallel_category;
      
      typedef std::size_t vertex_descriptor;
  
      typedef detail::matrix_edge_desc_impl<directed_category,
        vertex_descriptor> edge_descriptor;
    };
  
    struct adjacency_matrix_class_tag { };
  
    struct adj_matrix_traversal_tag :
      public virtual adjacency_matrix_tag,
      public virtual vertex_list_graph_tag,
      public virtual incidence_graph_tag,
      public virtual adjacency_graph_tag,
      public virtual edge_list_graph_tag { };
    
    //=========================================================================
    // Adjacency Matrix Class
    template <typename Directed = directedS,
              typename VertexProperty = no_property,
              typename EdgeProperty = no_property,
              typename GraphProperty = no_property,
              typename Allocator = std::allocator<bool> >
    class adjacency_matrix {
      typedef adjacency_matrix self;
      typedef adjacency_matrix_traits<Directed> Traits;
    public: // should be private
      typedef typename ct_if_t<typename has_property<EdgeProperty>::type,
        std::pair<bool, EdgeProperty>, char>::type StoredEdge;
  #if defined(BOOST_MSVC) && BOOST_MSVC <= 1300
      typedef std::vector<StoredEdge> Matrix;
  #else
      // This causes internal compiler error for MSVC
      typedef typename Allocator::template rebind<StoredEdge>::other Alloc;
      typedef std::vector<StoredEdge, Alloc> Matrix;
  #endif
      typedef typename Matrix::iterator MatrixIter;
      typedef typename Matrix::size_type size_type;
    public:
      // Graph concept required types
      typedef typename Traits::vertex_descriptor vertex_descriptor;
      typedef typename Traits::edge_descriptor edge_descriptor;
      typedef typename Traits::directed_category directed_category;
      typedef typename Traits::edge_parallel_category edge_parallel_category;
      typedef adj_matrix_traversal_tag traversal_category;
  
      //private: if friends worked, these would be private
  
      typedef detail::dir_adj_matrix_out_edge_iter_policies<
        vertex_descriptor, MatrixIter, size_type> DirOutEdgePolicies;
  
      typedef detail::undir_adj_matrix_out_edge_iter_policies<
        vertex_descriptor, MatrixIter, size_type> UnDirOutEdgePolicies;
  
      typedef typename ct_if_t<typename Directed::is_directed_t,
        DirOutEdgePolicies, UnDirOutEdgePolicies>::type OutEdgePolicies;
      typedef iterator_adaptor<MatrixIter, OutEdgePolicies,
        edge_descriptor, edge_descriptor, edge_descriptor*,
        multi_pass_input_iterator_tag, std::ptrdiff_t> unfiltered_out_edge_iter;
      
      typedef detail::adj_matrix_edge_iter_policies<
        Directed, MatrixIter, size_type> EdgePolicies;
      typedef iterator_adaptor<MatrixIter, EdgePolicies,
        edge_descriptor, edge_descriptor, edge_descriptor*,
        multi_pass_input_iterator_tag, std::ptrdiff_t> unfiltered_edge_iter;
      
      typedef filter_iterator_generator<detail::does_edge_exist,
        unfiltered_out_edge_iter, edge_descriptor, edge_descriptor,
        edge_descriptor*, multi_pass_input_iterator_tag, std::ptrdiff_t>
        OutEdgeFilterGen;
      typedef typename OutEdgeFilterGen::type::policies_type
        FilteredOutEdgePolicy;
  
      typedef filter_iterator_generator<detail::does_edge_exist,
        unfiltered_edge_iter, edge_descriptor, edge_descriptor, edge_descriptor*,
        multi_pass_input_iterator_tag, std::ptrdiff_t> EdgeFilterGen;
      typedef typename EdgeFilterGen::type::policies_type FilteredEdgePolicy;
    public:
  
      // IncidenceGraph concept required types
      typedef typename OutEdgeFilterGen::type out_edge_iterator;
  
      typedef size_type degree_size_type;
  
      // BidirectionalGraph required types
      typedef void in_edge_iterator;
  
      // AdjacencyGraph required types
      typedef typename adjacency_iterator_generator<self,
        vertex_descriptor, out_edge_iterator>::type adjacency_iterator;
  
      // VertexListGraph required types
      typedef size_type vertices_size_type;
      typedef integer_range<vertex_descriptor> VertexList;
      typedef typename VertexList::iterator vertex_iterator;
  
      // EdgeListGrpah required types
      typedef size_type edges_size_type;
      typedef typename EdgeFilterGen::type edge_iterator;
  
      // PropertyGraph required types
      typedef EdgeProperty edge_property_type;
      typedef VertexProperty vertex_property_type;
      typedef adjacency_matrix_class_tag graph_tag;
  
      // Constructor required by MutableGraph
      adjacency_matrix(vertices_size_type n_vertices) 
        : m_matrix(Directed::is_directed ? 
                   (n_vertices * n_vertices)
                   : (n_vertices * (n_vertices + 1) / 2)),
        m_vertex_set(0, n_vertices),
        m_vertex_properties(n_vertices) { }
  
  
      //private: if friends worked, these would be private
  
      typename Matrix::const_reference
      get_edge(vertex_descriptor u, vertex_descriptor v) const {
        if (Directed::is_directed)
          return m_matrix[u * m_vertex_set.size() + v];
        else {
          if (v > u)
            std::swap(u, v);
          return m_matrix[u * (u - 1)/2 + v];
        }
      }
      typename Matrix::reference
      get_edge(vertex_descriptor u, vertex_descriptor v) {
        if (Directed::is_directed)
          return m_matrix[u * m_vertex_set.size() + v];
        else {
          if (v > u)
            std::swap(u, v);
          return m_matrix[u * (u + 1)/2 + v];
        }
      }
  
      Matrix m_matrix;
      VertexList m_vertex_set;
      std::vector<VertexProperty> m_vertex_properties;
    };
    
    //=========================================================================
    // Functions required by the AdjacencyMatrix concept 
  
    template <typename D, typename VP, typename EP, typename GP, typename A>
    std::pair<typename adjacency_matrix<D,VP,EP,GP,A>::edge_descriptor,
              bool>
    edge(typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor u,
         typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor v,
         const adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      bool exists = detail::get_edge_exists(g.get_edge(u,v));
      typename adjacency_matrix<D,VP,EP,GP,A>::edge_descriptor
        e(exists, u, v, &detail::get_property(g.get_edge(u,v)));
      return std::make_pair(e, exists);
    }
  
    //=========================================================================
    // Functions required by the IncidenceGraph concept 
  
    // O(1)
    template <typename VP, typename EP, typename GP, typename A>
    std::pair<typename adjacency_matrix<directedS,VP,EP,GP,A>::out_edge_iterator,
              typename adjacency_matrix<directedS,VP,EP,GP,A>::out_edge_iterator>
    out_edges
      (typename adjacency_matrix<directedS,VP,EP,GP,A>::vertex_descriptor u,
       const adjacency_matrix<directedS,VP,EP,GP,A>& g_)
    {
      typedef adjacency_matrix<directedS,VP,EP,GP,A> Graph;
      Graph& g = const_cast<Graph&>(g_);
      typename Graph::vertices_size_type offset = u * g.m_vertex_set.size();
      typename Graph::MatrixIter f = g.m_matrix.begin() + offset;
      typename Graph::MatrixIter l = f + g.m_vertex_set.size();
      typename Graph::OutEdgePolicies oep(u, g.m_vertex_set.size());
      typename Graph::unfiltered_out_edge_iter first(f, oep), last(l, oep);
      detail::does_edge_exist pred;
      typename Graph::FilteredOutEdgePolicy fp(pred, last);
      typedef typename Graph::out_edge_iterator out_edge_iterator;
      return std::make_pair(out_edge_iterator(first, fp), 
                            out_edge_iterator(last, fp));
    }
  
    // O(1)
    template <typename VP, typename EP, typename GP, typename A>
    std::pair<
      typename adjacency_matrix<undirectedS,VP,EP,GP,A>::out_edge_iterator,
      typename adjacency_matrix<undirectedS,VP,EP,GP,A>::out_edge_iterator>
    out_edges
      (typename adjacency_matrix<undirectedS,VP,EP,GP,A>::vertex_descriptor u,
       const adjacency_matrix<undirectedS,VP,EP,GP,A>& g_)
    {
      typedef adjacency_matrix<undirectedS,VP,EP,GP,A> Graph;
      Graph& g = const_cast<Graph&>(g_);
      typename Graph::vertices_size_type offset = u * (u + 1) / 2;
      typename Graph::MatrixIter f = g.m_matrix.begin() + offset;
      typename Graph::MatrixIter l = g.m_matrix.end() + u;
      typename Graph::OutEdgePolicies oep(u, g.m_vertex_set.size());
      typename Graph::unfiltered_out_edge_iter first(f, oep), last(l, oep);
      detail::does_edge_exist pred;
      typename Graph::FilteredOutEdgePolicy fp(pred, last);
      typedef typename Graph::out_edge_iterator out_edge_iterator;
      return std::make_pair(out_edge_iterator(first, fp), 
                            out_edge_iterator(last, fp));
    }
    
    // O(N)
    template <typename D, typename VP, typename EP, typename GP, typename A>  
    typename adjacency_matrix<D,VP,EP,GP,A>::degree_size_type
    out_degree(typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor u,
               const adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      typename adjacency_matrix<D,VP,EP,GP,A>::degree_size_type n = 0;
      typename adjacency_matrix<D,VP,EP,GP,A>::out_edge_iterator f, l;
      for (tie(f, l) = out_edges(u, g); f != l; ++f)
        ++n;
      return n;
    }
  
    // O(1)
    template <typename D, typename VP, typename EP, typename GP, typename A,
      typename Dir, typename Vertex>  
    typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor
    source(const detail::matrix_edge_desc_impl<Dir,Vertex>& e,
           const adjacency_matrix<D,VP,EP,GP,A>&)
    {
      return e.m_source;
    }
  
    // O(1)
    template <typename D, typename VP, typename EP, typename GP, typename A,
      typename Dir, typename Vertex>  
    typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor
    target(const detail::matrix_edge_desc_impl<Dir,Vertex>& e,
           const adjacency_matrix<D,VP,EP,GP,A>&)
    {
      return e.m_target;
    }
  
    //=========================================================================
    // Functions required by the AdjacencyGraph concept 
  
    template <typename D, typename VP, typename EP, typename GP, typename A>
    std::pair<typename adjacency_matrix<D,VP,EP,GP,A>::adjacency_iterator,
              typename adjacency_matrix<D,VP,EP,GP,A>::adjacency_iterator>
    adjacent_vertices
      (typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor u,
       const adjacency_matrix<D,VP,EP,GP,A>& g_)
    {
        typedef adjacency_matrix<D,VP,EP,GP,A> Graph;
        const Graph& cg = static_cast<const Graph&>(g_);
        Graph& g = const_cast<Graph&>(cg);
        typedef typename Graph::adjacency_iterator adjacency_iterator;
        typename Graph::out_edge_iterator first, last;
        boost::tie(first, last) = out_edges(u, g);
        return std::make_pair(adjacency_iterator(first, &g),
                              adjacency_iterator(last, &g));
    }
  
    //=========================================================================
    // Functions required by the VertexListGraph concept 
  
    template <typename D, typename VP, typename EP, typename GP, typename A>
    std::pair<typename adjacency_matrix<D,VP,EP,GP,A>::vertex_iterator,
              typename adjacency_matrix<D,VP,EP,GP,A>::vertex_iterator>
    vertices(const adjacency_matrix<D,VP,EP,GP,A>& g_) {
      typedef adjacency_matrix<D,VP,EP,GP,A> Graph;
      Graph& g = const_cast<Graph&>(g_);
      return std::make_pair(g.m_vertex_set.begin(), g.m_vertex_set.end());
    }
  
    template <typename D, typename VP, typename EP, typename GP, typename A>
    typename adjacency_matrix<D,VP,EP,GP,A>::vertices_size_type
    num_vertices(const adjacency_matrix<D,VP,EP,GP,A>& g) {
      return g.m_vertex_set.size();
    }
    
    //=========================================================================
    // Functions required by the EdgeListGraph concept 
    
    template <typename D, typename VP, typename EP, typename GP, typename A>
    std::pair<typename adjacency_matrix<D,VP,EP,GP,A>::edge_iterator,
              typename adjacency_matrix<D,VP,EP,GP,A>::edge_iterator>
    edges(const adjacency_matrix<D,VP,EP,GP,A>& g_)
    {
      typedef adjacency_matrix<D,VP,EP,GP,A> Graph;
      Graph& g = const_cast<Graph&>(g_);
      typename Graph::EdgePolicies ep(g.m_matrix.begin(), 
                                      g.m_vertex_set.size()); 
      typename Graph::unfiltered_edge_iter
        first(g.m_matrix.begin(), ep),
        last(g.m_matrix.end(), ep);
      detail::does_edge_exist pred;
      typename Graph::FilteredEdgePolicy fp(pred, last);
      typedef typename Graph::edge_iterator edge_iterator;
      return std::make_pair(edge_iterator(first, fp),
                            edge_iterator(last, fp));
    }
  
    template <typename D, typename VP, typename EP, typename GP, typename A>
    typename adjacency_matrix<D,VP,EP,GP,A>::edges_size_type
    num_edges(const adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      typedef adjacency_matrix<D,VP,EP,GP,A> Graph;
      typename Graph::edges_size_type num_e = 0;
      typename Graph::vertex_iterator vi, vi_end;
      for (tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
        num_e += out_degree(*vi, g);
      return num_e;
    }
    
    //=========================================================================
    // Functions required by the MutableGraph concept 
  
    // O(1)
    template <typename D, typename VP, typename EP, typename GP, typename A>
    std::pair<typename adjacency_matrix<D,VP,EP,GP,A>::edge_descriptor, bool>
    add_edge(typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor u,
             typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor v,
             const EP& ep,
             adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      typedef typename adjacency_matrix<D,VP,EP,GP,A>::edge_descriptor 
        edge_descriptor;
      if (detail::get_edge_exists(g.get_edge(u,v)) == false) {
        detail::set_property(g.get_edge(u,v), ep);
        detail::set_edge_exists(g.get_edge(u,v), true);
        return std::make_pair
          (edge_descriptor(true, u, v, &detail::get_property(g.get_edge(u,v))), 
           true);
      } else
        return std::make_pair
          (edge_descriptor(true, u, v, &detail::get_property(g.get_edge(u,v))),
           false);
    }
    // O(1)
    template <typename D, typename VP, typename EP, typename GP, typename A>
    std::pair<typename adjacency_matrix<D,VP,EP,GP,A>::edge_descriptor, bool>
    add_edge(typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor u,
             typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor v,
             adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      EP ep;
      return add_edge(u, v, ep, g);
    }
  
    // O(1)  
    template <typename D, typename VP, typename EP, typename GP, typename A>
    void
    remove_edge(typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor u,
                typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor v,
                adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      detail::set_edge_exists(g.get_edge(u,v), false);
    }
  
    // O(1)
    template <typename D, typename VP, typename EP, typename GP, typename A>
    void
    remove_edge(typename adjacency_matrix<D,VP,EP,GP,A>::edge_descriptor e,
                adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      remove_edge(source(e, g), target(e, g), g);
    }
  
    
    template <typename D, typename VP, typename EP, typename GP, typename A>
    inline typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor
    add_vertex(adjacency_matrix<D,VP,EP,GP,A>& g) {
      // UNDER CONSTRUCTION
      assert(false);
      return *vertices(g).first;
    }
  
    template <typename D, typename VP, typename EP, typename GP, typename A>
    inline typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor
    add_vertex(const VP& vp, adjacency_matrix<D,VP,EP,GP,A>& g) {
      // UNDER CONSTRUCTION
      assert(false);
      return *vertices(g).first;
    }
  
    template <typename D, typename VP, typename EP, typename GP, typename A>
    inline void
    remove_vertex(typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor u,
                  adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      // UNDER CONSTRUCTION
      assert(false);
    }
  
    // O(V)
    template <typename VP, typename EP, typename GP, typename A>
    void
    clear_vertex
      (typename adjacency_matrix<directedS,VP,EP,GP,A>::vertex_descriptor u,
       adjacency_matrix<directedS,VP,EP,GP,A>& g)
    {
      typename adjacency_matrix<directedS,VP,EP,GP,A>::vertex_iterator 
        vi, vi_end;
      for (tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
        remove_edge(u, *vi, g);
      for (tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
        remove_edge(*vi, u, g);
    }
  
    // O(V)
    template <typename VP, typename EP, typename GP, typename A>
    void
    clear_vertex
      (typename adjacency_matrix<undirectedS,VP,EP,GP,A>::vertex_descriptor u,
       adjacency_matrix<undirectedS,VP,EP,GP,A>& g)
    {
      typename adjacency_matrix<undirectedS,VP,EP,GP,A>::vertex_iterator
        vi, vi_end;
      for (tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
        remove_edge(u, *vi, g);
    }
  
    //=========================================================================
    // Vertex Property Map
    
    template <typename GraphPtr, typename Vertex, typename T, typename R, 
      typename Tag> 
    class adj_matrix_vertex_property_map 
      : public put_get_helper<R,
           adj_matrix_vertex_property_map<GraphPtr, Vertex, T, R, Tag> >
    {
    public:
      typedef T value_type;
      typedef R reference;
      typedef Vertex key_type;
      typedef boost::lvalue_property_map_tag category;
      adj_matrix_vertex_property_map() { }
      adj_matrix_vertex_property_map(GraphPtr g) : m_g(g) { }
      inline reference operator[](key_type v) const {
        return get_property_value(m_g->m_vertex_properties[v], Tag());
      }
      GraphPtr m_g;
    };
  
    template <class Property, class Vertex>
    struct adj_matrix_vertex_id_map
      : public boost::put_get_helper<Vertex,
          adj_matrix_vertex_id_map<Property, Vertex> >
    {
      typedef Vertex value_type;
      typedef Vertex reference;
      typedef Vertex key_type;
      typedef boost::readable_property_map_tag category;
       adj_matrix_vertex_id_map() { }
      template <class Graph>
      inline adj_matrix_vertex_id_map(const Graph&) { }
      inline value_type operator[](key_type v) const { return v; }
    };
  
    namespace detail {
  
      struct adj_matrix_any_vertex_pa {
        template <class Tag, class Graph, class Property>
        struct bind_ {
          typedef typename property_value<Property,Tag>::type Value;
          typedef typename boost::graph_traits<Graph>::vertex_descriptor Vertex;
          
          typedef adj_matrix_vertex_property_map<Graph*, Vertex, Value, Value&,
            Tag> type;
          typedef adj_matrix_vertex_property_map<const Graph*, Vertex, Value, 
            const Value&, Tag> const_type;
        };
      };
      struct adj_matrix_id_vertex_pa {
        template <class Tag, class Graph, class Property>
        struct bind_ {
          typedef typename Graph::vertex_descriptor Vertex;
          typedef adj_matrix_vertex_id_map<Property, Vertex> type;
          typedef adj_matrix_vertex_id_map<Property, Vertex> const_type;
        };
      };
  
      template <class Tag>
      struct adj_matrix_choose_vertex_pa_helper {
        typedef adj_matrix_any_vertex_pa type;
      };
      template <>
      struct adj_matrix_choose_vertex_pa_helper<vertex_index_t> {
        typedef adj_matrix_id_vertex_pa type;
      };
  
      template <class Tag, class Graph, class Property>
      struct adj_matrix_choose_vertex_pa {
        typedef typename adj_matrix_choose_vertex_pa_helper<Tag>::type Helper;
        typedef typename Helper::template bind_<Tag,Graph,Property> Bind;
        typedef typename Bind::type type;
        typedef typename Bind::const_type const_type;
      };
  
      struct adj_matrix_vertex_property_selector {
        template <class Graph, class Property, class Tag>
        struct bind_ {
          typedef adj_matrix_choose_vertex_pa<Tag,Graph,Property> Choice;
          typedef typename Choice::type type;
          typedef typename Choice::const_type const_type;
        };
      };
  
    } // namespace detail
  
    template <>
    struct vertex_property_selector<adjacency_matrix_class_tag> {
      typedef detail::adj_matrix_vertex_property_selector type;
    };
    
    //=========================================================================
    // Edge Property Map
  
  
    template <typename Directed, typename Property, typename Vertex, 
      typename T, typename R, typename Tag> 
    class adj_matrix_edge_property_map 
      : public put_get_helper<R,
           adj_matrix_edge_property_map<Directed, Property, Vertex, T, R, Tag> >
    {
    public:
      typedef T value_type;
      typedef R reference;
      typedef detail::matrix_edge_desc_impl<Directed, Vertex> key_type;
      typedef boost::lvalue_property_map_tag category;
      inline reference operator[](key_type e) const {
        Property& p = *(Property*)e.get_property();
        return get_property_value(p, Tag());
      }
    };
    struct adj_matrix_edge_property_selector {
      template <class Graph, class Property, class Tag>
      struct bind_ {
        typedef typename property_value<Property,Tag>::type T;
        typedef typename Graph::vertex_descriptor Vertex;
        typedef adj_matrix_edge_property_map<typename Graph::directed_category,
          Property, Vertex, T, T&, Tag> type;
        typedef adj_matrix_edge_property_map<typename Graph::directed_category,
          Property, Vertex, T, const T&, Tag> const_type;
      };
    };
    template <>
    struct edge_property_selector<adjacency_matrix_class_tag> {
      typedef adj_matrix_edge_property_selector type;
    };
  
    //=========================================================================
    // Functions required by PropertyGraph
  
    namespace detail {
  
      template <typename Property, typename D, typename VP, typename EP, 
                typename GP, typename A>
      typename boost::property_map<adjacency_matrix<D,VP,EP,GP,A>, 
        Property>::type
      get_dispatch(adjacency_matrix<D,VP,EP,GP,A>& g, Property,
                   vertex_property_tag)
      {
        typedef adjacency_matrix<D,VP,EP,GP,A> Graph;
        typedef typename boost::property_map<adjacency_matrix<D,VP,EP,GP,A>, 
          Property>::type PA;
        return PA(&g);
      }
      template <typename Property, typename D, typename VP, typename EP, 
                typename GP, typename A>
      typename boost::property_map<adjacency_matrix<D,VP,EP,GP,A>, 
        Property>::type
      get_dispatch(adjacency_matrix<D,VP,EP,GP,A>& g, Property,
                   edge_property_tag)
      {
        typedef typename boost::property_map<adjacency_matrix<D,VP,EP,GP,A>, 
          Property>::type PA;
        return PA();
      }
      template <typename Property, typename D, typename VP, typename EP, 
                typename GP, typename A>
      typename boost::property_map<adjacency_matrix<D,VP,EP,GP,A>, 
        Property>::const_type
      get_dispatch(const adjacency_matrix<D,VP,EP,GP,A>& g, Property,
                   vertex_property_tag)
      {
        typedef adjacency_matrix<D,VP,EP,GP,A> Graph;
        typedef typename boost::property_map<adjacency_matrix<D,VP,EP,GP,A>, 
          Property>::const_type PA;
        return PA(&g);
      }
      template <typename Property, typename D, typename VP, typename EP, 
                typename GP, typename A>
      typename boost::property_map<adjacency_matrix<D,VP,EP,GP,A>, 
        Property>::const_type
      get_dispatch(const adjacency_matrix<D,VP,EP,GP,A>& g, Property,
                   edge_property_tag)
      {
        typedef typename boost::property_map<adjacency_matrix<D,VP,EP,GP,A>, 
          Property>::const_type PA;
        return PA();
      }
  
    } // namespace detail
  
    template <typename Property, typename D, typename VP, typename EP, 
              typename GP, typename A>
    inline
    typename property_map<adjacency_matrix<D,VP,EP,GP,A>, Property>::type
    get(Property p, adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      typedef typename property_kind<Property>::type Kind;
      return detail::get_dispatch(g, p, Kind());
    }
  
    template <typename Property, typename D, typename VP, typename EP, 
              typename GP, typename A>
    inline
    typename property_map<adjacency_matrix<D,VP,EP,GP,A>, Property>::const_type
    get(Property p, const adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      typedef typename property_kind<Property>::type Kind;
      return detail::get_dispatch(g, p, Kind());
    }
  
    template <typename Property, typename D, typename VP, typename EP, 
              typename GP, typename A, typename Key>
    inline
    typename property_traits<
      typename property_map<adjacency_matrix<D,VP,EP,GP,A>, Property>::const_type
    >::value_type
    get(Property p, const adjacency_matrix<D,VP,EP,GP,A>& g,
        const Key& key)
    {
      return get(get(p, g), key);
    }
  
    template <typename Property, typename D, typename VP, typename EP, 
              typename GP, typename A, typename Key, typename Value>
    inline void
    put(Property p, adjacency_matrix<D,VP,EP,GP,A>& g,
        const Key& key, const Value& value)
    {
      typedef adjacency_matrix<D,VP,EP,GP,A> Graph;
      typedef typename boost::property_map<Graph, Property>::type Map;
      Map pmap = get(p, g);
      put(pmap, key, value);
    }
    
    //=========================================================================
    // Other Functions
  
    template <typename D, typename VP, typename EP, typename GP, typename A>  
    typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor
    vertex(typename adjacency_matrix<D,VP,EP,GP,A>::vertices_size_type n,
           const adjacency_matrix<D,VP,EP,GP,A>& g)
    {
      return n;
    }
  
  
  } // namespace boost
  
  #endif // BOOST_ADJACENCY_MATRIX_HPP
  