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boost/graph/compressed_sparse_row_graph.hpp

// Copyright 2005-2009 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: Jeremiah Willcock
//           Douglas Gregor
//           Andrew Lumsdaine

// Compressed sparse row graph type

#ifndef BOOST_GRAPH_COMPRESSED_SPARSE_ROW_GRAPH_HPP
#define BOOST_GRAPH_COMPRESSED_SPARSE_ROW_GRAPH_HPP

#include <vector>
#include <utility>
#include <algorithm>
#include <climits>
#include <boost/assert.hpp>
#include <iterator>
#if 0
#include <iostream> // For some debugging code below
#endif
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/properties.hpp>
#include <boost/graph/filtered_graph.hpp> // For keep_all
#include <boost/graph/detail/indexed_properties.hpp>
#include <boost/graph/detail/compressed_sparse_row_struct.hpp>
#include <boost/graph/iteration_macros.hpp>
#include <boost/iterator/counting_iterator.hpp>
#include <boost/iterator/reverse_iterator.hpp>
#include <boost/iterator/zip_iterator.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/integer.hpp>
#include <boost/iterator/iterator_facade.hpp>
#include <boost/mpl/if.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/graph/graph_selectors.hpp>
#include <boost/graph/detail/is_distributed_selector.hpp>
#include <boost/graph/properties.hpp>
#include <boost/static_assert.hpp>
#include <boost/functional/hash.hpp>
#include <boost/next_prior.hpp>
#include <boost/property_map/transform_value_property_map.hpp>
#include <boost/mpl/print.hpp>

namespace boost
{

// A tag type indicating that the graph in question is a compressed
// sparse row graph. This is an internal detail of the BGL.
struct csr_graph_tag;

// A type (edges_are_sorted_t) and a value (edges_are_sorted) used to indicate
// that the edge list passed into the CSR graph is already sorted by source
// vertex.
enum edges_are_sorted_t
{
    edges_are_sorted
};

// A type (edges_are_sorted_global_t) and a value (edges_are_sorted_global)
// used to indicate that the edge list passed into the CSR graph is already
// sorted by source vertex.
enum edges_are_sorted_global_t
{
    edges_are_sorted_global
};

// A type (edges_are_unsorted_t) and a value (edges_are_unsorted) used to
// indicate that the edge list passed into the CSR graph is not sorted by
// source vertex.  This version caches the edge information in memory, and thus
// requires only a single pass over the input data.
enum edges_are_unsorted_t
{
    edges_are_unsorted
};

// A type (edges_are_unsorted_multi_pass_t) and a value
// (edges_are_unsorted_multi_pass) used to indicate that the edge list passed
// into the CSR graph is not sorted by source vertex.  This version uses less
// memory but requires multi-pass capability on the iterators.
enum edges_are_unsorted_multi_pass_t
{
    edges_are_unsorted_multi_pass
};

// A type (edges_are_unsorted_multi_pass_global_t) and a value
// (edges_are_unsorted_multi_pass_global) used to indicate that the edge list
// passed into the CSR graph is not sorted by source vertex.  This version uses
// less memory but requires multi-pass capability on the iterators.  The
// global mapping and filtering is done here because it is often faster and it
// greatly simplifies handling of edge properties.
enum edges_are_unsorted_multi_pass_global_t
{
    edges_are_unsorted_multi_pass_global
};

// A type (construct_inplace_from_sources_and_targets_t) and a value
// (construct_inplace_from_sources_and_targets) used to indicate that mutable
// vectors of sources and targets (and possibly edge properties) are being used
// to construct the CSR graph.  These vectors are sorted in-place and then the
// targets and properties are swapped into the graph data structure.
enum construct_inplace_from_sources_and_targets_t
{
    construct_inplace_from_sources_and_targets
};

// A type (construct_inplace_from_sources_and_targets_global_t) and a value
// (construct_inplace_from_sources_and_targets_global) used to indicate that
// mutable vectors of sources and targets (and possibly edge properties) are
// being used to construct the CSR graph.  These vectors are sorted in-place
// and then the targets and properties are swapped into the graph data
// structure.  It is assumed that global indices (for distributed CSR) are
// used, and a map is required to convert those to local indices.  This
// constructor is intended for internal use by the various CSR graphs
// (sequential and distributed).
enum construct_inplace_from_sources_and_targets_global_t
{
    construct_inplace_from_sources_and_targets_global
};

// A type (edges_are_unsorted_global_t) and a value (edges_are_unsorted_global)
// used to indicate that the edge list passed into the CSR graph is not sorted
// by source vertex.  The data is also stored using global vertex indices, and
// must be filtered to choose only local vertices.  This constructor caches the
// edge information in memory, and thus requires only a single pass over the
// input data.  This constructor is intended for internal use by the
// distributed CSR constructors.
enum edges_are_unsorted_global_t
{
    edges_are_unsorted_global
};

/****************************************************************************
 * Local helper macros to reduce typing and clutter later on.               *
 ****************************************************************************/
#define BOOST_CSR_GRAPH_TEMPLATE_PARMS                                 \
    typename Directed, typename VertexProperty, typename EdgeProperty, \
        typename GraphProperty, typename Vertex, typename EdgeIndex
#define BOOST_CSR_GRAPH_TYPE                                             \
    compressed_sparse_row_graph< Directed, VertexProperty, EdgeProperty, \
        GraphProperty, Vertex, EdgeIndex >
#define BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS                                  \
    typename VertexProperty, typename EdgeProperty, typename GraphProperty, \
        typename Vertex, typename EdgeIndex
#define BOOST_DIR_CSR_GRAPH_TYPE                                          \
    compressed_sparse_row_graph< directedS, VertexProperty, EdgeProperty, \
        GraphProperty, Vertex, EdgeIndex >
#define BOOST_BIDIR_CSR_GRAPH_TEMPLATE_PARMS                                \
    typename VertexProperty, typename EdgeProperty, typename GraphProperty, \
        typename Vertex, typename EdgeIndex
#define BOOST_BIDIR_CSR_GRAPH_TYPE                                             \
    compressed_sparse_row_graph< bidirectionalS, VertexProperty, EdgeProperty, \
        GraphProperty, Vertex, EdgeIndex >

namespace detail
{
    template < typename T >
    struct default_construct_iterator
    : public boost::iterator_facade< default_construct_iterator< T >, T,
          boost::random_access_traversal_tag, const T& >
    {
        typedef boost::iterator_facade< default_construct_iterator< T >, T,
            std::random_access_iterator_tag, const T& >
            base_type;
        T saved_value;
        const T& dereference() const { return saved_value; }
        bool equal(default_construct_iterator /*i*/) const { return true; }
        void increment() {}
        void decrement() {}
        void advance(typename base_type::difference_type) {}
        typename base_type::difference_type distance_to(
            default_construct_iterator) const
        {
            return 0;
        }
    };

    template < typename Less > struct compare_first
    {
        Less less;
        compare_first(Less less = Less()) : less(less) {}
        template < typename Tuple >
        bool operator()(const Tuple& a, const Tuple& b) const
        {
            return less(a.template get< 0 >(), b.template get< 0 >());
        }
    };

    template < int N, typename Result > struct my_tuple_get_class
    {
        typedef const Result& result_type;
        template < typename Tuple > result_type operator()(const Tuple& t) const
        {
            return t.template get< N >();
        }
    };
}

/** Compressed sparse row graph.
 *
 * Vertex and EdgeIndex should be unsigned integral types and should
 * specialize numeric_limits.
 */
template < typename Directed = directedS, typename VertexProperty = no_property,
    typename EdgeProperty = no_property, typename GraphProperty = no_property,
    typename Vertex = std::size_t,
    typename EdgeIndex = Vertex >
class compressed_sparse_row_graph; // Not defined

template < typename VertexProperty, typename EdgeProperty,
    typename GraphProperty, typename Vertex, typename EdgeIndex >
class compressed_sparse_row_graph< directedS, VertexProperty, EdgeProperty,
    GraphProperty, Vertex, EdgeIndex >
: public detail::indexed_vertex_properties< BOOST_DIR_CSR_GRAPH_TYPE,
      VertexProperty, Vertex, typed_identity_property_map< Vertex > >
{
public:
    typedef detail::indexed_vertex_properties< compressed_sparse_row_graph,
        VertexProperty, Vertex, typed_identity_property_map< Vertex > >
        inherited_vertex_properties;

    // Some tests to prevent use of "void" is a property type (as was done in
    // some test cases):
    BOOST_STATIC_ASSERT((!is_same< VertexProperty, void >::value));
    BOOST_STATIC_ASSERT((!is_same< EdgeProperty, void >::value));
    BOOST_STATIC_ASSERT((!is_same< GraphProperty, void >::value));

public:
    // For Property Graph
    typedef GraphProperty graph_property_type;
    typedef typename lookup_one_property< GraphProperty, graph_bundle_t >::type
        graph_bundled;

    typedef detail::compressed_sparse_row_structure< EdgeProperty, Vertex,
        EdgeIndex >
        forward_type;

public:
    /* At this time, the compressed sparse row graph can only be used to
     * create directed and bidirectional graphs. In the future,
     * undirected CSR graphs will also be supported.
     */
    // BOOST_STATIC_ASSERT((is_same<Directed, directedS>::value));

    // Concept requirements:
    // For Graph
    typedef Vertex vertex_descriptor;
    typedef detail::csr_edge_descriptor< Vertex, EdgeIndex > edge_descriptor;
    typedef directed_tag directed_category;
    typedef allow_parallel_edge_tag edge_parallel_category;

    class traversal_category : public incidence_graph_tag,
                               public adjacency_graph_tag,
                               public vertex_list_graph_tag,
                               public edge_list_graph_tag
    {
    };

    static vertex_descriptor null_vertex() { return vertex_descriptor(-1); }

    // For VertexListGraph
    typedef counting_iterator< Vertex > vertex_iterator;
    typedef Vertex vertices_size_type;

    // For EdgeListGraph
    typedef EdgeIndex edges_size_type;

    // For IncidenceGraph
    typedef detail::csr_out_edge_iterator< compressed_sparse_row_graph >
        out_edge_iterator;
    typedef EdgeIndex degree_size_type;

    // For AdjacencyGraph
    typedef typename std::vector< Vertex >::const_iterator adjacency_iterator;

    // For EdgeListGraph
    typedef detail::csr_edge_iterator< compressed_sparse_row_graph >
        edge_iterator;

    // For BidirectionalGraph (not implemented)
    typedef void in_edge_iterator;

    // For internal use
    typedef csr_graph_tag graph_tag;

    typedef typename forward_type::inherited_edge_properties::edge_bundled
        edge_bundled;
    typedef
        typename forward_type::inherited_edge_properties::edge_push_back_type
            edge_push_back_type;
    typedef typename forward_type::inherited_edge_properties::edge_property_type
        edge_property_type;

    // Constructors

    // Default constructor: an empty graph.
    compressed_sparse_row_graph() : m_property() {}

    //  With numverts vertices
    compressed_sparse_row_graph(vertices_size_type numverts)
    : inherited_vertex_properties(numverts), m_forward(numverts)
    {
    }

    //  From number of vertices and unsorted list of edges
    template < typename MultiPassInputIterator >
    compressed_sparse_row_graph(edges_are_unsorted_multi_pass_t,
        MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
        vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numverts), m_property(prop)
    {
        m_forward.assign_unsorted_multi_pass_edges(edge_begin, edge_end,
            numverts, typed_identity_property_map< vertices_size_type >(),
            keep_all());
    }

    //  From number of vertices and unsorted list of edges, plus edge properties
    template < typename MultiPassInputIterator, typename EdgePropertyIterator >
    compressed_sparse_row_graph(edges_are_unsorted_multi_pass_t,
        MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
        EdgePropertyIterator ep_iter, vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numverts), m_forward(), m_property(prop)
    {
        m_forward.assign_unsorted_multi_pass_edges(edge_begin, edge_end,
            ep_iter, numverts,
            typed_identity_property_map< vertices_size_type >(), keep_all());
    }

    //  From number of vertices and unsorted list of edges, with filter and
    //  global-to-local map
    template < typename MultiPassInputIterator, typename GlobalToLocal,
        typename SourcePred >
    compressed_sparse_row_graph(edges_are_unsorted_multi_pass_global_t,
        MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
        vertices_size_type numlocalverts, const GlobalToLocal& global_to_local,
        const SourcePred& source_pred,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numlocalverts), m_forward(), m_property(prop)
    {
        m_forward.assign_unsorted_multi_pass_edges(
            edge_begin, edge_end, numlocalverts, global_to_local, source_pred);
    }

    //  From number of vertices and unsorted list of edges, plus edge
    //  properties, with filter and global-to-local map
    template < typename MultiPassInputIterator, typename EdgePropertyIterator,
        typename GlobalToLocal, typename SourcePred >
    compressed_sparse_row_graph(edges_are_unsorted_multi_pass_global_t,
        MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
        EdgePropertyIterator ep_iter, vertices_size_type numlocalverts,
        const GlobalToLocal& global_to_local, const SourcePred& source_pred,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numlocalverts), m_forward(), m_property(prop)
    {
        m_forward.assign_unsorted_multi_pass_edges(edge_begin, edge_end,
            ep_iter, numlocalverts, global_to_local, source_pred);
    }

    //  From number of vertices and sorted list of edges (new interface)
    template < typename InputIterator >
    compressed_sparse_row_graph(edges_are_sorted_t, InputIterator edge_begin,
        InputIterator edge_end, vertices_size_type numverts,
        edges_size_type numedges = 0,
        const GraphProperty& prop = GraphProperty())
    : m_property(prop)
    {
        m_forward.assign_from_sorted_edges(edge_begin, edge_end,
            typed_identity_property_map< vertices_size_type >(), keep_all(),
            numverts, numedges);
        inherited_vertex_properties::resize(numverts);
    }

    //  From number of vertices and sorted list of edges (new interface)
    template < typename InputIterator, typename EdgePropertyIterator >
    compressed_sparse_row_graph(edges_are_sorted_t, InputIterator edge_begin,
        InputIterator edge_end, EdgePropertyIterator ep_iter,
        vertices_size_type numverts, edges_size_type numedges = 0,
        const GraphProperty& prop = GraphProperty())
    : m_property(prop)
    {
        m_forward.assign_from_sorted_edges(edge_begin, edge_end, ep_iter,
            typed_identity_property_map< vertices_size_type >(), keep_all(),
            numverts, numedges);
        inherited_vertex_properties::resize(numverts);
    }

    //  From number of vertices and sorted list of edges, filtered and global
    //  (new interface)
    template < typename InputIterator, typename GlobalToLocal,
        typename SourcePred >
    compressed_sparse_row_graph(edges_are_sorted_global_t,
        InputIterator edge_begin, InputIterator edge_end,
        const GlobalToLocal& global_to_local, const SourcePred& source_pred,
        vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : m_property(prop)
    {
        m_forward.assign_from_sorted_edges(
            edge_begin, edge_end, global_to_local, source_pred, numverts, 0);
        inherited_vertex_properties::resize(numverts);
    }

    //  From number of vertices and sorted list of edges (new interface)
    template < typename InputIterator, typename EdgePropertyIterator,
        typename GlobalToLocal, typename SourcePred >
    compressed_sparse_row_graph(edges_are_sorted_global_t,
        InputIterator edge_begin, InputIterator edge_end,
        EdgePropertyIterator ep_iter, const GlobalToLocal& global_to_local,
        const SourcePred& source_pred, vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : m_property(prop)
    {
        m_forward.assign_from_sorted_edges(edge_begin, edge_end, ep_iter,
            global_to_local, source_pred, numverts, 0);
        inherited_vertex_properties::resize(numverts);
    }

    //  From number of vertices and mutable vectors of sources and targets;
    //  vectors are returned with unspecified contents but are guaranteed not to
    //  share storage with the constructed graph.
    compressed_sparse_row_graph(construct_inplace_from_sources_and_targets_t,
        std::vector< vertex_descriptor >& sources,
        std::vector< vertex_descriptor >& targets, vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numverts), m_property(prop)
    {
        m_forward.assign_sources_and_targets_global(sources, targets, numverts,
            boost::typed_identity_property_map< vertices_size_type >());
    }

    //  From number of vertices and mutable vectors of sources and targets,
    //  expressed with global vertex indices; vectors are returned with
    //  unspecified contents but are guaranteed not to share storage with the
    //  constructed graph.  This constructor should only be used by the
    //  distributed CSR graph.
    template < typename GlobalToLocal >
    compressed_sparse_row_graph(
        construct_inplace_from_sources_and_targets_global_t,
        std::vector< vertex_descriptor >& sources,
        std::vector< vertex_descriptor >& targets,
        vertices_size_type numlocalverts, GlobalToLocal global_to_local,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numlocalverts), m_property(prop)
    {
        m_forward.assign_sources_and_targets_global(
            sources, targets, numlocalverts, global_to_local);
    }

    //  From number of vertices and mutable vectors of sources, targets, and
    //  edge properties; vectors are returned with unspecified contents but are
    //  guaranteed not to share storage with the constructed graph.
    compressed_sparse_row_graph(construct_inplace_from_sources_and_targets_t,
        std::vector< vertex_descriptor >& sources,
        std::vector< vertex_descriptor >& targets,
        std::vector<
            typename forward_type::inherited_edge_properties::edge_bundled >&
            edge_props,
        vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numverts), m_property(prop)
    {
        m_forward.assign_sources_and_targets_global(sources, targets,
            edge_props, numverts,
            boost::typed_identity_property_map< vertices_size_type >());
    }

    //  From number of vertices and mutable vectors of sources and targets and
    //  edge properties, expressed with global vertex indices; vectors are
    //  returned with unspecified contents but are guaranteed not to share
    //  storage with the constructed graph.  This constructor should only be
    //  used by the distributed CSR graph.
    template < typename GlobalToLocal >
    compressed_sparse_row_graph(
        construct_inplace_from_sources_and_targets_global_t,
        std::vector< vertex_descriptor >& sources,
        std::vector< vertex_descriptor >& targets,
        std::vector<
            typename forward_type::inherited_edge_properties::edge_bundled >&
            edge_props,
        vertices_size_type numlocalverts, GlobalToLocal global_to_local,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numlocalverts), m_property(prop)
    {
        m_forward.assign_sources_and_targets_global(
            sources, targets, edge_props, numlocalverts, global_to_local);
    }

    //  From number of vertices and single-pass range of unsorted edges.  Data
    //  is cached in coordinate form before creating the actual graph.
    template < typename InputIterator >
    compressed_sparse_row_graph(edges_are_unsorted_t, InputIterator edge_begin,
        InputIterator edge_end, vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numverts), m_property(prop)
    {
        std::vector< vertex_descriptor > sources, targets;
        boost::graph::detail::split_into_separate_coords(
            edge_begin, edge_end, sources, targets);
        m_forward.assign_sources_and_targets_global(sources, targets, numverts,
            boost::typed_identity_property_map< vertices_size_type >());
    }

    //  From number of vertices and single-pass range of unsorted edges and
    //  single-pass range of edge properties.  Data is cached in coordinate form
    //  before creating the actual graph.
    template < typename InputIterator, typename EdgePropertyIterator >
    compressed_sparse_row_graph(edges_are_unsorted_t, InputIterator edge_begin,
        InputIterator edge_end, EdgePropertyIterator ep_iter,
        vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numverts), m_property(prop)
    {
        std::vector< vertex_descriptor > sources, targets;
        boost::graph::detail::split_into_separate_coords(
            edge_begin, edge_end, sources, targets);
        size_t numedges = sources.size();
        std::vector<
            typename forward_type::inherited_edge_properties::edge_bundled >
            edge_props(numedges);
        for (size_t i = 0; i < numedges; ++i)
        {
            edge_props[i] = *ep_iter++;
        }
        m_forward.assign_sources_and_targets_global(sources, targets,
            edge_props, numverts,
            boost::typed_identity_property_map< vertices_size_type >());
    }

    //  From number of vertices and single-pass range of unsorted edges.  Data
    //  is cached in coordinate form before creating the actual graph.  Edges
    //  are filtered and transformed for use in a distributed graph.
    template < typename InputIterator, typename GlobalToLocal,
        typename SourcePred >
    compressed_sparse_row_graph(edges_are_unsorted_global_t,
        InputIterator edge_begin, InputIterator edge_end,
        vertices_size_type numlocalverts, GlobalToLocal global_to_local,
        const SourcePred& source_pred,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numlocalverts), m_property(prop)
    {
        std::vector< vertex_descriptor > sources, targets;
        boost::graph::detail::split_into_separate_coords_filtered(
            edge_begin, edge_end, sources, targets, source_pred);
        m_forward.assign_sources_and_targets_global(
            sources, targets, numlocalverts, global_to_local);
    }

    //  From number of vertices and single-pass range of unsorted edges and
    //  single-pass range of edge properties.  Data is cached in coordinate form
    //  before creating the actual graph.  Edges are filtered and transformed
    //  for use in a distributed graph.
    template < typename InputIterator, typename EdgePropertyIterator,
        typename GlobalToLocal, typename SourcePred >
    compressed_sparse_row_graph(edges_are_unsorted_global_t,
        InputIterator edge_begin, InputIterator edge_end,
        EdgePropertyIterator ep_iter, vertices_size_type numlocalverts,
        GlobalToLocal global_to_local, const SourcePred& source_pred,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numlocalverts), m_property(prop)
    {
        std::vector< vertex_descriptor > sources, targets;
        std::vector< edge_bundled > edge_props;
        boost::graph::detail::split_into_separate_coords_filtered(edge_begin,
            edge_end, ep_iter, sources, targets, edge_props, source_pred);
        m_forward.assign_sources_and_targets_global(
            sources, targets, edge_props, numlocalverts, global_to_local);
    }

    //   Requires IncidenceGraph and a vertex index map
    template < typename Graph, typename VertexIndexMap >
    compressed_sparse_row_graph(const Graph& g, const VertexIndexMap& vi,
        vertices_size_type numverts, edges_size_type numedges)
    : m_property()
    {
        assign(g, vi, numverts, numedges);
        inherited_vertex_properties::resize(numverts);
    }

    //   Requires VertexListGraph and EdgeListGraph
    template < typename Graph, typename VertexIndexMap >
    compressed_sparse_row_graph(const Graph& g, const VertexIndexMap& vi)
    : m_property()
    {
        typename graph_traits< Graph >::edges_size_type numedges = num_edges(g);
        if (is_same< typename graph_traits< Graph >::directed_category,
                undirectedS >::value)
        {
            numedges *= 2; // Double each edge (actual doubling done by
                           // out_edges function)
        }
        vertices_size_type numverts = num_vertices(g);
        assign(g, vi, numverts, numedges);
        inherited_vertex_properties::resize(numverts);
    }

    // Requires vertex index map plus requirements of previous constructor
    template < typename Graph >
    explicit compressed_sparse_row_graph(const Graph& g) : m_property()
    {
        typename graph_traits< Graph >::edges_size_type numedges = num_edges(g);
        if (is_same< typename graph_traits< Graph >::directed_category,
                undirectedS >::value)
        {
            numedges *= 2; // Double each edge (actual doubling done by
                           // out_edges function)
        }
        assign(g, get(vertex_index, g), num_vertices(g), numedges);
    }

    // From any graph (slow and uses a lot of memory)
    //   Requires IncidenceGraph and a vertex index map
    //   Internal helper function
    //   Note that numedges must be doubled for undirected source graphs
    template < typename Graph, typename VertexIndexMap >
    void assign(const Graph& g, const VertexIndexMap& vi,
        vertices_size_type numverts, edges_size_type numedges)
    {
        m_forward.assign(g, vi, numverts, numedges);
        inherited_vertex_properties::resize(numverts);
    }

    // Requires the above, plus VertexListGraph and EdgeListGraph
    template < typename Graph, typename VertexIndexMap >
    void assign(const Graph& g, const VertexIndexMap& vi)
    {
        typename graph_traits< Graph >::edges_size_type numedges = num_edges(g);
        if (is_same< typename graph_traits< Graph >::directed_category,
                undirectedS >::value)
        {
            numedges *= 2; // Double each edge (actual doubling done by
                           // out_edges function)
        }
        vertices_size_type numverts = num_vertices(g);
        m_forward.assign(g, vi, numverts, numedges);
        inherited_vertex_properties::resize(numverts);
    }

    // Requires the above, plus a vertex_index map.
    template < typename Graph > void assign(const Graph& g)
    {
        typename graph_traits< Graph >::edges_size_type numedges = num_edges(g);
        if (is_same< typename graph_traits< Graph >::directed_category,
                undirectedS >::value)
        {
            numedges *= 2; // Double each edge (actual doubling done by
                           // out_edges function)
        }
        vertices_size_type numverts = num_vertices(g);
        m_forward.assign(g, get(vertex_index, g), numverts, numedges);
        inherited_vertex_properties::resize(numverts);
    }

    // Add edges from a sorted (smallest sources first) range of pairs and edge
    // properties
    template < typename BidirectionalIteratorOrig, typename EPIterOrig,
        typename GlobalToLocal >
    void add_edges_sorted_internal(BidirectionalIteratorOrig first_sorted,
        BidirectionalIteratorOrig last_sorted, EPIterOrig ep_iter_sorted,
        const GlobalToLocal& global_to_local)
    {
        m_forward.add_edges_sorted_internal(
            first_sorted, last_sorted, ep_iter_sorted, global_to_local);
    }

    template < typename BidirectionalIteratorOrig, typename EPIterOrig >
    void add_edges_sorted_internal(BidirectionalIteratorOrig first_sorted,
        BidirectionalIteratorOrig last_sorted, EPIterOrig ep_iter_sorted)
    {
        m_forward.add_edges_sorted_internal(first_sorted, last_sorted,
            ep_iter_sorted,
            typed_identity_property_map< vertices_size_type >());
    }

    // Add edges from a sorted (smallest sources first) range of pairs
    template < typename BidirectionalIteratorOrig >
    void add_edges_sorted_internal(BidirectionalIteratorOrig first_sorted,
        BidirectionalIteratorOrig last_sorted)
    {
        m_forward.add_edges_sorted_internal(first_sorted, last_sorted,
            detail::default_construct_iterator< edge_bundled >());
    }

    template < typename BidirectionalIteratorOrig, typename GlobalToLocal >
    void add_edges_sorted_internal_global(
        BidirectionalIteratorOrig first_sorted,
        BidirectionalIteratorOrig last_sorted,
        const GlobalToLocal& global_to_local)
    {
        m_forward.add_edges_sorted_internal(first_sorted, last_sorted,
            detail::default_construct_iterator< edge_bundled >(),
            global_to_local);
    }

    template < typename BidirectionalIteratorOrig, typename EPIterOrig,
        typename GlobalToLocal >
    void add_edges_sorted_internal_global(
        BidirectionalIteratorOrig first_sorted,
        BidirectionalIteratorOrig last_sorted, EPIterOrig ep_iter_sorted,
        const GlobalToLocal& global_to_local)
    {
        m_forward.add_edges_sorted_internal(
            first_sorted, last_sorted, ep_iter_sorted, global_to_local);
    }

    // Add edges from a range of (source, target) pairs that are unsorted
    template < typename InputIterator, typename GlobalToLocal >
    inline void add_edges_internal(InputIterator first, InputIterator last,
        const GlobalToLocal& global_to_local)
    {
        typedef compressed_sparse_row_graph Graph;
        typedef
            typename boost::graph_traits< Graph >::vertex_descriptor vertex_t;
        typedef std::vector< std::pair< vertex_t, vertex_t > > edge_vector_t;
        edge_vector_t new_edges(first, last);
        if (new_edges.empty())
            return;
        std::sort(new_edges.begin(), new_edges.end());
        this->add_edges_sorted_internal_global(
            new_edges.begin(), new_edges.end(), global_to_local);
    }

    template < typename InputIterator >
    inline void add_edges_internal(InputIterator first, InputIterator last)
    {
        this->add_edges_internal(
            first, last, typed_identity_property_map< vertices_size_type >());
    }

    // Add edges from a range of (source, target) pairs and edge properties that
    // are unsorted
    template < typename InputIterator, typename EPIterator,
        typename GlobalToLocal >
    inline void add_edges_internal(InputIterator first, InputIterator last,
        EPIterator ep_iter, EPIterator ep_iter_end,
        const GlobalToLocal& global_to_local)
    {
        typedef compressed_sparse_row_graph Graph;
        typedef
            typename boost::graph_traits< Graph >::vertex_descriptor vertex_t;
        typedef std::pair< vertex_t, vertex_t > vertex_pair;
        typedef std::vector< boost::tuple< vertex_pair, edge_bundled > >
            edge_vector_t;
        edge_vector_t new_edges(
            boost::make_zip_iterator(boost::make_tuple(first, ep_iter)),
            boost::make_zip_iterator(boost::make_tuple(last, ep_iter_end)));
        if (new_edges.empty())
            return;
        std::sort(new_edges.begin(), new_edges.end(),
            boost::detail::compare_first< std::less< vertex_pair > >());
        m_forward.add_edges_sorted_internal(
            boost::make_transform_iterator(new_edges.begin(),
                boost::detail::my_tuple_get_class< 0, vertex_pair >()),
            boost::make_transform_iterator(new_edges.end(),
                boost::detail::my_tuple_get_class< 0, vertex_pair >()),
            boost::make_transform_iterator(new_edges.begin(),
                boost::detail::my_tuple_get_class< 1, edge_bundled >()),
            global_to_local);
    }

    // Add edges from a range of (source, target) pairs and edge properties that
    // are unsorted
    template < typename InputIterator, typename EPIterator >
    inline void add_edges_internal(InputIterator first, InputIterator last,
        EPIterator ep_iter, EPIterator ep_iter_end)
    {
        this->add_edges_internal(first, last, ep_iter, ep_iter_end,
            typed_identity_property_map< vertices_size_type >());
    }

    using inherited_vertex_properties::operator[];

    // Directly access a edge or edge bundle
    edge_push_back_type& operator[](const edge_descriptor& v)
    {
        return m_forward.m_edge_properties[get(edge_index, *this, v)];
    }

    const edge_push_back_type& operator[](const edge_descriptor& v) const
    {
        return m_forward.m_edge_properties[get(edge_index, *this, v)];
    }

    // Directly access a graph bundle
    graph_bundled& operator[](graph_bundle_t) { return get_property(*this); }

    const graph_bundled& operator[](graph_bundle_t) const
    {
        return get_property(*this);
    }

    // private: non-portable, requires friend templates
    inherited_vertex_properties& vertex_properties() { return *this; }
    const inherited_vertex_properties& vertex_properties() const
    {
        return *this;
    }
    typename forward_type::inherited_edge_properties& edge_properties()
    {
        return m_forward;
    }
    const typename forward_type::inherited_edge_properties&
    edge_properties() const
    {
        return m_forward;
    }

    forward_type m_forward;
    GraphProperty m_property;
};

template < typename VertexProperty, typename EdgeProperty,
    typename GraphProperty, typename Vertex, typename EdgeIndex >
class compressed_sparse_row_graph< bidirectionalS, VertexProperty, EdgeProperty,
    GraphProperty, Vertex, EdgeIndex >
: public detail::indexed_vertex_properties< BOOST_BIDIR_CSR_GRAPH_TYPE,
      VertexProperty, Vertex, typed_identity_property_map< Vertex > >
{
public:
    typedef detail::indexed_vertex_properties< compressed_sparse_row_graph,
        VertexProperty, Vertex, typed_identity_property_map< Vertex > >
        inherited_vertex_properties;

public:
    // For Property Graph
    typedef GraphProperty graph_property_type;
    typedef typename lookup_one_property< GraphProperty, graph_bundle_t >::type
        graph_bundled;
    // typedef GraphProperty graph_property_type;

    typedef detail::compressed_sparse_row_structure< EdgeProperty, Vertex,
        EdgeIndex >
        forward_type;
    typedef EdgeIndex /* typename boost::mpl::if_c<boost::is_same<EdgeProperty,
                         boost::no_property>, boost::no_property, EdgeIndex> */
        backward_edge_property;
    typedef detail::compressed_sparse_row_structure< backward_edge_property,
        Vertex, EdgeIndex >
        backward_type;

public:
    // Concept requirements:
    // For Graph
    typedef Vertex vertex_descriptor;
    typedef detail::csr_edge_descriptor< Vertex, EdgeIndex > edge_descriptor;
    typedef bidirectional_tag directed_category;
    typedef allow_parallel_edge_tag edge_parallel_category;

    class traversal_category : public bidirectional_graph_tag,
                               public adjacency_graph_tag,
                               public vertex_list_graph_tag,
                               public edge_list_graph_tag
    {
    };

    static vertex_descriptor null_vertex() { return vertex_descriptor(-1); }

    // For VertexListGraph
    typedef counting_iterator< Vertex > vertex_iterator;
    typedef Vertex vertices_size_type;

    // For EdgeListGraph
    typedef EdgeIndex edges_size_type;

    // For IncidenceGraph
    typedef detail::csr_out_edge_iterator< compressed_sparse_row_graph >
        out_edge_iterator;
    typedef EdgeIndex degree_size_type;

    // For AdjacencyGraph
    typedef typename std::vector< Vertex >::const_iterator adjacency_iterator;

    // For EdgeListGraph
    typedef detail::csr_edge_iterator< compressed_sparse_row_graph >
        edge_iterator;

    // For BidirectionalGraph (not implemented)
    typedef detail::csr_in_edge_iterator< compressed_sparse_row_graph >
        in_edge_iterator;

    // For internal use
    typedef csr_graph_tag graph_tag;

    typedef typename forward_type::inherited_edge_properties::edge_bundled
        edge_bundled;
    typedef
        typename forward_type::inherited_edge_properties::edge_push_back_type
            edge_push_back_type;
    typedef typename forward_type::inherited_edge_properties::edge_property_type
        edge_property_type;

    // Constructors

    // Default constructor: an empty graph.
    compressed_sparse_row_graph() : m_property() {}

    //  With numverts vertices
    compressed_sparse_row_graph(vertices_size_type numverts)
    : inherited_vertex_properties(numverts)
    , m_forward(numverts)
    , m_backward(numverts)
    {
    }

private:
    void set_up_backward_property_links()
    {
        std::pair< edge_iterator, edge_iterator > e = edges(*this);
        m_backward.assign_unsorted_multi_pass_edges(
            detail::transpose_edges(detail::make_edge_to_index_pair_iter(
                *this, get(vertex_index, *this), e.first)),
            detail::transpose_edges(detail::make_edge_to_index_pair_iter(
                *this, get(vertex_index, *this), e.second)),
            boost::counting_iterator< EdgeIndex >(0),
            m_forward.m_rowstart.size() - 1,
            typed_identity_property_map< Vertex >(), keep_all());
    }

public:
    //  From number of vertices and unsorted list of edges
    template < typename MultiPassInputIterator >
    compressed_sparse_row_graph(edges_are_unsorted_multi_pass_t,
        MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
        vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numverts), m_property(prop)
    {
        m_forward.assign_unsorted_multi_pass_edges(edge_begin, edge_end,
            numverts, typed_identity_property_map< Vertex >(), keep_all());
        set_up_backward_property_links();
    }

    //  From number of vertices and unsorted list of edges, plus edge properties
    template < typename MultiPassInputIterator, typename EdgePropertyIterator >
    compressed_sparse_row_graph(edges_are_unsorted_multi_pass_t,
        MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
        EdgePropertyIterator ep_iter, vertices_size_type numverts,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numverts), m_forward(), m_property(prop)
    {
        m_forward.assign_unsorted_multi_pass_edges(edge_begin, edge_end,
            ep_iter, numverts, typed_identity_property_map< Vertex >(),
            keep_all());
        set_up_backward_property_links();
    }

    //  From number of vertices and unsorted list of edges, with filter and
    //  global-to-local map
    template < typename MultiPassInputIterator, typename GlobalToLocal,
        typename SourcePred >
    compressed_sparse_row_graph(edges_are_unsorted_multi_pass_global_t,
        MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
        vertices_size_type numlocalverts, const GlobalToLocal& global_to_local,
        const SourcePred& source_pred,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numlocalverts), m_forward(), m_property(prop)
    {
        m_forward.assign_unsorted_multi_pass_edges(
            edge_begin, edge_end, numlocalverts, global_to_local, source_pred);
        set_up_backward_property_links();
    }

    //  From number of vertices and unsorted list of edges, plus edge
    //  properties, with filter and global-to-local map
    template < typename MultiPassInputIterator, typename EdgePropertyIterator,
        typename GlobalToLocal, typename SourcePred >
    compressed_sparse_row_graph(edges_are_unsorted_multi_pass_global_t,
        MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
        EdgePropertyIterator ep_iter, vertices_size_type numlocalverts,
        const GlobalToLocal& global_to_local, const SourcePred& source_pred,
        const GraphProperty& prop = GraphProperty())
    : inherited_vertex_properties(numlocalverts), m_forward(), m_property(prop)
    {
        m_forward.assign_unsorted_multi_pass_edges(edge_begin, edge_end,
            ep_iter, numlocalverts, global_to_local, source_pred);
        set_up_backward_property_links();
    }

    //   Requires IncidenceGraph and a vertex index map
    template < typename Graph, typename VertexIndexMap >
    compressed_sparse_row_graph(const Graph& g, const VertexIndexMap& vi,
        vertices_size_type numverts, edges_size_type numedges)
    : m_property()
    {
        assign(g, vi, numverts, numedges);
        inherited_vertex_properties::resize(numverts);
    }

    //   Requires VertexListGraph and EdgeListGraph
    template < typename Graph, typename VertexIndexMap >
    compressed_sparse_row_graph(const Graph& g, const VertexIndexMap& vi)
    : m_property()
    {
        typename graph_traits< Graph >::edges_size_type numedges = num_edges(g);
        if (is_same< typename graph_traits< Graph >::directed_category,
                undirectedS >::value)
        {
            numedges *= 2; // Double each edge (actual doubling done by
                           // out_edges function)
        }
        vertices_size_type numverts = num_vertices(g);
        assign(g, vi, numverts, numedges);
        inherited_vertex_properties::resize(numverts);
    }

    // Requires vertex index map plus requirements of previous constructor
    template < typename Graph >
    explicit compressed_sparse_row_graph(const Graph& g) : m_property()
    {
        typename graph_traits< Graph >::edges_size_type numedges = num_edges(g);
        if (is_same< typename graph_traits< Graph >::directed_category,
                undirectedS >::value)
        {
            numedges *= 2; // Double each edge (actual doubling done by
                           // out_edges function)
        }
        assign(g, get(vertex_index, g), num_vertices(g), numedges);
    }

    // From any graph (slow and uses a lot of memory)
    //   Requires IncidenceGraph and a vertex index map
    //   Internal helper function
    //   Note that numedges must be doubled for undirected source graphs
    template < typename Graph, typename VertexIndexMap >
    void assign(const Graph& g, const VertexIndexMap& vi,
        vertices_size_type numverts, edges_size_type numedges)
    {
        m_forward.assign(g, vi, numverts, numedges);
        inherited_vertex_properties::resize(numverts);
        set_up_backward_property_links();
    }

    // Requires the above, plus VertexListGraph and EdgeListGraph
    template < typename Graph, typename VertexIndexMap >
    void assign(const Graph& g, const VertexIndexMap& vi)
    {
        typename graph_traits< Graph >::edges_size_type numedges = num_edges(g);
        if (is_same< typename graph_traits< Graph >::directed_category,
                undirectedS >::value)
        {
            numedges *= 2; // Double each edge (actual doubling done by
                           // out_edges function)
        }
        vertices_size_type numverts = num_vertices(g);
        m_forward.assign(g, vi, numverts, numedges);
        inherited_vertex_properties::resize(numverts);
        set_up_backward_property_links();
    }

    // Requires the above, plus a vertex_index map.
    template < typename Graph > void assign(const Graph& g)
    {
        typename graph_traits< Graph >::edges_size_type numedges = num_edges(g);
        if (is_same< typename graph_traits< Graph >::directed_category,
                undirectedS >::value)
        {
            numedges *= 2; // Double each edge (actual doubling done by
                           // out_edges function)
        }
        vertices_size_type numverts = num_vertices(g);
        m_forward.assign(g, get(vertex_index, g), numverts, numedges);
        inherited_vertex_properties::resize(numverts);
        set_up_backward_property_links();
    }

    using inherited_vertex_properties::operator[];

    // Directly access a edge or edge bundle
    edge_push_back_type& operator[](const edge_descriptor& v)
    {
        return m_forward.m_edge_properties[get(edge_index, *this, v)];
    }

    const edge_push_back_type& operator[](const edge_descriptor& v) const
    {
        return m_forward.m_edge_properties[get(edge_index, *this, v)];
    }

    // private: non-portable, requires friend templates
    inherited_vertex_properties& vertex_properties() { return *this; }
    const inherited_vertex_properties& vertex_properties() const
    {
        return *this;
    }
    typename forward_type::inherited_edge_properties& edge_properties()
    {
        return m_forward;
    }
    const typename forward_type::inherited_edge_properties&
    edge_properties() const
    {
        return m_forward;
    }

    forward_type m_forward;
    backward_type m_backward;
    GraphProperty m_property;
};

// Construction functions
template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline Vertex add_vertex(BOOST_CSR_GRAPH_TYPE& g)
{
    add_vertex(g, typename BOOST_CSR_GRAPH_TYPE::vertex_bundled());
}

template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS >
inline Vertex add_vertex(BOOST_DIR_CSR_GRAPH_TYPE& g,
    typename BOOST_DIR_CSR_GRAPH_TYPE::vertex_bundled const& p)
{
    Vertex old_num_verts_plus_one = g.m_forward.m_rowstart.size();
    g.m_forward.m_rowstart.push_back(g.m_forward.m_rowstart.back());
    g.vertex_properties().push_back(p);
    return old_num_verts_plus_one - 1;
}

template < BOOST_BIDIR_CSR_GRAPH_TEMPLATE_PARMS >
inline Vertex add_vertex(BOOST_BIDIR_CSR_GRAPH_TYPE& g,
    typename BOOST_BIDIR_CSR_GRAPH_TYPE::vertex_bundled const& p)
{
    Vertex old_num_verts_plus_one = g.m_forward.m_rowstart.size();
    g.m_forward.m_rowstart.push_back(g.m_forward.m_rowstart.back());
    g.m_backward.m_rowstart.push_back(g.m_backward.m_rowstart.back());
    g.vertex_properties().push_back(p);
    return old_num_verts_plus_one - 1;
}

template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS >
inline Vertex add_vertices(
    typename BOOST_DIR_CSR_GRAPH_TYPE::vertices_size_type count,
    BOOST_DIR_CSR_GRAPH_TYPE& g)
{
    Vertex old_num_verts_plus_one = g.m_forward.m_rowstart.size();
    EdgeIndex numedges = g.m_forward.m_rowstart.back();
    g.m_forward.m_rowstart.resize(old_num_verts_plus_one + count, numedges);
    g.vertex_properties().resize(num_vertices(g));
    return old_num_verts_plus_one - 1;
}

// Add edges from a sorted (smallest sources first) range of pairs and edge
// properties
template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS,
    typename BidirectionalIteratorOrig, typename EPIterOrig >
void add_edges_sorted(BidirectionalIteratorOrig first_sorted,
    BidirectionalIteratorOrig last_sorted, EPIterOrig ep_iter_sorted,
    BOOST_DIR_CSR_GRAPH_TYPE& g)
{
    g.add_edges_sorted_internal(first_sorted, last_sorted, ep_iter_sorted);
}

// Add edges from a sorted (smallest sources first) range of pairs
template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS,
    typename BidirectionalIteratorOrig >
void add_edges_sorted(BidirectionalIteratorOrig first_sorted,
    BidirectionalIteratorOrig last_sorted, BOOST_DIR_CSR_GRAPH_TYPE& g)
{
    g.add_edges_sorted_internal(first_sorted, last_sorted);
}

template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS,
    typename BidirectionalIteratorOrig, typename EPIterOrig,
    typename GlobalToLocal >
void add_edges_sorted_global(BidirectionalIteratorOrig first_sorted,
    BidirectionalIteratorOrig last_sorted, EPIterOrig ep_iter_sorted,
    const GlobalToLocal& global_to_local, BOOST_DIR_CSR_GRAPH_TYPE& g)
{
    g.add_edges_sorted_internal_global(
        first_sorted, last_sorted, ep_iter_sorted, global_to_local);
}

// Add edges from a sorted (smallest sources first) range of pairs
template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS,
    typename BidirectionalIteratorOrig, typename GlobalToLocal >
void add_edges_sorted_global(BidirectionalIteratorOrig first_sorted,
    BidirectionalIteratorOrig last_sorted, const GlobalToLocal& global_to_local,
    BOOST_DIR_CSR_GRAPH_TYPE& g)
{
    g.add_edges_sorted_internal_global(
        first_sorted, last_sorted, global_to_local);
}

// Add edges from a range of (source, target) pairs that are unsorted
template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS, typename InputIterator,
    typename GlobalToLocal >
inline void add_edges_global(InputIterator first, InputIterator last,
    const GlobalToLocal& global_to_local, BOOST_DIR_CSR_GRAPH_TYPE& g)
{
    g.add_edges_internal(first, last, global_to_local);
}

// Add edges from a range of (source, target) pairs that are unsorted
template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS, typename InputIterator >
inline void add_edges(
    InputIterator first, InputIterator last, BOOST_DIR_CSR_GRAPH_TYPE& g)
{
    g.add_edges_internal(first, last);
}

// Add edges from a range of (source, target) pairs and edge properties that
// are unsorted
template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS, typename InputIterator,
    typename EPIterator >
inline void add_edges(InputIterator first, InputIterator last,
    EPIterator ep_iter, EPIterator ep_iter_end, BOOST_DIR_CSR_GRAPH_TYPE& g)
{
    g.add_edges_internal(first, last, ep_iter, ep_iter_end);
}

template < BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS, typename InputIterator,
    typename EPIterator, typename GlobalToLocal >
inline void add_edges_global(InputIterator first, InputIterator last,
    EPIterator ep_iter, EPIterator ep_iter_end,
    const GlobalToLocal& global_to_local, BOOST_DIR_CSR_GRAPH_TYPE& g)
{
    g.add_edges_internal(first, last, ep_iter, ep_iter_end, global_to_local);
}

// From VertexListGraph
template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline Vertex num_vertices(const BOOST_CSR_GRAPH_TYPE& g)
{
    return g.m_forward.m_rowstart.size() - 1;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
std::pair< counting_iterator< Vertex >,
    counting_iterator< Vertex > > inline vertices(const BOOST_CSR_GRAPH_TYPE& g)
{
    return std::make_pair(counting_iterator< Vertex >(0),
        counting_iterator< Vertex >(num_vertices(g)));
}

// From IncidenceGraph
template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline Vertex source(typename BOOST_CSR_GRAPH_TYPE::edge_descriptor e,
    const BOOST_CSR_GRAPH_TYPE&)
{
    return e.src;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline Vertex target(typename BOOST_CSR_GRAPH_TYPE::edge_descriptor e,
    const BOOST_CSR_GRAPH_TYPE& g)
{
    return g.m_forward.m_column[e.idx];
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline std::pair< typename BOOST_CSR_GRAPH_TYPE::out_edge_iterator,
    typename BOOST_CSR_GRAPH_TYPE::out_edge_iterator >
out_edges(Vertex v, const BOOST_CSR_GRAPH_TYPE& g)
{
    typedef typename BOOST_CSR_GRAPH_TYPE::edge_descriptor ed;
    typedef typename BOOST_CSR_GRAPH_TYPE::out_edge_iterator it;
    EdgeIndex v_row_start = g.m_forward.m_rowstart[v];
    EdgeIndex next_row_start = g.m_forward.m_rowstart[v + 1];
    return std::make_pair(it(ed(v, v_row_start)), it(ed(v, next_row_start)));
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline EdgeIndex out_degree(Vertex v, const BOOST_CSR_GRAPH_TYPE& g)
{
    EdgeIndex v_row_start = g.m_forward.m_rowstart[v];
    EdgeIndex next_row_start = g.m_forward.m_rowstart[v + 1];
    return next_row_start - v_row_start;
}

template < BOOST_BIDIR_CSR_GRAPH_TEMPLATE_PARMS >
inline std::pair< typename BOOST_BIDIR_CSR_GRAPH_TYPE::in_edge_iterator,
    typename BOOST_BIDIR_CSR_GRAPH_TYPE::in_edge_iterator >
in_edges(Vertex v, const BOOST_BIDIR_CSR_GRAPH_TYPE& g)
{
    typedef typename BOOST_BIDIR_CSR_GRAPH_TYPE::in_edge_iterator it;
    EdgeIndex v_row_start = g.m_backward.m_rowstart[v];
    EdgeIndex next_row_start = g.m_backward.m_rowstart[v + 1];
    return std::make_pair(it(g, v_row_start), it(g, next_row_start));
}

template < BOOST_BIDIR_CSR_GRAPH_TEMPLATE_PARMS >
inline EdgeIndex in_degree(Vertex v, const BOOST_BIDIR_CSR_GRAPH_TYPE& g)
{
    EdgeIndex v_row_start = g.m_backward.m_rowstart[v];
    EdgeIndex next_row_start = g.m_backward.m_rowstart[v + 1];
    return next_row_start - v_row_start;
}

// From AdjacencyGraph
template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline std::pair< typename BOOST_CSR_GRAPH_TYPE::adjacency_iterator,
    typename BOOST_CSR_GRAPH_TYPE::adjacency_iterator >
adjacent_vertices(Vertex v, const BOOST_CSR_GRAPH_TYPE& g)
{
    EdgeIndex v_row_start = g.m_forward.m_rowstart[v];
    EdgeIndex next_row_start = g.m_forward.m_rowstart[v + 1];
    return std::make_pair(g.m_forward.m_column.begin() + v_row_start,
        g.m_forward.m_column.begin() + next_row_start);
}

// Extra, common functions
template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename graph_traits< BOOST_CSR_GRAPH_TYPE >::vertex_descriptor vertex(
    typename graph_traits< BOOST_CSR_GRAPH_TYPE >::vertex_descriptor i,
    const BOOST_CSR_GRAPH_TYPE&)
{
    return i;
}

// edge() can be provided in linear time for the new interface

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline std::pair< typename BOOST_CSR_GRAPH_TYPE::edge_descriptor, bool > edge(
    Vertex i, Vertex j, const BOOST_CSR_GRAPH_TYPE& g)
{
    typedef typename BOOST_CSR_GRAPH_TYPE::out_edge_iterator out_edge_iter;
    std::pair< out_edge_iter, out_edge_iter > range = out_edges(i, g);
    for (; range.first != range.second; ++range.first)
    {
        if (target(*range.first, g) == j)
            return std::make_pair(*range.first, true);
    }
    return std::make_pair(
        typename BOOST_CSR_GRAPH_TYPE::edge_descriptor(), false);
}

// Find an edge given its index in the graph
template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename BOOST_CSR_GRAPH_TYPE::edge_descriptor edge_from_index(
    EdgeIndex idx, const BOOST_CSR_GRAPH_TYPE& g)
{
    typedef typename std::vector< EdgeIndex >::const_iterator row_start_iter;
    BOOST_ASSERT(idx < num_edges(g));
    row_start_iter src_plus_1 = std::upper_bound(
        g.m_forward.m_rowstart.begin(), g.m_forward.m_rowstart.end(), idx);
    // Get last source whose rowstart is at most idx
    // upper_bound returns this position plus 1
    Vertex src = (src_plus_1 - g.m_forward.m_rowstart.begin()) - 1;
    return typename BOOST_CSR_GRAPH_TYPE::edge_descriptor(src, idx);
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline EdgeIndex num_edges(const BOOST_CSR_GRAPH_TYPE& g)
{
    return g.m_forward.m_column.size();
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
std::pair< typename BOOST_CSR_GRAPH_TYPE::edge_iterator,
    typename BOOST_CSR_GRAPH_TYPE::edge_iterator >
edges(const BOOST_CSR_GRAPH_TYPE& g)
{
    typedef typename BOOST_CSR_GRAPH_TYPE::edge_iterator ei;
    typedef typename BOOST_CSR_GRAPH_TYPE::edge_descriptor edgedesc;
    if (g.m_forward.m_rowstart.size() == 1 || g.m_forward.m_column.empty())
    {
        return std::make_pair(ei(), ei());
    }
    else
    {
        // Find the first vertex that has outgoing edges
        Vertex src = 0;
        while (g.m_forward.m_rowstart[src + 1] == 0)
            ++src;
        return std::make_pair(
            ei(g, edgedesc(src, 0), g.m_forward.m_rowstart[src + 1]),
            ei(g, edgedesc(num_vertices(g), g.m_forward.m_column.size()), 0));
    }
}

// For Property Graph

// Graph properties
template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, class Tag, class Value >
inline void set_property(BOOST_CSR_GRAPH_TYPE& g, Tag tag, const Value& value)
{
    get_property_value(g.m_property, tag) = value;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, class Tag >
inline typename graph_property< BOOST_CSR_GRAPH_TYPE, Tag >::type& get_property(
    BOOST_CSR_GRAPH_TYPE& g, Tag tag)
{
    return get_property_value(g.m_property, tag);
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, class Tag >
inline const typename graph_property< BOOST_CSR_GRAPH_TYPE, Tag >::type&
get_property(const BOOST_CSR_GRAPH_TYPE& g, Tag tag)
{
    return get_property_value(g.m_property, tag);
}

template < typename G, typename Tag, typename Kind >
struct csr_property_map_helper
{
};
// Kind == void for invalid property tags, so we can use that to SFINAE out

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, typename Tag >
struct csr_property_map_helper< BOOST_CSR_GRAPH_TYPE, Tag, vertex_property_tag >
{
    typedef vertex_all_t all_tag;
    typedef
        typename property_traits< typename property_map< BOOST_CSR_GRAPH_TYPE,
            vertex_all_t >::type >::key_type key_type;
    typedef VertexProperty plist_type;
    typedef typename property_map< BOOST_CSR_GRAPH_TYPE, vertex_all_t >::type
        all_type;
    typedef
        typename property_map< BOOST_CSR_GRAPH_TYPE, vertex_all_t >::const_type
            all_const_type;
    typedef transform_value_property_map<
        detail::lookup_one_property_f< plist_type, Tag >, all_type >
        type;
    typedef transform_value_property_map<
        detail::lookup_one_property_f< const plist_type, Tag >, all_const_type >
        const_type;
};

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, typename Tag >
struct csr_property_map_helper< BOOST_CSR_GRAPH_TYPE, Tag, edge_property_tag >
{
    typedef edge_all_t all_tag;
    typedef
        typename property_traits< typename property_map< BOOST_CSR_GRAPH_TYPE,
            edge_all_t >::type >::key_type key_type;
    typedef EdgeProperty plist_type;
    typedef typename property_map< BOOST_CSR_GRAPH_TYPE, edge_all_t >::type
        all_type;
    typedef
        typename property_map< BOOST_CSR_GRAPH_TYPE, edge_all_t >::const_type
            all_const_type;
    typedef transform_value_property_map<
        detail::lookup_one_property_f< plist_type, Tag >, all_type >
        type;
    typedef transform_value_property_map<
        detail::lookup_one_property_f< const plist_type, Tag >, all_const_type >
        const_type;
};

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, typename Tag >
struct csr_property_map_helper< BOOST_CSR_GRAPH_TYPE, Tag, graph_property_tag >
{
    typedef graph_all_t all_tag;
    typedef BOOST_CSR_GRAPH_TYPE* key_type;
    typedef GraphProperty plist_type;
    typedef typename property_map< BOOST_CSR_GRAPH_TYPE, graph_all_t >::type
        all_type;
    typedef
        typename property_map< BOOST_CSR_GRAPH_TYPE, graph_all_t >::const_type
            all_const_type;
    typedef transform_value_property_map<
        detail::lookup_one_property_f< plist_type, Tag >, all_type >
        type;
    typedef transform_value_property_map<
        detail::lookup_one_property_f< const plist_type, Tag >, all_const_type >
        const_type;
};

// disable_if isn't truly necessary but required to avoid ambiguity with
// specializations below
template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, typename Tag >
struct property_map< BOOST_CSR_GRAPH_TYPE, Tag,
    typename disable_if< detail::is_distributed_selector< Vertex > >::type >
: csr_property_map_helper< BOOST_CSR_GRAPH_TYPE, Tag,
      typename detail::property_kind_from_graph< BOOST_CSR_GRAPH_TYPE,
          Tag >::type >
{
};

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, typename Tag >
typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::type get(
    Tag tag, BOOST_CSR_GRAPH_TYPE& g)
{
    return typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::type(tag,
        get(typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::all_tag(), g));
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, typename Tag >
typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::const_type get(
    Tag tag, const BOOST_CSR_GRAPH_TYPE& g)
{
    return typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::const_type(tag,
        get(typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::all_tag(), g));
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, typename Tag >
typename property_traits<
    typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::type >::reference
get(Tag tag, BOOST_CSR_GRAPH_TYPE& g,
    typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::key_type k)
{
    typedef typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::all_tag all_tag;
    typedef
        typename property_map< BOOST_CSR_GRAPH_TYPE, all_tag >::type outer_pm;
    return lookup_one_property<
        typename property_traits< outer_pm >::value_type,
        Tag >::lookup(get(all_tag(), g, k), tag);
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, typename Tag >
typename property_traits<
    typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::const_type >::reference
get(Tag tag, const BOOST_CSR_GRAPH_TYPE& g,
    typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::key_type k)
{
    typedef typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::all_tag all_tag;
    typedef typename property_map< BOOST_CSR_GRAPH_TYPE, all_tag >::const_type
        outer_pm;
    return lookup_one_property<
        const typename property_traits< outer_pm >::value_type,
        Tag >::lookup(get(all_tag(), g, k), tag);
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS, typename Tag >
void put(Tag tag, BOOST_CSR_GRAPH_TYPE& g,
    typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::key_type k,
    typename lookup_one_property<
        typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::plist_type,
        Tag >::type val)
{
    typedef typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::all_tag all_tag;
    lookup_one_property<
        typename property_map< BOOST_CSR_GRAPH_TYPE, Tag >::plist_type,
        Tag >::lookup(get(all_tag(), g, k), tag)
        = val;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
struct property_map< BOOST_CSR_GRAPH_TYPE, vertex_index_t,
    typename disable_if< detail::is_distributed_selector< Vertex > >::type >
{
    typedef typed_identity_property_map< Vertex > type;
    typedef type const_type;
};

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
struct property_map< BOOST_CSR_GRAPH_TYPE, edge_index_t,
    typename disable_if< detail::is_distributed_selector< Vertex > >::type >
{
    typedef detail::csr_edge_index_map< Vertex, EdgeIndex > type;
    typedef type const_type;
};

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
struct property_map< BOOST_CSR_GRAPH_TYPE, vertex_all_t,
    typename disable_if< detail::is_distributed_selector< Vertex > >::type >
{
    typedef typename BOOST_CSR_GRAPH_TYPE::inherited_vertex_properties::
        vertex_map_type type;
    typedef typename BOOST_CSR_GRAPH_TYPE::inherited_vertex_properties::
        const_vertex_map_type const_type;
};

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
struct property_map< BOOST_CSR_GRAPH_TYPE, edge_all_t,
    typename disable_if< detail::is_distributed_selector< Vertex > >::type >
{
    typedef typename BOOST_CSR_GRAPH_TYPE::forward_type::
        inherited_edge_properties::edge_map_type type;
    typedef typename BOOST_CSR_GRAPH_TYPE::forward_type::
        inherited_edge_properties::const_edge_map_type const_type;
};

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
struct property_map< BOOST_CSR_GRAPH_TYPE, graph_all_t,
    typename disable_if< detail::is_distributed_selector< Vertex > >::type >
{
    typedef boost::ref_property_map< BOOST_CSR_GRAPH_TYPE*,
        typename BOOST_CSR_GRAPH_TYPE::graph_property_type >
        type;
    typedef boost::ref_property_map< BOOST_CSR_GRAPH_TYPE*,
        const typename BOOST_CSR_GRAPH_TYPE::graph_property_type >
        const_type;
};

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typed_identity_property_map< Vertex > get(
    vertex_index_t, const BOOST_CSR_GRAPH_TYPE&)
{
    return typed_identity_property_map< Vertex >();
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline Vertex get(vertex_index_t, const BOOST_CSR_GRAPH_TYPE&, Vertex v)
{
    return v;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typed_identity_property_map< Vertex > get(
    vertex_index_t, BOOST_CSR_GRAPH_TYPE&)
{
    return typed_identity_property_map< Vertex >();
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline Vertex get(vertex_index_t, BOOST_CSR_GRAPH_TYPE&, Vertex v)
{
    return v;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename property_map< BOOST_CSR_GRAPH_TYPE, edge_index_t >::const_type
get(edge_index_t, const BOOST_CSR_GRAPH_TYPE&)
{
    typedef
        typename property_map< BOOST_CSR_GRAPH_TYPE, edge_index_t >::const_type
            result_type;
    return result_type();
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline EdgeIndex get(edge_index_t, const BOOST_CSR_GRAPH_TYPE&,
    typename BOOST_CSR_GRAPH_TYPE::edge_descriptor e)
{
    return e.idx;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename property_map< BOOST_CSR_GRAPH_TYPE, edge_index_t >::const_type
get(edge_index_t, BOOST_CSR_GRAPH_TYPE&)
{
    typedef
        typename property_map< BOOST_CSR_GRAPH_TYPE, edge_index_t >::const_type
            result_type;
    return result_type();
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline EdgeIndex get(edge_index_t, BOOST_CSR_GRAPH_TYPE&,
    typename BOOST_CSR_GRAPH_TYPE::edge_descriptor e)
{
    return e.idx;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename property_map< BOOST_CSR_GRAPH_TYPE, vertex_all_t >::type get(
    vertex_all_t, BOOST_CSR_GRAPH_TYPE& g)
{
    return g.get_vertex_bundle(get(vertex_index, g));
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename property_map< BOOST_CSR_GRAPH_TYPE, vertex_all_t >::const_type
get(vertex_all_t, const BOOST_CSR_GRAPH_TYPE& g)
{
    return g.get_vertex_bundle(get(vertex_index, g));
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline VertexProperty& get(vertex_all_t, BOOST_CSR_GRAPH_TYPE& g, Vertex v)
{
    return get(vertex_all, g)[v];
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline const VertexProperty& get(
    vertex_all_t, const BOOST_CSR_GRAPH_TYPE& g, Vertex v)
{
    return get(vertex_all, g)[v];
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline void put(
    vertex_all_t, BOOST_CSR_GRAPH_TYPE& g, Vertex v, const VertexProperty& val)
{
    put(get(vertex_all, g), v, val);
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename property_map< BOOST_CSR_GRAPH_TYPE, edge_all_t >::type get(
    edge_all_t, BOOST_CSR_GRAPH_TYPE& g)
{
    return g.m_forward.get_edge_bundle(get(edge_index, g));
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename property_map< BOOST_CSR_GRAPH_TYPE, edge_all_t >::const_type
get(edge_all_t, const BOOST_CSR_GRAPH_TYPE& g)
{
    return g.m_forward.get_edge_bundle(get(edge_index, g));
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline EdgeProperty& get(edge_all_t, BOOST_CSR_GRAPH_TYPE& g,
    const typename BOOST_CSR_GRAPH_TYPE::edge_descriptor& e)
{
    return get(edge_all, g)[e];
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline const EdgeProperty& get(edge_all_t, const BOOST_CSR_GRAPH_TYPE& g,
    const typename BOOST_CSR_GRAPH_TYPE::edge_descriptor& e)
{
    return get(edge_all, g)[e];
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline void put(edge_all_t, BOOST_CSR_GRAPH_TYPE& g,
    const typename BOOST_CSR_GRAPH_TYPE::edge_descriptor& e,
    const EdgeProperty& val)
{
    put(get(edge_all, g), e, val);
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename property_map< BOOST_CSR_GRAPH_TYPE, graph_all_t >::type get(
    graph_all_t, BOOST_CSR_GRAPH_TYPE& g)
{
    return typename property_map< BOOST_CSR_GRAPH_TYPE, graph_all_t >::type(
        g.m_property);
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline typename property_map< BOOST_CSR_GRAPH_TYPE, graph_all_t >::const_type
get(graph_all_t, const BOOST_CSR_GRAPH_TYPE& g)
{
    return
        typename property_map< BOOST_CSR_GRAPH_TYPE, graph_all_t >::const_type(
            g.m_property);
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline GraphProperty& get(
    graph_all_t, BOOST_CSR_GRAPH_TYPE& g, BOOST_CSR_GRAPH_TYPE*)
{
    return g.m_property;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline const GraphProperty& get(
    graph_all_t, const BOOST_CSR_GRAPH_TYPE& g, BOOST_CSR_GRAPH_TYPE*)
{
    return g.m_property;
}

template < BOOST_CSR_GRAPH_TEMPLATE_PARMS >
inline void put(graph_all_t, BOOST_CSR_GRAPH_TYPE& g, BOOST_CSR_GRAPH_TYPE*,
    const GraphProperty& val)
{
    g.m_property = val;
}

#undef BOOST_CSR_GRAPH_TYPE
#undef BOOST_CSR_GRAPH_TEMPLATE_PARMS
#undef BOOST_DIR_CSR_GRAPH_TYPE
#undef BOOST_DIR_CSR_GRAPH_TEMPLATE_PARMS
#undef BOOST_BIDIR_CSR_GRAPH_TYPE
#undef BOOST_BIDIR_CSR_GRAPH_TEMPLATE_PARMS

} // end namespace boost

#endif // BOOST_GRAPH_COMPRESSED_SPARSE_ROW_GRAPH_HPP