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  <head>
    <title>Compressed Sparse Row Graph</title>

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    <IMG SRC="../../../boost.png" 
      ALT="C++ Boost" width="277" height="86"></img>
    <h1>Compressed Sparse Row Graph</h1>
          
    <p>The class template <code>compressed_sparse_row_graph</code> is
    a graph class that uses the compact Compressed Sparse Row (CSR)
    format to store directed (and bidirectional) graphs. While CSR graphs have
    much less
    overhead than many other graph formats (e.g., <a
    href="adjacency_list.html"><code>adjacency_list</code></a>), they
    do not provide any mutability: one cannot add or remove vertices
    or edges from a CSR graph. Use this format in high-performance
    applications or for very large graphs that you do not need to
    change.</p>

    <p>The CSR format stores vertices and edges in separate arrays,
    with the indices into these arrays corresponding to the identifier
    for the vertex or edge, respectively. The edge array is sorted by
    the source of each edge, but contains only the targets for the
    edges. The vertex array stores offsets into the edge array,
    providing the offset of the first edge outgoing from each
    vertex. Iteration over the out-edges for the <i>i</i><sup>th</sup>
    vertex in the graph is achieved by
    visiting <tt>edge_array[vertex_array[i]]</tt>,
    <tt>edge_array[vertex_array[i]+1]</tt>,
    ..., <tt>edge_array[vertex_array[i+1]]</tt>. This format minimizes
    memory use to <i>O(n + m)</i>, where <i>n</i> and <i>m</i> are the
    number of vertices and edges, respectively. The constants
    multiplied by <i>n</i> and <i>m</i> are based on the size of the
    integers needed to represent indices into the edge and vertex
    arrays, respectively, which can be controlled using
    the <a href="#template-parms">template parameters</a>.  The
    <tt>Directed</tt> template parameter controls whether one edge direction
    (the default) or both directions are stored.  A directed CSR graph has
    <tt>Directed</tt> = <tt>directedS</tt> and a bidirectional CSR graph (with
    a limited set of constructors)
    has <tt>Directed</tt> = <tt>bidirectionalS</tt>.</p>

    <ul>
      <li><a href="#synopsis">Synopsis</a></li>
      <li><a href="#where">Where Defined</a></li>
      <li><a href="#models">Models</a></li>
      <li><a href="#template-parms">Template parameters</a></li>
      <li><a href="#properties">Properties</a></li>
      <li><a href="#member-functions">Member functions</a>
        <ul>
          <li><a href="#constructors">Constructors</a></li>
          <li><a href="#mutators">Mutators</a></li>
          <li><a href="#property-access">Property access</a></li>
        </ul></li>

      <li><a href="#non-members">Non-member functions</a>
        <ul>
          <li><a href="#vertex-access">Vertex access</a></li>
          <li><a href="#edge-access">Edge access</a></li>
          <li><a href="#property-map-accessors">Property map accessors</a></li>
          <li><a href="#incremental-construction-functions">Incremental construction functions</a></li>
        </ul></li>

      <li><a href="#example">Example</a></li>
    </ul>

    <a name="synopsis"></a><h2>Synopsis</h2>

    <pre>
namespace boost {

template&lt;typename <a href="#Directed">Directed</a> = directedS, typename <a href="#VertexProperty">VertexProperty</a> = no_property, 
         typename <a href="#EdgeProperty">EdgeProperty</a> = no_property, typename <a href="#GraphProperty">GraphProperty</a> = no_property, 
         typename <a href="#Vertex">Vertex</a> = std::size_t, typename <a href="#EdgeIndex">EdgeIndex</a> = Vertex&gt;
class compressed_sparse_row_graph
{
public:
  <i>// <a href="#constructors">Graph constructors</a></i>
  <a href="#default-const">compressed_sparse_row_graph</a>();

  <i>// Unsorted edge list constructors </i>
  template&lt;typename InputIterator&gt;
  <a href="#edge-const">compressed_sparse_row_graph</a>(edges_are_unsorted_t,
                              InputIterator edge_begin, InputIterator edge_end,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());

  template&lt;typename InputIterator, typename EdgePropertyIterator&gt;
  <a href="#edge-prop-const">compressed_sparse_row_graph</a>(edges_are_unsorted_t,
                              InputIterator edge_begin, InputIterator edge_end,
                              EdgePropertyIterator ep_iter,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());

  template&lt;typename MultiPassInputIterator&gt;
  <a href="#edge-multi-const">compressed_sparse_row_graph</a>(edges_are_unsorted_multi_pass_t,
                              MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());

  template&lt;typename MultiPassInputIterator, typename EdgePropertyIterator&gt;
  <a href="#edge-multi-prop-const">compressed_sparse_row_graph</a>(edges_are_unsorted_multi_pass_t,
                              MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
                              EdgePropertyIterator ep_iter,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());

  <i>// New sorted edge list constructors <b>(directed only)</b></i>
  template&lt;typename InputIterator&gt;
  <a href="#edge-sorted-const">compressed_sparse_row_graph</a>(edges_are_sorted_t,
                              InputIterator edge_begin, InputIterator edge_end,
                              vertices_size_type numverts,
                              edges_size_type numedges = 0,
                              const GraphProperty&amp; prop = GraphProperty());

  template&lt;typename InputIterator, typename EdgePropertyIterator&gt;
  <a href="#edge-sorted-prop-const">compressed_sparse_row_graph</a>(edges_are_sorted_t,
                              InputIterator edge_begin, InputIterator edge_end,
                              EdgePropertyIterator ep_iter,
                              vertices_size_type numverts,
                              edges_size_type numedges = 0,
                              const GraphProperty&amp; prop = GraphProperty());

  <i>// In-place unsorted edge list constructors <b>(directed only)</b></i>
  template&lt;typename InputIterator&gt;
  <a href="#edge-inplace-const">compressed_sparse_row_graph</a>(construct_inplace_from_sources_and_targets_t,
                              std::vector&lt;vertex_descriptor&gt;&amp; sources,
                              std::vector&lt;vertex_descriptor&gt;&amp; targets,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());

  template&lt;typename InputIterator&gt;
  <a href="#edge-inplace-prop-const">compressed_sparse_row_graph</a>(construct_inplace_from_sources_and_targets_t,
                              std::vector&lt;vertex_descriptor&gt;&amp; sources,
                              std::vector&lt;vertex_descriptor&gt;&amp; targets,
                              std::vector&lt;EdgeProperty&gt;&amp; edge_props,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());

  <i>// Miscellaneous constructors <b>(directed only)</b></i>
  template&lt;typename Graph, typename VertexIndexMap&gt;
  <a href="#graph-const">compressed_sparse_row_graph</a>(const Graph&amp; g, const VertexIndexMap&amp; vi,
                              vertices_size_type numverts,
                              edges_size_type numedges); 

  template&lt;typename Graph, typename VertexIndexMap&gt;
  compressed_sparse_row_graph(const Graph&amp; g, const VertexIndexMap&amp; vi);

  template&lt;typename Graph&gt;
  explicit <a href="#graph-const">compressed_sparse_row_graph</a>(const Graph&amp; g);

  <i>// <a href="#mutators">Graph mutators <b>(directed only)</b></a></i>
  template&lt;typename Graph, typename VertexIndexMap&gt;
  void <a href="#assign">assign</a>(const Graph&amp; g, const VertexIndexMap&amp; vi,
              vertices_size_type numverts, edges_size_type numedges);

  template&lt;typename Graph, typename VertexIndexMap&gt;
  void <a href="#assign">assign</a>(const Graph&amp; g, const VertexIndexMap&amp; vi);

  template&lt;typename Graph&gt;
  void <a href="#assign">assign</a>(const Graph&amp; g);

  <i>// <a href="#property-access">Property Access</a></i>
  VertexProperty&amp; <a href="#vertex-subscript">operator[]</a>(vertex_descriptor v);
  const VertexProperty&amp; <a href="#vertex-subscript">operator[]</a>(vertex_descriptor v) const;
  EdgeProperty&amp; <a href="#edge-subscript">operator[]</a>(edge_descriptor v);
  const EdgeProperty&amp; <a href="#edge-subscript">operator[]</a>(edge_descriptor v) const;
};

<i>// <a href="IncidenceGraph.html">Incidence Graph requirements</a></i>
vertex_descriptor source(edge_descriptor, const compressed_sparse_row_graph&amp;);
vertex_descriptor target(edge_descriptor, const compressed_sparse_row_graph&amp;);
std::pair&lt;out_edge_iterator, out_edge_iterator&gt; 
  out_edges(vertex_descriptor, const compressed_sparse_row_graph&amp;);
degree_size_type out_degree(vertex_descriptor v, const compressed_sparse_row_graph&amp;);

<i>// <a href="BidirectionalGraph.html">Bidirectional Graph requirements <b>(bidirectional only)</b></a></i>
std::pair&lt;in_edge_iterator, in_edge_iterator&gt; 
  in_edges(vertex_descriptor, const compressed_sparse_row_graph&amp;);
degree_size_type in_degree(vertex_descriptor v, const compressed_sparse_row_graph&amp;);

<i>// <a href="AdjacencyGraph.html">Adjacency Graph requirements</a></i>
std::pair&lt;adjacency_iterator, adjacency_iterator&gt; 
  adjacent_vertices(vertex_descriptor, const compressed_sparse_row_graph&amp;);

<i>// <a href="VertexListGraph.html">Vertex List Graph requirements</a></i>
std::pair&lt;vertex_iterator, vertex_iterator&gt; vertices(const compressed_sparse_row_graph&amp;);
vertices_size_type num_vertices(const compressed_sparse_row_graph&amp;);

<i>// <a href="EdgeListGraph.html">Edge List Graph requirements</a></i>
std::pair&lt;edge_iterator, edge_iterator&gt; edges(const compressed_sparse_row_graph&amp;);
edges_size_type num_edges(const compressed_sparse_row_graph&amp;);

<i>// <a href="#vertex-access">Vertex access</a></i>
vertex_descriptor <a href="#vertex-lookup">vertex</a>(vertices_size_type i, const compressed_sparse_row_graph&amp;);

<i>// <a href="#edge-access">Edge access</a></i>
std::pair&lt;edge_descriptor, bool&gt; 
  <a href="#edge">edge</a>(vertex_descriptor u, vertex_descriptor v, const compressed_sparse_row_graph&amp;);
edge_descriptor <a href="#edge_from_index">edge_from_index</a>(edges_size_type i, const compressed_sparse_row_graph&amp;);

<i>// <a href="#property-map-accessors">Property map accessors</a></i>
template&lt;typename <a href="./PropertyTag.html">PropertyTag</a>&gt;
property_map&lt;compressed_sparse_row_graph, PropertyTag&gt;::type
<a href="#get">get</a>(PropertyTag, compressed_sparse_row_graph&amp; g)

template&lt;typename <a href="./PropertyTag.html">PropertyTag</a>&gt;
property_map&lt;compressed_sparse_row_graph, Tag&gt;::const_type
<a href="#get">get</a>(PropertyTag, const compressed_sparse_row_graph&amp; g)

template&lt;typename <a href="./PropertyTag.html">PropertyTag</a>, class X&gt;
typename property_traits&lt;property_map&lt;compressed_sparse_row_graph, PropertyTag&gt;::const_type&gt;::value_type
<a href="#get-x">get</a>(PropertyTag, const compressed_sparse_row_graph&amp; g, X x)

template&lt;typename <a href="./PropertyTag.html">PropertyTag</a>, class X, class Value&gt;
void <a href="#put-x">put</a>(PropertyTag, const compressed_sparse_row_graph&amp; g, X x, const Value&amp; value);

template&lt;typename <a href="./PropertyTag.html#GraphPropertyTag">GraphPropertyTag</a>&gt;
typename graph_property&lt;compressed_sparse_row_graph, GraphPropertyTag&gt;::type&amp;
<a href="#get_property">get_property</a>(compressed_sparse_row_graph&amp; g, GraphPropertyTag);

template&lt;typename <a href="./PropertyTag.html#GraphPropertyTag">GraphPropertyTag</a>&gt;
typename graph_property&lt;compressed_sparse_row_graph, GraphPropertyTag&gt;::type const &amp;
<a href="#get_property">get_property</a>(const compressed_sparse_row_graph&amp; g, GraphPropertyTag);

template&lt;typename <a href="./PropertyTag.html#GraphPropertyTag">GraphPropertyTag</a>&gt;
void <a href="#set_property">set_property</a>(const compressed_sparse_row_graph&amp; g, GraphPropertyTag,
                  const typename graph_property&lt;compressed_sparse_row_graph, GraphPropertyTag&gt;::type&amp; value);

<i>// <a href="#incremental-construction-functions">Incremental construction functions</a></i>
<b>(directed only)</b>
template&lt;typename InputIterator, typename Graph&gt;
void <a href="#add_edges">add_edges</a>(InputIterator first, InputIterator last, compressed_sparse_row_graph&amp; g);

<b>(directed only)</b>
template&lt;typename InputIterator, typename EPIter, typename Graph&gt;
void <a href="#add_edges_prop">add_edges</a>(InputIterator first, InputIterator last, EPIter ep_first, EPIter ep_last, compressed_sparse_row_graph&amp; g);

<b>(directed only)</b>
template&lt;typename BidirectionalIterator, typename Graph&gt;
void <a href="#add_edges_sorted">add_edges_sorted</a>(BidirectionalIterator first, BidirectionalIterator last, compressed_sparse_row_graph&amp; g);

<b>(directed only)</b>
template&lt;typename BidirectionalIterator, typename EPIter, typename Graph&gt;
void <a href="#add_edges_sorted_prop">add_edges_sorted</a>(BidirectionalIterator first, BidirectionalIterator last, EPIter ep_iter, compressed_sparse_row_graph&amp; g);

} <i>// end namespace boost</i>
   </pre>

    <a name="where"></a><h2>Where Defined</h2>
    <p><code>&lt;<a href="../../../boost/graph/compressed_sparse_row_graph.hpp">boost/graph/compressed_sparse_row_graph.hpp</a>&gt;</code></p>

    <a name="models"></a><h2>Models</h2>
    
    <p>The <tt>compressed_sparse_row_graph</tt> class template models
    (i.e., implements the requirements of) many of the
    BGL <a href="graph_concepts.html">graph concepts</a>, allowing it
    to be used with most of the BGL algorithms. In particular, it
    models the following specific graph concepts:</p>

    <ul>
      <li><a href="Graph.html">Graph</a></li>
      <li><a href="IncidenceGraph.html">IncidenceGraph</a></li>
      <li><a href="AdjacencyGraph.html">AdjacencyGraph</a></li>
      <li><a href="VertexListGraph.html">VertexListGraph</a></li>
      <li><a href="EdgeListGraph.html">EdgeListGraph</a></li>
      <li><a href="PropertyGraph.html">PropertyGraph</a></li>
    </ul>

    <a name="template-parms"></a><h2>Template Parameters</h2>

    <p>The <tt>compressed_sparse_row_graph</tt> class has several
      template parameters that can customize the layout in memory and
      what properties are attached to the graph itself. All
      parameters have defaults, so users interested only in the
      structure of a graph can use the
      type <tt>compressed_sparse_row_graph&lt;&gt;</tt> and ignore
      the parameters.</p>

    <b>Parameters</b>
    <br>
    <br>

    <a name="Directed"></a><code>Directed</code>
      <blockquote>
        A selector that determines whether the graph will be directed,
        bidirectional or undirected. At this time, the CSR graph type
        only supports directed and bidirectional graphs, so this value must
        be either <code>boost::directedS</code> or
        <code>boost::bidirectionalS</code>.<br>
        <b>Default</b>: <code>boost::directedS</code>
      </blockquote>

    <a name="VertexProperty"></a><code>VertexProperty</code>
      <blockquote>
        A class type that will be
        attached to each vertex in the graph. If this value
        is <code>void</code>, no properties will be attached to
        the vertices of the graph.<br>
        <b>Default</b>: <code>void</code>
      </blockquote>

    <a name="EdgeProperty"></a><code>EdgeProperty</code>
    <blockquote>
      A class type that will be attached to each edge in the graph. If
        this value is <code>void</code>, no properties will be
        attached to the edges of the graph.<br>
        <b>Default</b>: <code>void</code>
    </blockquote>

    <a name="GraphProperty"></a><code>GraphProperty</code>
    <blockquote>
      A nested set
        of <code>property</code> templates that describe the
        properties of the graph itself.  If this value
        is <code>no_property</code>, no properties will be attached to
        the graph.<br>
        <b>Default</b>: <code>no_property</code>
    </blockquote>

    <a name="Vertex"></a><code>Vertex</code>
    <blockquote>
      An unsigned integral type that will be
      used as both the index into the array of vertices and as the
      vertex descriptor itself. Larger types permit the CSR graph to
      store more vertices; smaller types reduce the storage required
      per vertex.<br>
        <b>Default</b>: <code>std::size_t</code>
    </blockquote>

    <a name="EdgeIndex"></a><code>EdgeIndex</code>
    <blockquote>
      An unsigned integral type that will be used as the index into
        the array of edges. As with the <code>Vertex</code> parameter,
        larger types permit more edges whereas smaller types reduce
        the amount of storage needed per
        edge. The <code>EdgeIndex</code> type shall not be smaller
        than the <code>Vertex</code> type, but it may be larger. For
        instance, <code>Vertex</code> may be a 16-bit integer
        (allowing 32,767 vertices in the graph)
        whereas <code>EdgeIndex</code> could then be a 32-bit integer
        to allow a complete graph to be stored in the CSR format.<br>
        <b>Default</b>: <code>Vertex</code>
    </blockquote>

    <a name="properties"></a><h2>Interior Properties</h2>

    <p> The <tt>compressed_sparse_row_graph</tt> allows properties to
    be attached to its vertices, edges, or to the graph itself by way
    of its <a href="#template-parms">template parameters</a>. These
    properties may be accessed via
    the <a href="#property-access">member</a>
    and <a href="#property-map-accessors">non-member</a> property
    access functions, using the <a href="bundles.html">bundled
    properties</a> scheme.</p>

    <p>The CSR graph provides two kinds of built-in
    properties: <tt>vertex_index</tt>, which maps from vertices to
      values in <tt>[0, n)</tt> and <tt>edge_index</tt>, which maps
      from edges to values in <tt>[0, m)</tt>, where <tt>n</tt>
    and <tt>m</tt> are the number of vertices and edges in the graph,
    respectively. </p>

    <a name="member-functions"></a><h2>Member Functions</h2>

    <a name="constructors"></a><h3>Constructors</h3>
    <pre><a name="default-const"></a>
  compressed_sparse_row_graph();
    </pre>
    <p class="indent">Constructs a graph with no vertices or edges.</p>

    <hr></hr>

    <pre><a name="edge-const"></a>
  template&lt;typename InputIterator&gt;
  compressed_sparse_row_graph(edges_are_unsorted_t,
                              InputIterator edge_begin, InputIterator edge_end,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());
    </pre>

    <p class="indent">
      Constructs a graph with <code>numverts</code> vertices whose
      edges are specified by the iterator range <code>[edge_begin,
      edge_end)</code>. The <tt>InputIterator</tt> must be a model of
      <a
      href="http://www.boost.org/sgi/stl/InputIterator.html">InputIterator</a>
      whose <code>value_type</code> is an <code>std::pair</code> of
      integer values. These integer values are the source and target
      vertices for the edges, and must fall within the range <code>[0,
      numverts)</code>. The edges in <code>[edge_begin,
      edge_end)</code> do not need to be sorted.  This constructor uses extra
      memory to save the edge information before adding it to the graph,
      avoiding the requirement for the iterator to have multi-pass capability.
    </p>

    <p class="indent">
      The value <code>prop</code> will be used to initialize the graph
      property.
    </p>

    <hr></hr>

    <pre><a name="edge-prop-const"></a>
  template&lt;typename InputIterator, typename EdgePropertyIterator&gt;
  compressed_sparse_row_graph(edges_are_unsorted_t,
                              InputIterator edge_begin, InputIterator edge_end,
                              EdgePropertyIterator ep_iter,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());
    </pre>
    <p class="indent">
      This constructor constructs a graph with <code>numverts</code>
      vertices and the edges provided in the iterator range
      <code>[edge_begin, edge_end)</code>. Its semantics are identical
      to the <a href="#edge-const">edge range constructor</a>, except
      that edge properties are also initialized. The type
      <tt>EdgePropertyIterator</tt> must be a model of the <a
      href="http://www.boost.org/sgi/stl/InputIterator.html">InputIterator</a>
      concept whose <tt>value_type</tt> is convertible to
      <tt>EdgeProperty</tt>. The iterator range <tt>[ep_iter, ep_ter +
        m)</tt> will be used to initialize the properties on the edges
      of the graph, where <tt>m</tt> is distance from
      <tt>edge_begin</tt> to <tt>edge_end</tt>.  This constructor uses extra
      memory to save the edge information before adding it to the graph,
      avoiding the requirement for the iterator to have multi-pass capability.
    </p>

    <hr></hr>

    <pre><a name="edge-multi-const"></a>
  template&lt;typename MultiPassInputIterator&gt;
  compressed_sparse_row_graph(edges_are_unsorted_multi_pass_t,
                              MultiPassInputIterator edge_begin, MultiPassInputIterator edge_end,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());
    </pre>

    <p class="indent">
      Constructs a graph with <code>numverts</code> vertices whose
      edges are specified by the iterator range <code>[edge_begin,
      edge_end)</code>. The <tt>MultiPassInputIterator</tt> must be a model of
      <a
      href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>
      whose <code>value_type</code> is an <code>std::pair</code> of
      integer values. These integer values are the source and target
      vertices for the edges, and must fall within the range <code>[0,
      numverts)</code>. The edges in <code>[edge_begin,
      edge_end)</code> do not need to be sorted.  Multiple passes will be made
      over the edge range.
    </p>

    <p class="indent">
      The value <code>prop</code> will be used to initialize the graph
      property.
    </p>

    <hr></hr>

    <pre><a name="edge-multi-prop-const"></a>
  template&lt;typename MultiPassInputIterator, typename EdgePropertyIterator&gt;
  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&amp; prop = GraphProperty());
    </pre>
    <p class="indent">
      This constructor constructs a graph with <code>numverts</code>
      vertices and the edges provided in the iterator range
      <code>[edge_begin, edge_end)</code>. Its semantics are identical
      to the <a href="#edge-const">edge range constructor</a>, except
      that edge properties are also initialized. The type
      <tt>EdgePropertyIterator</tt> must be a model of the <a
      href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>
      concept whose <tt>value_type</tt> is convertible to
      <tt>EdgeProperty</tt>. The iterator range <tt>[ep_iter, ep_ter +
        m)</tt> will be used to initialize the properties on the edges
      of the graph, where <tt>m</tt> is distance from
      <tt>edge_begin</tt> to <tt>edge_end</tt>.  Multiple passes will be made
      over the edge and property ranges.
    </p>

    <hr></hr>

    <pre><a name="edge-sorted-const"></a>
  template&lt;typename InputIterator&gt;
  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&amp; prop = GraphProperty());
    </pre>

    <p class="indent">
      Constructs a graph with <code>numverts</code> vertices whose
      edges are specified by the iterator range <code>[edge_begin,
      edge_end)</code>. The argument of type <code>edges_are_sorted_t</code> is
      a tag used to distinguish this constructor; the value
      <code>edges_are_sorted</code> can be used to initialize this parameter.
      The <tt>InputIterator</tt> must be a model of
      <a
      href="http://www.boost.org/sgi/stl/InputIterator.html">InputIterator</a>
      whose <code>value_type</code> is an <code>std::pair</code> of
      integer values. These integer values are the source and target
      vertices for the edges, and must fall within the range <code>[0,
      numverts)</code>. The edges in <code>[edge_begin,
      edge_end)</code> must be sorted so that all edges originating
      from vertex <i>i</i> precede any edges originating from all
      vertices <i>j</i> where <i>j &gt; i</i>.
    </p>

    <p class="indent">
      The value <code>numedges</code>, if provided, tells how many
      edges are in the range <code>[edge_begin, edge_end)</code> and
      will be used to preallocate data structures to save both memory
      and time during construction.
    </p>

    <p class="indent">
      The value <code>prop</code> will be used to initialize the graph
      property.
    </p>

    <hr></hr>

    <pre><a name="edge-sorted-prop-const"></a>
  template&lt;typename InputIterator, typename EdgePropertyIterator&gt;
  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&amp; prop = GraphProperty());
    </pre>
    <p class="indent">
      This constructor constructs a graph with <code>numverts</code>
      vertices and the edges provided in the iterator range
      <code>[edge_begin, edge_end)</code>. Its semantics are identical
      to the <a href="#edge-const">edge range constructor</a>, except
      that edge properties are also initialized. The type
      <tt>EdgePropertyIterator</tt> must be a model of the <a
      href="http://www.boost.org/sgi/stl/InputIterator.html">InputIterator</a>
      concept whose <tt>value_type</tt> is convertible to
      <tt>EdgeProperty</tt>. The iterator range <tt>[ep_iter, ep_ter +
        m)</tt> will be used to initialize the properties on the edges
      of the graph, where <tt>m</tt> is distance from
      <tt>edge_begin</tt> to <tt>edge_end</tt>.
    </p>

    <hr></hr>

    <pre><a name="edge-inplace-const"></a>
  template&lt;typename InputIterator&gt;
  compressed_sparse_row_graph(construct_inplace_from_sources_and_targets_t,
                              std::vector&lt;vertex_descriptor&gt;&amp; sources,
                              std::vector&lt;vertex_descriptor&gt;&amp; targets,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());
    </pre>
    <p class="indent">
      This constructor constructs a graph with <code>numverts</code> vertices
      and the edges provided in the two vectors <code>sources</code> and
      <code>targets</code>.  The two vectors are mutated in-place to sort them
      by source vertex.  They are returned with unspecified values, but do not
      share storage with the constructed graph (and so are safe to destroy).
      The parameter <code>prop</code>, if provided, is used to initialize the
      graph property.
    </p>

    <hr></hr>

    <pre><a name="edge-inplace-prop-const"></a>
  template&lt;typename InputIterator&gt;
  compressed_sparse_row_graph(construct_inplace_from_sources_and_targets_t,
                              std::vector&lt;vertex_descriptor&gt;&amp; sources,
                              std::vector&lt;vertex_descriptor&gt;&amp; targets,
                              std::vector&lt;EdgeProperty&gt;&amp; edge_props,
                              vertices_size_type numverts,
                              const GraphProperty&amp; prop = GraphProperty());
    </pre>
    <p class="indent">
      This constructor constructs a graph with <code>numverts</code> vertices
      and the edges provided in the two vectors <code>sources</code> and
      <code>targets</code>.  Edge properties are initialized from the vector
      <code>edge_props</code>.  The three vectors are mutated in-place to sort
      them by source vertex.  They are returned with unspecified values, but do
      not share storage with the constructed graph (and so are safe to
      destroy).  The parameter <code>prop</code>, if provided, is used to
      initialize the graph property.
    </p>

    <hr></hr>

    <pre><a name="graph-const"></a>
  template&lt;typename Graph, typename VertexIndexMap&gt;
  compressed_sparse_row_graph(const Graph&amp; g, const VertexIndexMap&amp; vi,
                              vertices_size_type numverts,
                              edges_size_type numedges); 

  template&lt;typename Graph, typename VertexIndexMap&gt;
  compressed_sparse_row_graph(const Graph&amp; g, const VertexIndexMap&amp; vi);

  template&lt;typename Graph&gt;
  explicit compressed_sparse_row_graph(const Graph&amp; g);
    </pre>

    <p class="indent">
      Calls the <a href="#assign"><tt>assign</tt></a> function with
      all of the arguments it is given.
    </p>

    <hr></hr>

    <a name="mutators"></a><h3>Mutators</h3>
    <pre><a name="assign"></a>
  template&lt;typename Graph, typename VertexIndexMap&gt;
  void assign(const Graph&amp; g, const VertexIndexMap&amp; vi,
              vertices_size_type numverts, edges_size_type numedges);

  template&lt;typename Graph, typename VertexIndexMap&gt;
  void assign(const Graph&amp; g, const VertexIndexMap&amp; vi);

  template&lt;typename Graph&gt;
  void assign(const Graph&amp; g);
    </pre>

    <p class="indent">
      Clears the CSR graph and builds a CSR graph in place from the
      structure of another graph. The graph type <tt>Graph</tt> must
      be a model of <a href="IncidenceGraph.html">IncidenceGraph</a>.

      <br><b>Parameters</b>

      <ul>
        <li><tt>g</tt>: The incoming graph.</li>
        
        <li><tt>vi</tt>: A map from vertices to indices. If not
          provided, <tt>get(vertex_index, g)</tt> will be used.</li>
        
        <li><tt>numverts</tt>: The number of vertices in the graph
          <tt>g</tt>. If not provided, <tt>Graph</tt> must be a model of
          <a href="VertexListGraph.html">VertexListGraph</a>.</li>
        
        <li><tt>numedges</tt>: The number of edges in the graph
          <tt>g</tt>. If not provided, <tt>Graph</tt> must be a model of
          <a href="EdgeListGraph.html">EdgeListGraph</a>.</li>
      </ul>
    </p>

    <hr></hr>

    <a name="property-access"></a><h3>Property Access</h3>

    <pre><a name="vertex-subscript"></a>
  VertexProperty&amp; operator[](vertex_descriptor v);
  const VertexProperty&amp; operator[](vertex_descriptor v) const;
    </pre>

    <p class="indent">
      Retrieves the property value associated with vertex
      <tt>v</tt>. Only valid when <tt>VertexProperty</tt> is a class
      type that is not <tt>no_property</tt>.
    </p>

    <hr></hr>

    <pre><a name="edge-subscript">
  EdgeProperty&amp; operator[](edge_descriptor v);
  const EdgeProperty&amp; operator[](edge_descriptor v) const;
    </pre>

    <p class="indent">
      Retrieves the property value associated with edge
      <tt>v</tt>. Only valid when <tt>EdgeProperty</tt> is a class
      type that is not <tt>no_property</tt>.
    </p>

    <hr></hr>
    <a name="non-members"></a><h2>Non-member Functions</h2>

    <a name="vertex-access"></a><h3>Vertex access</h3>

    <pre><a name="vertex-lookup"></a>
  vertex_descriptor vertex(vertices_size_type i, const compressed_sparse_row_graph&amp;);
    </pre>
    <p class="indent">
      Retrieves the <i>i</i><sup>th</sup> vertex in the graph in
      constant time.
    </p>

    <hr></hr>

    <a name="edge-access"></a><h3>Edge access</h3>

    <pre><a name="edge"></a>
  std::pair&lt;edge_descriptor, bool&gt; 
    edge(vertex_descriptor u, vertex_descriptor v, const compressed_sparse_row_graph&amp;);
    </pre>

    <p class="indent">
      If there exists an edge <i>(u, v)</i> in the graph, returns the
      descriptor for that edge and <tt>true</tt>; otherwise, the
      second value in the pair will be <tt>false</tt>. If multiple
      edges exist from <tt>u</tt> to <tt>v</tt>, the first edge will
      be returned; use <a href="IncidenceGraph.html"><tt>out_edges</tt></a> and a
      conditional statement
      to retrieve all edges to a given target.  This function requires linear
      time in the
      number of edges outgoing from <tt>u</tt>.
    </p>

    <hr></hr>

    <pre><a name="edge_from_index"></a>
  edge_descriptor edge_from_index(edges_size_type i, const compressed_sparse_row_graph&amp;);
    </pre>

    <p class="indent">
      Returns the <i>i</i><sup>th</sup> edge in the graph. This
      operation requires logarithmic time in the number of vertices.
    </p>

    <hr></hr>

    <h3><a name="property-map-accessors">Property Map Accessors</a></h3>

    <pre><a name="get"></a>
template&lt;typename <a href="./PropertyTag.html">PropertyTag</a>&gt;
property_map&lt;compressed_sparse_row_graph, PropertyTag&gt;::type
get(PropertyTag, compressed_sparse_row_graph&amp; g)

template&lt;typename <a href="./PropertyTag.html">PropertyTag</a>&gt;
property_map&lt;compressed_sparse_row_graph, Tag&gt;::const_type
get(PropertyTag, const compressed_sparse_row_graph&amp; g)
    </pre>
    
    <p class="indent">
      Returns the property map object for the vertex property
      specified by <TT>PropertyTag</TT>. The <TT>PropertyTag</TT> must
      be a member pointer to access one of the fields in
      <tt>VertexProperty</tt> or <tt>EdgeProperty</tt>.
    </p>

    <hr></hr>

    <pre><a name="get-x"></a>
template&lt;typename <a href="./PropertyTag.html">PropertyTag</a>, class X&gt;
typename property_traits&lt;property_map&lt;compressed_sparse_row_graph, PropertyTag&gt;::const_type&gt::value_type
get(PropertyTag, const compressed_sparse_row_graph&amp; g, X x)
    </pre>

    <p class="indent">
      This returns the property value for <tt>x</tt>, where <tt>x</tt>
      is either a vertex or edge descriptor.
    </p>

    <hr></hr>

    <pre><a name="put-x"></a>
template&lt;typename <a href="./PropertyTag.html">PropertyTag</a>, class X, class Value&gt;
void put(PropertyTag, const compressed_sparse_row_graph&amp; g, X x, const Value&amp; value);
    </pre>

    <p class="indent">
      This sets the property value for <tt>x</tt> to
      <tt>value</tt>. <tt>x</tt> is either a vertex or edge
      descriptor.  <tt>Value</tt> must be convertible to <tt>typename
      property_traits&lt;property_map&lt;compressed_sparse_row_graph,
      PropertyTag&gt;::type&gt::value_type</tt>
    </p>

    <hr></hr>

    <pre><a name="get_property"></a>
template&lt;typename <a href="./PropertyTag.html#GraphPropertyTag">GraphPropertyTag</a>&gt;
typename graph_property&lt;compressed_sparse_row_graph, GraphPropertyTag&gt;::type&amp;
get_property(compressed_sparse_row_graph&amp; g, GraphPropertyTag);

template&lt;typename <a href="./PropertyTag.html#GraphPropertyTag">GraphPropertyTag</a>&gt;
typename graph_property&lt;compressed_sparse_row_graph, GraphPropertyTag&gt;::type const &amp;
get_property(const compressed_sparse_row_graph&amp; g, GraphPropertyTag);
    </pre>

    <p class="indent">
      Return the property specified by <tt>GraphPropertyTag</tt> that
      is attached to the graph object <tt>g</tt>. 
    </p>

    <hr></hr>

    <pre><a name="set_property"></a>
template&lt;typename <a href="./PropertyTag.html#GraphPropertyTag">GraphPropertyTag</a>&gt;
void set_property(const compressed_sparse_row_graph&amp; g, GraphPropertyTag,
                  const typename graph_property&lt;compressed_sparse_row_graph, GraphPropertyTag&gt;::type&amp; value);
    </pre>

    <p class="indent">
      Set the property specified by <tt>GraphPropertyTag</tt> that
      is attached to the graph object <tt>g</tt>.
    </p>

    <hr></hr>

    <h3><a name="incremental-construction-functions">Incremental construction functions</a></h3>

    <pre><a name="add_edges"></a>
template&lt;typename InputIterator&gt;
void add_edges(InputIterator first, InputIterator last, compressed_sparse_row_graph&amp; g)
    </pre>
    
    <p class="indent">
      Add a range of edges (from <tt>first</tt> to <tt>last</tt>) to the graph.
      The <tt>InputIterator</tt> must be a model of <a
      href="http://www.boost.org/sgi/stl/InputIterator.html">InputIterator</a>
      whose <code>value_type</code> is an <code>std::pair</code> of integer
      values. These integer values are the source and target vertices of the
      new edges.  The edges do not need to be sorted.
    </p>

    <hr></hr>

    <pre><a name="add_edges_prop"></a>
template&lt;typename InputIterator, typename EPIter&gt;
void add_edges(InputIterator first, InputIterator last, EPIter ep_first, EPIter ep_last, compressed_sparse_row_graph&amp; g)
    </pre>
    
    <p class="indent">
      Add a range of edges (from <tt>first</tt> to <tt>last</tt>) with
      corresponding edge properties (from <tt>ep_first</tt> to
      <tt>ep_last</tt>) to the graph.  The <tt>InputIterator</tt> and
      <tt>EPIter</tt> must be models of <a
      href="http://www.boost.org/sgi/stl/InputIterator.html">InputIterator</a>;
      the <code>value_type</code> of <tt>InputIterator</tt> must be an
      <code>std::pair</code> of integer values, and the <code>value_type</code>
      of <tt>EPIter</tt> must be the edge property type of the graph. The
      integer values produced by the <tt>InputIterator</tt> are the source and
      target vertices of the new edges.  The edges do not need to be sorted.
    </p>

    <hr></hr>

    <pre><a name="add_edges_sorted"></a>
template&lt;typename BidirectionalIterator&gt;
void add_edges_sorted(BidirectionalIterator first, BidirectionalIterator last, compressed_sparse_row_graph&amp; g)
    </pre>
    
    <p class="indent">
      Add a range of edges (from <tt>first</tt> to <tt>last</tt>) to the graph.
      The <tt>BidirectionalIterator</tt> must be a model of <a
      href="http://www.boost.org/sgi/stl/BidirectionalIterator.html">BidirectionalIterator</a>
      whose <code>value_type</code> is an <code>std::pair</code> of integer
      values. These integer values are the source and target vertices of the
      new edges.  The edges must be sorted in increasing order by source vertex
      index.
    </p>

    <hr></hr>

    <pre><a name="add_edges_sorted_prop"></a>
template&lt;typename BidirectionalIterator, typename EPIter&gt;
void add_edges_sorted(BidirectionalIterator first, BidirectionalIterator last, EPIter ep_iter, compressed_sparse_row_graph&amp; g)
    </pre>
    
    <p class="indent">
      Add a range of edges (from <tt>first</tt> to <tt>last</tt>) to the graph.
      The <tt>BidirectionalIterator</tt> and <tt>EPIter</tt> must be models of
      <a
      href="http://www.boost.org/sgi/stl/BidirectionalIterator.html">BidirectionalIterator</a>.
      The <code>value_type</code> of the <tt>BidirectionalIterator</tt> must be
      an <code>std::pair</code> of integer
      values. These integer values are the source and target vertices of the
      new edges.
      The <code>value_type</code> of the <tt>EPIter</tt> must be the edge
      property type of the graph.
      The edges must be sorted in increasing order by source vertex
      index.
    </p>

    <hr></hr>
    <a name="example"></a><h2>Example</h2>

    <br>[<a
    href="../example/csr-example.cpp">libs/graph/example/csr-example.cpp</a>]

    <p>We will use the <tt>compressed_sparse_row_graph</tt> graph
    class to store a simple Web graph. In this web graph the vertices
    represent web pages and the edges represent links from one web
    page to another. With each web page we want to associate a URL, so
    we initially create a <tt>WebPage</tt> class that stores the
    URL. Then we can create our graph type by providing
    <tt>WebPage</tt> as a parameter to the
    <tt>compressed_sparse_row_graph</tt> class template.</p>

    <pre>
class WebPage
{
 public:
  std::string url;
};

// ...

typedef compressed_sparse_row_graph&lt;directedS, WebPage&gt; WebGraph;
WebGraph g(&the_edges[0], &the_edges[0] + sizeof(the_edges)/sizeof(E), 6);
    </pre>

    <p>We can then set the properties on the vertices of the graph
    using the <a href="bundles.html">bundled properties</a> syntax,
    and display the edges for the user.</p>

    <pre>
// Set the URLs of each vertex
int index = 0;
BGL_FORALL_VERTICES(v, g, WebGraph)
  g[v].url = urls[index++];

// Output each of the links
std::cout &lt;&lt; "The web graph:" &lt;&lt; std::endl;
BGL_FORALL_EDGES(e, g, WebGraph)
  std::cout &lt;&lt; "  " &lt;&lt; g[source(e, g)].url &lt;&lt; " -> " &lt;&lt; g[target(e, g)].url 
            &lt;&lt; std::endl;
    </pre>

    <p>See the <a href="../example/csr-example.cpp">complete example
    source</a> for other operations one can perform with a
    <tt>compressed_sparse_row_graph</tt>.</p>
<br>
<HR>
<TABLE>
<TR valign=top>
<TD nowrap>Copyright &copy; 2005</TD><TD>
<A HREF="http://www.boost.org/people/doug_gregor.html">Doug Gregor</A>, Indiana University (<script language="Javascript">address("cs.indiana.edu", "dgregor")</script>)<br>
Jeremiah Willcock, Indiana University (<script language="Javascript">address("osl.iu.edu", "jewillco")</script>)<br>
  <A HREF="https://homes.cs.washington.edu/~al75">Andrew Lumsdaine</A>,
Indiana University (<script language="Javascript">address("osl.iu.edu", "lums")</script>)
</TD></TR></TABLE>
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