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    <IMG SRC="../../../boost.png" 
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    <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 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>.</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> = void, 
         typename <a href="#EdgeProperty">EdgeProperty</a> = void, 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>();

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

  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</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="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">vertex</a>(vertices_size_type i, const compressed_sparse_row_graph&amp;);

<i>// <a href="#edge-access">Edge access</a></i>
std::pair&lt;out_edge_iterator, out_edge_iterator&gt; 
  <a href="#edge_range">edge_range</a>(vertex_descriptor u, vertex_descriptor v, const compressed_sparse_row_graph&amp;);
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>
template&lt;typename Graph&gt;
vertex_descriptor <a href=#add_vertex">add_vertex</a>(compressed_sparse_row_graph&amp; g);

template&lt;typename Graph&gt;
vertex_descriptor <a href=#add_vertices">add_vertices</a>(vertices_size_type count, compressed_sparse_row_graph&amp; g);

template&lt;typename Graph&gt;
edge_descriptor <a href=#add_edge">add_vertices</a>(vertex_descriptor src, vertex_descriptor tgt, 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 graphs, so this value must
        be <code>boost::directedS</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(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 <tt>InputIterator</tt> must be a model of
      <a
      href="http://www.sgi.com/tech/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> preceed 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-prop-const"></a>
  template&lt;typename InputIterator, typename EdgePropertyIterator&gt;
  compressed_sparse_row_graph(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.sgi.com/tech/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="#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>
      and have a <tt>vertex(i, g)</tt> function that retrieves the
      <i>i</i><sup>th</sup> vertex in the graph.

      <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"></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_range"></a>
  std::pair&lt;out_edge_iterator, out_edge_iterator&gt; 
    edge_range(vertex_descriptor u, vertex_descriptor v, const compressed_sparse_row_graph&amp;);
    </pre>

    <p class="indent">
      Returns all edges from <tt>u</tt> to <tt>v</tt>. Requires time
      linear in the number of edges outgoing from <tt>u</tt>.
    </p>

    <hr></hr>

    <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="#edge_range"><tt>edge_range</tt></a>
      to retrieve all edges.
    </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_vertex"></a>
vertex_descriptor add_vertex(compressed_sparse_row_graph&amp; g)
    </pre>
    
    <p class="indent">
      Add a new vertex to the end of the graph <tt>g</tt>, and return a
      descriptor for that vertex.  The new vertex will be greater than any of
      the previous vertices in <tt>g</tt>.
    </p>

    <hr></hr>

    <pre><a name="add_vertices"></a>
vertex_descriptor add_vertices(vertices_size_type count, compressed_sparse_row_graph&amp; g)
    </pre>
    
    <p class="indent">
      Add <tt>count</tt> new vertices to the end of the graph <tt>g</tt>, and
      return a descriptor for the smallest new vertex.  The new vertices will
      be greater than any of the previous vertices in <tt>g</tt>.
    </p>

    <hr></hr>

    <pre><a name="add_edge"></a>
edge_descriptor add_edge(vertex_descriptor src, vertex_descriptor tgt, compressed_sparse_row_graph&amp; g)
    </pre>
    
    <p class="indent">
      Add a new edge from <tt>src</tt> to <tt>tgt</tt> in the graph <tt>g</tt>,
      and return a descriptor for it.  There must not be an edge in <tt>g</tt>
      whose source vertex is greater than <tt>src</tt>.  If the vertex
      <tt>src</tt> has out edges before this operation is called, there must be
      none whose target is larger than <tt>tgt</tt>.
    </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=http://www.osl.iu.edu/~lums>Andrew Lumsdaine</A>,
Indiana University (<script language="Javascript">address("osl.iu.edu", "lums")</script>)
</TD></TR></TABLE>
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