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<Head>
<Title>Graph</Title>
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<H2><A NAME="concept:Graph"></A>
Graph
</H2>

<P>
The Graph concept contains a few requirements that are common to all
the graph concepts. These include some associated types for
<tt>vertex_descriptor</tt>, <tt>edge_descriptor</tt>, etc. One should
note that a model of Graph is <B>not</B> required to be a model of <a
href="http://www.boost.org/sgi/stl/Assignable.html">Assignable</a>,
so algorithms should pass graph objects by reference.

<P>

<h3>Notation</h3>

<Table>
<TR>
<TD><tt>G</tt></TD>
<TD>A type that is a model of Graph.</TD>
</TR>

<TR>
<TD><tt>g</tt></TD>
<TD>An object of type <tt>G</tt>.</TD>
</TR>
</table>

<H3>Associated Types</H3>

<table border>
<tr>
<td><pre>boost::graph_traits&lt;G&gt;::vertex_descriptor</pre>
A vertex descriptor corresponds to a unique vertex in an abstract
graph instance. A vertex descriptor must be
<a
href="http://www.boost.org/sgi/stl/DefaultConstructible.html">Default Constructible</a>,
<a href="http://www.boost.org/sgi/stl/Assignable.html">Assignable</a>, and
<a href="http://www.boost.org/sgi/stl/EqualityComparable.html">Equality Comparable</a>.
</td>
</tr>

<tr>
<td><pre>boost::graph_traits&lt;G&gt;::edge_descriptor</pre>
An edge descriptor corresponds to a unique edge <i>(u,v)</i> in a
graph.  An edge descriptor must be <a
href="http://www.boost.org/sgi/stl/DefaultConstructible.html">Default Constructible</I>,
<a href="http://www.boost.org/sgi/stl/Assignable.html">Assignable</a>, and
<a href="http://www.boost.org/sgi/stl/EqualityComparable.html">Equality Comparable</a>.
</td>
</tr>

<tr>
<td><pre>boost::graph_traits&lt;G&gt;::directed_category</pre>
This type shall be convertible to <TT>directed_tag</TT> or <TT>undirected_tag</TT>.
</td>
</tr>

<tr>
<td><pre>boost::graph_traits&lt;G&gt;::edge_parallel_category</pre>
This describes whether the graph class allows the insertion of
parallel edges (edges with the same source and target). The two tags
are <TT>allow_parallel_edge_tag</TT> and <TT>disallow_parallel_edge_tag</TT>.
</td>
</tr>

<tr>
<td><pre>boost::graph_traits&lt;G&gt;::traversal_category</pre>
This describes the ways in which the vertices and edges of the
graph can be visited. The choices are <TT>incidence_graph_tag</TT>,
<TT>adjacency_graph_tag</TT>, <TT>bidirectional_graph_tag</TT>, 
<TT>vertex_list_graph_tag</TT>, <TT>edge_list_graph_tag</TT>, and 
<TT>adjacency_matrix_tag</TT>.
</td>
</tr>

</table>

<H3>Valid Expressions</H3>

<table border>

<tr>
<td><pre>boost::graph_traits&lt;G&gt;::null_vertex()</pre></td></TD>
<td>
Returns a special <tt>boost::graph_traits&lt;G&gt;::vertex_descriptor</tt> object which does not refer to
any vertex of graph object which type is <tt>G</tt>.
<td>
</tr>
</table>


<H3>Concept Checking Class</H3>

<PRE>
  template &lt;class G&gt;
  struct GraphConcept
  {
    typedef typename boost::graph_traits&lt;G&gt;::vertex_descriptor vertex_descriptor;
    typedef typename boost::graph_traits&lt;G&gt;::edge_descriptor edge_descriptor;
    typedef typename boost::graph_traits&lt;G&gt;::directed_category directed_category;
    typedef typename boost::graph_traits&lt;G&gt;::edge_parallel_category edge_parallel_category;
    typedef typename boost::graph_traits&lt;G&gt;::traversal_category traversal_category;

    void constraints() {
      BOOST_CONCEPT_ASSERT(( DefaultConstructibleConcept&lt;vertex_descriptor&gt; ));
      BOOST_CONCEPT_ASSERT(( EqualityComparableConcept&lt;vertex_descriptor&gt; ));
      BOOST_CONCEPT_ASSERT(( AssignableConcept&lt;vertex_descriptor&gt; ));
      BOOST_CONCEPT_ASSERT(( DefaultConstructibleConcept&lt;edge_descriptor&gt; ));
      BOOST_CONCEPT_ASSERT(( EqualityComparableConcept&lt;edge_descriptor&gt; ));
      BOOST_CONCEPT_ASSERT(( AssignableConcept&lt;edge_descriptor&gt; ));
    }
    G g;
  };
</PRE>

<H3>See Also</H3>

<a href="./graph_concepts.html">Graph concepts</a>

<br>
<HR>
<TABLE>
<TR valign=top>
<TD nowrap>Copyright &copy; 2000-2001</TD><TD>
<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>, Indiana University (<A HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)
</TD></TR></TABLE>

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