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<Head>
<Title>IncidenceGraph</Title>
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<H1><A NAME="concept:IncidenceGraph"></A>
IncidenceGraph
</H1>

The IncidenceGraph concept provides an interface for
efficient access to the out-edges of each vertex in the graph.


<H3>Refinement of</H3>

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

<h3>Notation</h3>

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

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

<TR>
<TD><tt>e</tt></TD>
<TD>An object of type <tt>boost::graph_traits&lt;G&gt;::edge_descriptor</tt>.</TD>
</TR>

<TR>
<TD><tt>u, v</tt></TD>
<TD>Are objects of type <tt>boost::graph_traits&lt;G&gt;::vertex_descriptor</tt>.</TD>
</TR>

</table>

<H3>Associated Types</H3>

<Table border>

<tr>
<td><tt>boost::graph_traits&lt;G&gt;::traversal_category</tt><br><br>
 This tag type must be convertible to <tt>incidence_graph_tag</tt>.
</td>
</tr>


<TR>
<TD>
<pre>boost::graph_traits&lt;G&gt;::out_edge_iterator</pre>
An out-edge iterator for a vertex <i>v</i> provides access to the
out-edges of the vertex.  As such, the value type of an out-edge
iterator is the edge descriptor type of its graph. An out-edge
iterator must meet the requirements of <a
href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>.
</TD>
</TR>

<TR>
<TD><pre>boost::graph_traits&lt;G&gt;::degree_size_type</pre>
The unsigned integral type used for representing the number
out-edges or incident edges of a vertex.
</TD>
</TR>

</table>

<h3>Valid Expressions</h3>

<Table border>

<tr>
<td><a name="sec:source"><TT>source(e,&nbsp;g)</TT></a></TD>
<TD>Returns the vertex descriptor for <i>u</i> of the edge <i>(u,v)</i> represented by <TT>e</TT>.<br>
Return type: <TT>vertex_descriptor</TT>
</TD>
</TR>


<tr>
<td><a name="sec:target"><TT>target(e,&nbsp;g)</TT></a></TD>
<TD>Returns the vertex descriptor for <i>v</i> of the edge <i>(u,v)</i> represented by <TT>e</TT>.<br>
Return type: <TT>vertex_descriptor</TT>
</td></tr>

<tr>
<td><a name="sec:out-edges"><TT>out_edges(u,&nbsp;g)</TT></a></TD>
<TD>Returns an iterator-range providing access to the out-edges (for
directed graphs) or incident edges (for undirected graphs) of vertex
<TT>u</TT> in graph <TT>g</TT>.  The source vertex of an edge obtained
via an out edge iterator is guaranteed (for both directed and
undirected graphs) to be the vertex <tt>u</tt> used in the call to
<tt>out_edges(u, g)</tt> and the target vertex must be a vertex
adjacent to <tt>u</tt>.<a href="#1">[1]</a>
<br>
Return type: <TT>std::pair&lt;out_edge_iterator, out_edge_iterator&gt;</TT>
</TD>
</tr>

<tr>
<TD><TT>out_degree(u,&nbsp;g)</TT></TD>
<TD>Returns the number of out-edges (for directed graphs) or the
number of incident edges (for undirected graphs) of vertex <TT>u</TT>
in graph <TT>g</TT>.<br>
Return type: <TT>degree_size_type</TT>
</TD>
</TR>

</TABLE>

<P>

<H3>Complexity guarantees</H3>

<P>
The <TT>source()</TT>, <TT>target()</TT>, and <TT>out_edges()</TT>
functions must all be constant time. The <tt>out_degree()</tt>
function must be linear in the number of out-edges.

<P>

<H3>See Also</H3>

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

<H3>Notes</H3>

<a name="1">[1]</a> For undirected graphs, the edge <tt>(u,v)</tt> is
the same as edge <tt>(v,u)</tt>, so without some extra guarantee an
implementation would be free use any ordering for the pair of vertices
in an out-edge. For example, if you call <tt>out_edges(u, g)</tt>, and
<tt>v</tt> is one of the vertices adjacent to <tt>u</tt>, then the
implementation would be free to return <tt>(v,u)</tt> as an out-edge
which would be non-intuitive and cause trouble for algorithms.
Therefore, the extra requirement is added that the out-edge connecting
<tt>u</tt> and <tt>v</tt> must be given as <tt>(u,v)</tt> and not
<tt>(v,u)</tt>.

<H3>Concept Checking Class</H3>

<PRE>
  template &lt;class G&gt;
  struct IncidenceGraphConcept
  {
    typedef typename boost::graph_traits&lt;G&gt;::out_edge_iterator out_edge_iterator;
    void constraints() {
      function_requires&lt; GraphConcept&lt;G&gt; &gt;();
      function_requires&lt; MultiPassInputIteratorConcept&lt;out_edge_iterator&gt; &gt;();

      p = out_edges(u, g);
      e = *p.first;
      u = source(e, g);
      v = target(e, g);
    }
    void const_constraints(const G&amp; g) {
      p = out_edges(u, g);
      e = *p.first;
      u = source(e, g);
      v = target(e, g);
    }
    std::pair&lt;out_edge_iterator, out_edge_iterator&gt; p;
    typename boost::graph_traits&lt;G&gt;::vertex_descriptor u, v;
    typename boost::graph_traits&lt;G&gt;::edge_descriptor e;
    G g;
  };
</PRE>


<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>)<br>
<A HREF="http://www.boost.org/people/liequan_lee.htm">Lie-Quan Lee</A>, Indiana University (<A HREF="mailto:llee@cs.indiana.edu">llee@cs.indiana.edu</A>)<br>
<A HREF="http://www.osl.iu.edu/~lums">Andrew Lumsdaine</A>,
Indiana University (<A
HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>

</BODY>
</HTML>

Summary ✨

This HTML code outputs a documentation page for the IncidenceGraph concept in Boost, a C++ library. It provides an interface for efficient access to out-edges of each vertex in a graph, including associated types, valid expressions, and complexity guarantees. The page includes notes on implementation requirements and constraints for algorithms using this concept.

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