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

 The AdjacencyGraph concept provides and interface for efficient access
 of the adjacent vertices to a vertex in a graph. This is quite similar
 to the <a href="./IncidenceGraph.html">IncidenceGraph</a> concept (the
 target of an out-edge is an adjacent vertex). Both concepts are
 provided because in some contexts there is only concern for the
 vertices, whereas in other contexts the edges are also important.

 <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 Graph.</TD>
 </TR>

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

 <TR>
 <TD><tt>v</tt></TD>
 <TD>An object 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>adjacency_graph_tag</tt>.
 </td>
 </tr>

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

 </table>

 <h3>Valid Expressions</h3>


 <table border>

 <tr>
 <td><a name="sec:adjacent-vertices"><TT>adjacent_vertices(v,&nbsp;g)</TT></a></TD>
 <TD>
 Returns an iterator-range providing access to the vertices adjacent to
 vertex <TT>v</TT> in graph <TT>g</TT>.<a
 href="#1">[1]</a>

 <br> Return type:
 <TT>std::pair&lt;adjacency_iterator,&nbsp;adjacency_iterator&gt;</TT>
 </TD>
 </TR>

 </table>

 <H3>Complexity guarantees</H3>

 The <TT>adjacent_vertices()</TT> function must return in constant time.

 <H3>See Also</H3>

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

 <H3>Concept Checking Class</H3>

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

       p = adjacent_vertices(v, g);
       v = *p.first;
       const_constraints(g);
     }
     void const_constraints(const G&amp; g) {
       p = adjacent_vertices(v, g);
     }
     std::pair&lt;adjacency_iterator,adjacency_iterator&gt; p;
     typename boost::graph_traits&lt;G&gt;::vertex_descriptor v;
     G g;
   };
 </PRE>

 <h3>Design Rationale</h3>

 The AdjacencyGraph concept is somewhat frivolous since <a
 href="./IncidenceGraph.html">IncidenceGraph</a> really covers the same
 functionality (and more).  The AdjacencyGraph concept exists because
 there are situations when <tt>adjacent_vertices()</tt> is more
 convenient to use than <tt>out_edges()</tt>. If you are constructing a
 graph class and do not want to put in the extra work of creating an
 adjacency iterator, have no fear. There is an adaptor class named <a
 href="./adjacency_iterator.html"> <tt>adjacency_iterator</tt></a> that
 you can use to create an adjacency iterator out of an out-edge
 iterator.

 <h3>Notes</h3>

 <a name="1">[1]</a>  The case of a
 <I>multigraph</I> (where multiple edges can connect the same two
 vertices) brings up an issue as to whether the iterators returned by
 the <TT>adjacent_vertices()</TT> function access a range that
 includes each adjacent vertex once, or whether it should match the
 behavior of the <TT>out_edges()</TT> function, and access a
 range that may include an adjacent vertex more than once. For now the
 behavior is defined to match that of <TT>out_edges()</TT>,
 though this decision may need to be reviewed in light of more
 experience with graph algorithm implementations.


 <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>

 </BODY>
 </HTML>
	<HTML>
	<!--
	Copyright (c) Jeremy Siek 2000

	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)
	-->
	<Head>
	<Title>AdjacencyGraph</Title>
	<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
	ALINK="#ff0000">
	<IMG SRC="../../../boost.png"
	ALT="C++ Boost" width="277" height="86">

	<BR Clear>



	<H2><A NAME="concept:AdjacencyGraph"></A>
	AdjacencyGraph
	</H2>

	The AdjacencyGraph concept provides and interface for efficient access
	of the adjacent vertices to a vertex in a graph. This is quite similar
	to the <a href="./IncidenceGraph.html">IncidenceGraph</a> concept (the
	target of an out-edge is an adjacent vertex). Both concepts are
	provided because in some contexts there is only concern for the
	vertices, whereas in other contexts the edges are also important.

	<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 Graph.</TD>
	</TR>

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

	<TR>
	<TD><tt>v</tt></TD>
	<TD>An object of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
	</TR>

	</table>


	<H3>Associated Types</H3>

	<Table border>

	<tr>
	<td><tt>boost::graph_traits<G>::traversal_category</tt><br><br>
	This tag type must be convertible to <tt>adjacency_graph_tag</tt>.
	</td>
	</tr>

	<TR>
	<TD><pre>boost::graph_traits<G>::adjacency_iterator</pre>
	An adjacency iterator for a vertex <i>v</i> provides access to the
	vertices adjacent to <i>v</i>. As such, the value type of an
	adjacency iterator is the vertex descriptor type of its graph. An
	adjacency iterator must meet the requirements of <a
	href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>.
	</TD>
	</TR>

	</table>

	<h3>Valid Expressions</h3>


	<table border>

	<tr>
	<td><a name="sec:adjacent-vertices"><TT>adjacent_vertices(v, g)</TT></a></TD>
	<TD>
	Returns an iterator-range providing access to the vertices adjacent to
	vertex <TT>v</TT> in graph <TT>g</TT>.<a
	href="#1">[1]</a>

	<br> Return type:
	<TT>std::pair<adjacency_iterator, adjacency_iterator></TT>
	</TD>
	</TR>

	</table>

	<H3>Complexity guarantees</H3>

	The <TT>adjacent_vertices()</TT> function must return in constant time.

	<H3>See Also</H3>

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

	<H3>Concept Checking Class</H3>

	<PRE>
	template <class G>
	struct AdjacencyGraphConcept
	{
	typedef typename boost::graph_traits<G>::adjacency_iterator
	adjacency_iterator;
	void constraints() {
	function_requires< IncidenceGraphConcept<G> >();
	function_requires< MultiPassInputIteratorConcept<adjacency_iterator> >();

	p = adjacent_vertices(v, g);
	v = *p.first;
	const_constraints(g);
	}
	void const_constraints(const G& g) {
	p = adjacent_vertices(v, g);
	}
	std::pair<adjacency_iterator,adjacency_iterator> p;
	typename boost::graph_traits<G>::vertex_descriptor v;
	G g;
	};
	</PRE>

	<h3>Design Rationale</h3>

	The AdjacencyGraph concept is somewhat frivolous since <a
	href="./IncidenceGraph.html">IncidenceGraph</a> really covers the same
	functionality (and more). The AdjacencyGraph concept exists because
	there are situations when <tt>adjacent_vertices()</tt> is more
	convenient to use than <tt>out_edges()</tt>. If you are constructing a
	graph class and do not want to put in the extra work of creating an
	adjacency iterator, have no fear. There is an adaptor class named <a
	href="./adjacency_iterator.html"> <tt>adjacency_iterator</tt></a> that
	you can use to create an adjacency iterator out of an out-edge
	iterator.

	<h3>Notes</h3>

	<a name="1">[1]</a> The case of a
	<I>multigraph</I> (where multiple edges can connect the same two
	vertices) brings up an issue as to whether the iterators returned by
	the <TT>adjacent_vertices()</TT> function access a range that
	includes each adjacent vertex once, or whether it should match the
	behavior of the <TT>out_edges()</TT> function, and access a
	range that may include an adjacent vertex more than once. For now the
	behavior is defined to match that of <TT>out_edges()</TT>,
	though this decision may need to be reviewed in light of more
	experience with graph algorithm implementations.



	<br>
	<HR>
	<TABLE>
	<TR valign=top>
	<TD nowrap>Copyright © 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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