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<HTML>
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-- 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)
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<Head>
<Title>Bidirectional</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:BidirectionalGraph"></A>
BidirectionalGraph
</H2>
<P>
The BidirectionalGraph concept refines <a
href="./IncidenceGraph.html">IncidenceGraph</a> and adds the
requirement for efficient access to the in-edges of each vertex. This
concept is separated from <a
href="./IncidenceGraph.html">IncidenceGraph</a> because for directed
graphs efficient access to in-edges typically requires more storage
space, and many algorithms do not require access to in-edges. For
undirected graphs this is not an issue, since the <TT>in_edges()</TT>
and <TT>out_edges()</TT> functions are the same, they both return the
edges incident to the vertex.
<H3>Refinement of</H3>
<a href="./IncidenceGraph.html">IncidenceGraph</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>bidirectional_graph_tag</tt>.
</td>
</tr>
<TR>
<TD><pre>boost::graph_traits<G>::in_edge_iterator</pre>
An in-edge iterator for a vertex <i>v</i> provides access to the
in-edges of <i>v</i>. As such, the value type of an in-edge iterator
is the edge descriptor type of its graph. An in-edge 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:in-edges"><TT>in_edges(v, g)</TT></a></TD>
<TD>
Returns an iterator-range providing access to the
in-edges (for directed graphs) or incident edges (for
undirected graphs) of vertex <TT>v</TT> in graph <TT>g</TT>.
For both directed and undirected graphs, the target of
an out-edge is required to be vertex <tt>v</tt> and the
source is required to be a vertex that is adjacent to <tt>v</tt>.
<br>
Return type: <TT>std::pair<in_edge_iterator, in_edge_iterator></TT>
</TD>
</TR>
<tr>
<TD><TT>in_degree(v, g)</TT></TD>
<TD>
Returns the number of in-edges (for directed graphs) or the
number of incident edges (for undirected graphs) of vertex <TT>v</TT>
in graph <TT>g</TT>.<br>
Return type: <TT>degree_size_type</TT>
</TD>
</TR>
<tr>
<TD><TT>degree(v, g)</TT></TD>
<TD>Returns the number of in-edges plus out-edges (for directed graphs) or the
number of incident edges (for undirected graphs) of vertex <TT>v</TT>
in graph <TT>g</TT>.<br>
Return type: <TT>degree_size_type</TT>
</TD>
</TR>
</Table>
<H3>Models</H3>
<ul>
<li><a href="./adjacency_list.html"><tt>adjacency_list</tt></a> with <tt>Directed=bidirectionalS</tt></li>
<li><a href="./adjacency_list.html"><tt>adjacency_list</tt></a> with <tt>Directed=undirectedS</tt></li>
</ul>
<H3>Complexity guarantees</H3>
The <TT>in_edges()</TT> function is required to be constant time. The
<tt>in_degree()</tt> and <tt>degree()</tt> functions must be linear in
the number of in-edges (for directed graphs) or incident edges (for
undirected graphs).
<H3>See Also</H3>
<a href="./graph_concepts.html">Graph concepts</a>
<H3>Concept Checking Class</H3>
<PRE>
template <class G>
struct BidirectionalGraphConcept
{
typedef typename boost::graph_traits<G>::in_edge_iterator
in_edge_iterator;
void constraints() {
function_requires< IncidenceGraphConcept<G> >();
function_requires< MultiPassInputIteratorConcept<in_edge_iterator> >();
p = in_edges(v, g);
e = *p.first;
const_constraints(g);
}
void const_constraints(const G& g) {
p = in_edges(v, g);
e = *p.first;
}
std::pair<in_edge_iterator, in_edge_iterator> p;
typename boost::graph_traits<G>::vertex_descriptor v;
typename boost::graph_traits<G>::edge_descriptor e;
G g;
};
</PRE>
<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>)
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