203 lines
5.5 KiB
HTML
203 lines
5.5 KiB
HTML
<HTML>
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<!--
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Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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-->
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<Head>
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<Title>IncidenceGraph</Title>
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<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
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ALINK="#ff0000">
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<IMG SRC="../../../boost.png"
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ALT="C++ Boost" width="277" height="86">
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<BR Clear>
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<H1><A NAME="concept:IncidenceGraph"></A>
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IncidenceGraph
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</H1>
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The IncidenceGraph concept provides an interface for
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efficient access to the out-edges of each vertex in the graph.
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<H3>Refinement of</H3>
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<a href="./Graph.html">Graph</a>
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<h3>Notation</h3>
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<Table>
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<TR>
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<TD><tt>G</tt></TD>
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<TD>A type that is a model of IncidenceGraph.</TD>
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</TR>
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<TR>
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<TD><tt>g</tt></TD>
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<TD>An object of type <tt>G</tt>.</TD>
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</TR>
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<TR>
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<TD><tt>e</tt></TD>
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<TD>An object of type <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
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</TR>
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<TR>
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<TD><tt>u, v</tt></TD>
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<TD>Are objects of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
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</TR>
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</table>
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<H3>Associated Types</H3>
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<Table border>
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<tr>
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<td><tt>boost::graph_traits<G>::traversal_category</tt><br><br>
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This tag type must be convertible to <tt>incidence_graph_tag</tt>.
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</td>
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</tr>
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<TR>
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<TD>
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<pre>boost::graph_traits<G>::out_edge_iterator</pre>
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An out-edge iterator for a vertex <i>v</i> provides access to the
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out-edges of the vertex. As such, the value type of an out-edge
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iterator is the edge descriptor type of its graph. An out-edge
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iterator must meet the requirements of <a
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href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>.
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</TD>
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</TR>
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<TR>
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<TD><pre>boost::graph_traits<G>::degree_size_type</pre>
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The unsigned integral type used for representing the number
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out-edges or incident edges of a vertex.
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</TD>
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</TR>
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</table>
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<h3>Valid Expressions</h3>
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<Table border>
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<tr>
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<td><a name="sec:source"><TT>source(e, g)</TT></a></TD>
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<TD>Returns the vertex descriptor for <i>u</i> of the edge <i>(u,v)</i> represented by <TT>e</TT>.<br>
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Return type: <TT>vertex_descriptor</TT>
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</TD>
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</TR>
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<tr>
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<td><a name="sec:target"><TT>target(e, g)</TT></a></TD>
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<TD>Returns the vertex descriptor for <i>v</i> of the edge <i>(u,v)</i> represented by <TT>e</TT>.<br>
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Return type: <TT>vertex_descriptor</TT>
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</td></tr>
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<tr>
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<td><a name="sec:out-edges"><TT>out_edges(u, g)</TT></a></TD>
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<TD>Returns an iterator-range providing access to the out-edges (for
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directed graphs) or incident edges (for undirected graphs) of vertex
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<TT>u</TT> in graph <TT>g</TT>. The source vertex of an edge obtained
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via an out edge iterator is guaranteed (for both directed and
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undirected graphs) to be the vertex <tt>u</tt> used in the call to
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<tt>out_edges(u, g)</tt> and the target vertex must be a vertex
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adjacent to <tt>u</tt>.<a href="#1">[1]</a>
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<br>
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Return type: <TT>std::pair<out_edge_iterator, out_edge_iterator></TT>
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</TD>
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</tr>
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<tr>
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<TD><TT>out_degree(u, g)</TT></TD>
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<TD>Returns the number of out-edges (for directed graphs) or the
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number of incident edges (for undirected graphs) of vertex <TT>u</TT>
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in graph <TT>g</TT>.<br>
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Return type: <TT>degree_size_type</TT>
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</TD>
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</TR>
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</TABLE>
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<P>
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<H3>Complexity guarantees</H3>
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<P>
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The <TT>source()</TT>, <TT>target()</TT>, and <TT>out_edges()</TT>
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functions must all be constant time. The <tt>out_degree()</tt>
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function must be linear in the number of out-edges.
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<P>
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<H3>See Also</H3>
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<a href="./graph_concepts.html">Graph concepts</a>
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<H3>Notes</H3>
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<a name="1">[1]</a> For undirected graphs, the edge <tt>(u,v)</tt> is
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the same as edge <tt>(v,u)</tt>, so without some extra guarantee an
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implementation would be free use any ordering for the pair of vertices
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in an out-edge. For example, if you call <tt>out_edges(u, g)</tt>, and
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<tt>v</tt> is one of the vertices adjacent to <tt>u</tt>, then the
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implementation would be free to return <tt>(v,u)</tt> as an out-edge
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which would be non-intuitive and cause trouble for algorithms.
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Therefore, the extra requirement is added that the out-edge connecting
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<tt>u</tt> and <tt>v</tt> must be given as <tt>(u,v)</tt> and not
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<tt>(v,u)</tt>.
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<H3>Concept Checking Class</H3>
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<PRE>
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template <class G>
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struct IncidenceGraphConcept
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{
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typedef typename boost::graph_traits<G>::out_edge_iterator out_edge_iterator;
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void constraints() {
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BOOST_CONCEPT_ASSERT(( GraphConcept<G> ));
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BOOST_CONCEPT_ASSERT(( MultiPassInputIteratorConcept<out_edge_iterator> ));
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p = out_edges(u, g);
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e = *p.first;
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u = source(e, g);
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v = target(e, g);
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}
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void const_constraints(const G& g) {
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p = out_edges(u, g);
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e = *p.first;
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u = source(e, g);
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v = target(e, g);
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}
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std::pair<out_edge_iterator, out_edge_iterator> p;
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typename boost::graph_traits<G>::vertex_descriptor u, v;
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typename boost::graph_traits<G>::edge_descriptor e;
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G g;
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};
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</PRE>
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<br>
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<HR>
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<TABLE>
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<TR valign=top>
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<TD nowrap>Copyright © 2000-2001</TD><TD>
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<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>,
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Indiana University (<A
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HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)<br>
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<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>
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<A HREF="https://homes.cs.washington.edu/~al75">Andrew Lumsdaine</A>,
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Indiana University (<A
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HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
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</TD></TR></TABLE>
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