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| <Head> |
| <Title>IncidenceGraph</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> |
| |
| <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<G>::edge_descriptor</tt>.</TD> |
| </TR> |
| |
| <TR> |
| <TD><tt>u, v</tt></TD> |
| <TD>Are objects 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>incidence_graph_tag</tt>. |
| </td> |
| </tr> |
| |
| |
| <TR> |
| <TD> |
| <pre>boost::graph_traits<G>::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<G>::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, 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, 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, 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<out_edge_iterator, out_edge_iterator></TT> |
| </TD> |
| </tr> |
| |
| <tr> |
| <TD><TT>out_degree(u, 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 <class G> |
| struct IncidenceGraphConcept |
| { |
| typedef typename boost::graph_traits<G>::out_edge_iterator out_edge_iterator; |
| void constraints() { |
| function_requires< GraphConcept<G> >(); |
| function_requires< MultiPassInputIteratorConcept<out_edge_iterator> >(); |
| |
| p = out_edges(u, g); |
| e = *p.first; |
| u = source(e, g); |
| v = target(e, g); |
| } |
| void const_constraints(const G& g) { |
| p = out_edges(u, g); |
| e = *p.first; |
| u = source(e, g); |
| v = target(e, g); |
| } |
| std::pair<out_edge_iterator, out_edge_iterator> p; |
| typename boost::graph_traits<G>::vertex_descriptor u, 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>)<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> |
| |
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