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<Head>
<Title>Bidirectional</Title>
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<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&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>bidirectional_graph_tag</tt>.
</td>
</tr>

<TR>
<TD><pre>boost::graph_traits&lt;G&gt;::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&lt;in_edge_iterator, in_edge_iterator&gt;</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 &lt;class G&gt;
  struct BidirectionalGraphConcept
  {
    typedef typename boost::graph_traits&lt;G&gt;::in_edge_iterator
      in_edge_iterator;
    void constraints() {
      BOOST_CONCEPT_ASSERT(( IncidenceGraphConcept&lt;G&gt; ));
      BOOST_CONCEPT_ASSERT(( MultiPassInputIteratorConcept&lt;in_edge_iterator&gt; ));

      p = in_edges(v, g);
      n = in_degree(v, g);
      n = degree(v, g);
      e = *p.first;
      const_constraints(g);
    }
    void const_constraints(const G&amp; g) {
      p = in_edges(v, g);
      n = in_degree(v, g);
      n = degree(v, g);
      e = *p.first;
    }
    std::pair&lt;in_edge_iterator, in_edge_iterator&gt; p;
    typename boost::graph_traits&lt;G&gt;::vertex_descriptor v;
    typename boost::graph_traits&lt;G&gt;::edge_descriptor e;
    typename boost::graph_traits&lt;G&gt;::degree_size_type n;
    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>)
</TD></TR></TABLE>

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