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<Head>
<Title>Boost Graph Library: Bandwidth</Title>
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<H1><A NAME="sec:bandwidth">
<TT>bandwidth</TT>
</H1>

<pre>
  (1)
  template &lt;typename Graph&gt;
  typename graph_traits&lt;Graph&gt;::vertices_size_type
  bandwidth(const Graph& g)

  (2)
  template &lt;typename Graph, typename VertexIndexMap&gt;
  typename graph_traits&lt;Graph&gt;::vertices_size_type
  bandwidth(const Graph& g, VertexIndexMap index_map)
</pre>

The <b><i>bandwidth</i></b> of an undirected graph is the maximum
distance between two adjacent vertices, with distance measured on a
line upon which the vertices have been placed at unit intervals. To
put it another way, if the vertices of an undirected graph
<i>G=(V,E)</i> are each assigned an index from zero to <i>|V| - 1</i>
given by <i>index[v]</i>, then the bandwidth of <i>G</i> is<br>
<br>
<i>B(G) = max { |index[u] - index[v]|&nbsp;&nbsp;| (u,v) in E }</i><br>


<h3>Defined in</h3>

<a href="../../../boost/graph/bandwidth.hpp"><tt>boost/graph/bandwidth.hpp</tt></a>


<hr>

<H1><A NAME="sec:ith-bandwidth">
<TT>ith_bandwidth</TT>
</H1>

<pre>
  (1)
  template &lt;typename Graph&gt;
  typename graph_traits&lt;Graph&gt;::vertices_size_type
  ith_bandwidth(typename graph_traits&lt;Graph&gt;::vertex_descriptor i,
		const Graph&amp; g)

  (2)
  template &lt;typename Graph, typename VertexIndexMap&gt;
  typename graph_traits&lt;Graph&gt;::vertices_size_type
  ith_bandwidth(typename graph_traits&lt;Graph&gt;::vertex_descriptor i,
		const Graph&amp; g,
		VertexIndexMap index)
</pre>

The <b><i>i-th bandwidth</i></b> a graph is the maximum distance
between the <i>i-th</i> vertex and any of its neighbors.<br>
<br>
<i>B<sub>i</sub>(G) = max { |index[i] - index[j]|&nbsp;&nbsp;| (i,j) in E }</i><br>
<br>
So the bandwidth <i>B(G)</i> can be expressed as the maximum
of the i-th bandwidths <i>B<sub>i</sub>(G)</i>.<br>
<br>
<i>B(G) = max { B<sub>i</sub>(G) &nbsp;&nbsp;| i=0...|V|-1 }</i><br>

<h3>Defined in</h3>

<a href="../../../boost/graph/bandwidth.hpp"><tt>boost/graph/bandwidth.hpp</tt></a>

<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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