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  <HTML>
  <!--
       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)
    -->
  <Head>
  <Title>Boost Graph Library: Bandwidth</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="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 a 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 a 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>
  
  </BODY>
  </HTML>