# `bandwidth`

      (1)
      template <typename Graph>
      typename graph_traits<Graph>::vertices_size_type
      bandwidth(const Graph& g)

      (2)
      template <typename Graph, typename VertexIndexMap>
      typename graph_traits<Graph>::vertices_size_type
      bandwidth(const Graph& g, VertexIndexMap index_map)

The bandwidth 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 G=(V,E) are each assigned an index from zero to |V| - 1 given by index[v], then the bandwidth of G is
B(G) = max { |index[u] - index[v]| | (u,v) in E }

### Defined in

`boost/graph/bandwidth.hpp`

# `ith_bandwidth`

      (1)
      template <typename Graph>
      typename graph_traits<Graph>::vertices_size_type
      ith_bandwidth(typename graph_traits<Graph>::vertex_descriptor i,
    		const Graph& g)

      (2)
      template <typename Graph, typename VertexIndexMap>
      typename graph_traits<Graph>::vertices_size_type
      ith_bandwidth(typename graph_traits<Graph>::vertex_descriptor i,
    		const Graph& g,
    		VertexIndexMap index)

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

### Defined in

`boost/graph/bandwidth.hpp`

Copyright © 2000-2001 | Jeremy Siek, Indiana University (jsiek@osl.iu.edu)