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MinimumBandwidthOrdering

MinimumBandwidthOrdering[g]
attempts to find a vertex ordering that minimizes the bandwidth of the undirected graph g.
MinimumBandwidthOrdering[m]
attempts to find row and column permutations that minimize the bandwidth of the matrix m.
  • For a graph {V, E} with vertex ordering f, the bandwidth of the graph is defined as
  • Max{u, v}E |f[u]-f[v]|
  • For a matrix m=(aij), the bandwidth is defined as
  • Maxaij ≠ 0 |i - j|
  • For a symmetric matrix, the envelope size is defined as
  • i Max(0, Maxaij≠0 i-j)
  • which is the sum of the distance from the first element in each row to the diagonal position.
  • MinimumBandwidthOrdering treats input graphs as undirected.
  • The following options can be given:
MethodAutomaticmethod to use
RefinementMethodAutomaticmethod used to improve ordering
RecursionMethodNonerecursion method to use