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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.
更多信息
- To use
, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"]. - For a graph
with vertex ordering f, the bandwidth of the graph is defined as
Max{u, v}
E |f[u]-f[v]|. - For a matrix
, the bandwidth is defined as 
. - For a symmetric matrix, the envelope size is defined as
, which is the sum of the distance from the first element in each row to the diagonal position. 
treats input graphs as undirected.- The following options can be given:
-
Method Automatic method to use RefinementMethod Automatic method used to improve ordering RecursionMethod None recursion method to use
范例打开所有单元
基本范例 (2)
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This numbers the vertices using ordering from VertexList:
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This finds the bandwidth of the graph with the given ordering:
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This finds a vertex ordering that attempts to minimize the bandwidth:
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This renumbers the vertices using the minimum bandwidth ordering:
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This finds the bandwidth using the vertex ordering given by 
:
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This defines a rectangular matrix:
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This finds the row and column ordering that attempts to minimize the bandwidth of the matrix:
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Plots of the matrix before and after the ordering show a decrease in bandwidth:
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