GRAPH UTILITIES 程序包 符号

# 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

## 范例范例打开所有单元关闭所有单元

### 基本范例 (2)基本范例 (2)

This defines a small graph:

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:

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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