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Legacy Documentation

Mathematica 8 (2010)

This is documentation for Mathematica 8, which was
based on an earlier version of Wolfram Language.

View current documentation (Version 14.3)

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BUILT-IN MATHEMATICA SYMBOL

GraphDistance AdjacencyMatrix GraphPower GraphRadius GraphDiameter GraphCenter GraphPeriphery

GraphDistanceMatrix

GraphDistanceMatrix [g]
gives the matrix of distances between vertices for the graph g.

GraphDistanceMatrix
gives the matrix of distances between vertices of maximal distance d in the graph g.

GraphDistanceMatrix returns a SparseArray object or an ordinary matrix.

The entries of the distance matrix give the shortest distance from vertex to vertex .

The diagonal entries of the distance matrix are always zero.

The entry is Infinity () if there is no path from vertex to vertex .

In GraphDistanceMatrix , an entry will be Infinity if there is no path from vertex to vertex in d steps or less.

The vertices are assumed to be in the order given by VertexList [g].

(1)

Give the matrix of distances for a complete graph:

Out[1]=

Out[2]//MatrixForm=

(5)

GraphDistanceMatrix works with undirected graphs:

Directed graphs:

Weighted graphs:

Extract a single matrix column for a graph of modest size:

Using GraphDistance to compute the same result takes more time:

Works with large graphs:

When just a single column is needed and the graph is large, using GraphDistance is faster:

(6)

The method is automatically chosen depending on input:

method will use the weight 1 for every edge:

can be used for graphs with positive edge weights only:

can be used for directed graphs including negative edge weights:

can be faster than the method on sparse graphs:

(2)

Find the vertex eccentricity, taking the entire graph into account:

For the strongly connected graph, the result is in agreement with VertexEccentricity :

Find the vertex eccentricity of every vertex in a connected graph:

Check the result:

(5)

Rows and columns of the distance matrix follow the order given by VertexList :

The diagonal entries of the distance matrix are always zero:

The distance matrix can be found using GraphDistance :

In a connected graph, the VertexEccentricity can be obtained from the distance matrix:

The distance between two vertices belonging to different connected components is Infinity :

(2)

The matrix indices may not have the expected correspondence to vertices:

The distance from to is not at the expected matrix position:

The reason is that vertices are not in the expected order:

Solve the problem by listing vertices explicitly when calling functions such as Graph :

Now the distance is found at the expected position:

is not a valid Method option:

Use , , or the default choice of Method instead:

(1)

GraphDistance bullet AdjacencyMatrix bullet GraphPower bullet GraphRadius bullet GraphDiameter bullet GraphCenter bullet GraphPeriphery

Graph Measures & Metrics

Paths and Cycles

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