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

# GraphDistanceMatrix

 GraphDistanceMatrix[g] gives the matrix of distances between vertices for the graph g. GraphDistanceMatrixgives the matrix of distances between vertices of maximal distance d in the graph g.
• 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 .
• The vertices are assumed to be in the order given by VertexList[g].
Give the matrix of distances for a complete graph:
Give the matrix of distances for a complete graph:
 Out[1]=
 Out[2]//MatrixForm=
 Scope   (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:
 Options   (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 used for directed graphs including negative edge weights:
can be faster than the method on sparse graphs:
 Applications   (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:
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:
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:
New in 8