GraphDistanceMatrix

GraphDistanceMatrix[g]
gives a matrix in which the (i, j)

entry is the length of a shortest path in g between vertices i and j.

GraphDistanceMatrix[g, Parent]
returns a three-dimensional matrix in which the (1, i, j)

entry is the length of a shortest path from i to j and the (2, i, j)

entry is the predecessor of j in a shortest path from i to j.

To use GraphDistanceMatrix, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].

	Method	Automatic	the method used to compute the shortest path
	Weighted	True	whether edge weights are to be taken into account

Needs["GraphUtilities`"]

This defines a simple directed graph:

Out[4]//MatrixForm=

Out[5]//MatrixForm=