Graph Distance Matrix

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix  consisting of all graph distances from vertex  to vertex .

The mean of all distances in a (connected) graph is known as the graph's mean distance. The maximum value of all distance matrix elements is known as the graph diameter.

The graph distance matrix can be computed in the Wolfram Language using the built-in function GraphDistanceMatrix[g], and precomputed distance matrices for many named graphs can be obtained using GraphData[graph, "DistanceMatrix"].

REFERENCES

Devillers, J. and A. T. Balaban (Eds.). Topological Indices and Related Descriptors in QSAR and QSPR. Amsterdam, Netherlands: Gordon and Breach, pp. 76-80, 2000.