all-pairs shortest path matrix

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(i j)) consisting of all graph distances from vertex v_i to vertex v_j. The distance matrix for graphs was introduced by Graham and Pollak. 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 characteristic polynomial of the graph distance matrix is known as the distance polynomial.

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