The average or mean of the distances between pairs of vertices in a connected graph is a natural measure of the compactness of that graph. Using graphs to represent shapes, or corridor arrangements, we arrive, through a limiting process, at a concept for mean distance in shapes. This paper gives...

In this paper we study the mean of the distances in a directed graph and compare the results obtained with the corresponding results for undirected graphs. We derive a formula which enables the computation of best possible upper and lower bounds for the mean of the distances in a directed graph....