The average connectivity of a digraph Original Research Article

In this paper we consider the concept of the average connectivity of a digraph D defined to be the average, over all ordered pairs (u,v) of vertices of D, of the maximum number of internally disjoint directed u–v paths. We determine sharp bounds on the average connectivity of orientations of graphs in terms of the number of vertices and edges and for tournaments and orientations of trees in terms of their orders. An efficient procedure for finding the maximum average connectivity among all orientations of a tree is described and it is shown that this maximum is always greater than 29 and at most 12.