Probability of diameter two for Steinhaus graphs

A Steinhaus graph is a graph with n vertices whose adjacency matrix satisfies the condition that or each . It is clear that a Steinhaus graph is determined by its first row. In ‘Almost all Steinhaus graphs have diameter two’, it is shown that almost all Steinhaus graphs have diameter two. Here the authors generalize to the case where the jth entry of the first row has probability of being 1. Under reasonable conditions it is shown that the probability measure of the set of Steinhaus graphs with diameter two approaches 1 as the number of vertices in the graph approaches infinity.