A NOTE ON THRESHOLDS AND CONNECTIVITY IN RANDOM DIRECTED GRAPHS

Abstract

Thresholds and phase transitions have been well studied for several properties of random undirected graphs. In this article we adapt a result of Pal asti to the context of directed graphs, thereby allowing thresholds for the uniform random directed graph model D(n;M) to be used in determining thresholds for the binomial random directed graph model D(n;p). We then determine the threshold for strong connectivity in D(n;p).