“…R ANDOM key graphs have received significant attention recently with applications spanning key predistribution in secure wireless sensor networks (WSNs) [2], [5], [8], [9], [13], social networks [7], [18], [39], recommender systems [25], clustering and classification analysis [4], [19], cryptanalysis of hash functions [3], circuit design [33], and the modeling of epidemics [1] and "small-world" networks [36]. They belong to a larger class of random graphs known as the random intersection graphs [2]- [7], [10], [14], [33]; in fact, they are referred to as the uniform random intersection graphs by some authors [2], [3], [6], [26], [30]- [32], [43], [44].…”