Random Key Graphs Can They be Small Worlds?

Random key graphs form a class of random graphs naturally associated with the random key predistribution scheme of Eschenauer and Gligor. We compute the clustering coefficients of random key graphs, and then compare them with Erdos-Renyi graphs in the many node regime when the expected average degrees are asymptotically equivalent. On the parameter range of practical relevance in wireless sensor networks, random key graphs are shown to be much more clustered than the corresponding Erdos-Renyi graphs. We also explore the suitability of random key graphs as small worlds in the sense of Watts and Strogatz.