Critical behavior of rumor propagation on random networks of cliques

We disclose a critical phenomenon induced by structural properties of the contact pattern in a stylized model of rumor propagation over a population of agents. The contact pattern is given by a random network of cliques, formed by fully interconnected groups of nodes of identical size with randomly distributed connections between groups. As demonstrated numerically using finite-size scaling analysis, the process exhibits a critical transition between a regime where the rumor remains confined to a negligible part of the population and a regime where it attains a finite portion of the system. We determine the critical point and the critical exponent of the transition for different clique sizes. The phenomenon is analogous to that observed for the same kind of process in Watts-Strogatz small-world networks, and is likely due to the combination of large clustering and short mean geodesic distances that also characterizes random networks of cliques.