Structural properties of random networks of cliques

Abstract

We introduce a class of networks formed by randomly interconnected cliques, with prescribed distribution of clique sizes and density of inter-clique connections. For these random networks of cliques, we determine the conditions for existence of a giant component and provide analytical expressions for clustering coefficients and assortativity. Also, we estimate their modularity and numerically find the average distance between nodes. As an application to real systems, we successfully compare our analytical predictions with the statistical structural properties of an intra-generational kinship (sibling and spouse) network built from genealogical data. The present model provides a tool for constructing networks with controlled structure, in particular, displaying small-world features.