Degree correlations in graphs with clique clustering

Abstract

Correlations among the degrees of nodes in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for nodes in the giant component of clustered configuration model networks which are comprised of higher-order subgraphs. We use this model to investigate, in detail, the organisation among nearest-neighbour subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbour in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.