Mann Peter, Smith V Anne, Mitchell John B O, Dobson Simon
School of Computer Science, University of St Andrews, St Andrews, Fife KY16 9SX, United Kingdom; School of Chemistry, University of St Andrews, St Andrews, Fife KY16 9ST, United Kingdom; and School of Biology, University of St Andrews, St Andrews, Fife KY16 9TH, United Kingdom.
Phys Rev E. 2022 Apr;105(4-1):044314. doi: 10.1103/PhysRevE.105.044314.
Correlations among the degrees of vertices in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for vertices in the giant component of clustered configuration model networks which are composed of clique subgraphs. We use this model to investigate, in detail, the organization among nearest-neighbor 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 neighbor 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.
