Generation of arbitrarily two-point-correlated random networks

Abstract

Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point degree-degree correlated undirected random networks without self-edges or multiple edges among vertices. With the goal to systematically investigate the influence of two-point correlations, we furthermore develop a formalism to construct a joint degree distribution P(j,k) , which allows one to fix an arbitrary degree distribution P(k) and an arbitrary average nearest neighbor function k_{nn}(k) simultaneously. Using the presented algorithm, this formalism is demonstrated with scale-free networks [P(k) proportional, variantk;{-gamma}] and empirical complex networks [ P(k) taken from network] as examples. Finally, we generalize our algorithm to annealed networks which allows networks to be represented in a mean-field-like manner.