Generation of arbitrarily two-point correlated random networks

TL;DR

This paper introduces an efficient algorithm for generating two-point correlated random networks with customizable degree distributions and correlations, applicable to scale-free and empirical networks, and extends to annealed networks.

Contribution

It presents a novel algorithm for creating correlated random networks with fixed degree and correlation properties, including a formalism for joint degree distributions.

Findings

Algorithm accurately generates correlated networks without self- or multiple-edges.

Demonstrates the method on scale-free and empirical networks.

Extends the approach to annealed networks for mean-field analysis.

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 correlated undirected random networks without self- 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 to fix an arbitrary degree distribution $P(k)$ and an arbitrary average nearest neighbor function $\knn(k)$ simultaneously. Using the presented algorithm, this formalism is demonstrated with scale-free networks ($P(k) \propto k^{-\gamma}$) 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.