Generation of degree-correlated networks using copulas

TL;DR

This paper introduces a novel method using copulas to generate random networks with customizable degree distributions and correlations, aiding the study of how topology influences dynamical processes.

Contribution

It presents a new formalism and algorithm for creating degree-correlated networks with arbitrary degree distributions using copulas, validated numerically.

Findings

Accurately generates networks with specified degree correlations.

Provides a systematic way to create null models for network analysis.

Enables exploration of topology-dynamics relationships.

Abstract

Dynamical processes on complex networks such as information propagation, innovation diffusion, cascading failures or epidemic spreading are highly affected by their underlying topologies as characterized by, for instance, degree-degree correlations. Here, we introduce the concept of copulas in order to artificially generate random networks with an arbitrary degree distribution and a rich a priori degree-degree correlation (or `association') structure. The accuracy of the proposed formalism and corresponding algorithm is numerically confirmed. The derived network ensembles can be systematically deployed as proper null models, in order to unfold the complex interplay between the topology of real networks and the dynamics on top of them.