Generation of uncorrelated random scale-free networks

TL;DR

This paper introduces a new model for generating uncorrelated scale-free networks that lack multiple and self-connections, serving as null models for analyzing dynamical processes on complex networks.

Contribution

It presents a modified configuration model with a degree restriction to produce uncorrelated scale-free networks without multiple or self-connections.

Findings

The model successfully generates scale-free networks with no degree correlations.

Numerical checks confirm absence of two- and three-vertex correlations.

The networks are suitable as null models for dynamical process analysis.

Abstract

Uncorrelated random scale-free networks are useful null models to check the accuracy an the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable to generate random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two and three vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree $k$, respectively.