Mean-field theory for scale-free random networks

TL;DR

This paper develops a mean-field theoretical framework to analyze the growth and connectivity distribution of scale-free random networks, providing analytical predictions for their scaling properties.

Contribution

It introduces a mean-field approach to predict the dynamics and degree distribution of scale-free networks, including variants lacking power-law scaling.

Findings

Derived analytical expressions for connectivity distribution

Predicted scaling exponents for scale-free networks

Extended method to variants without power-law scaling

Abstract

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.