Scale Free Networks from Self-Organisation

TL;DR

This paper demonstrates how scale-free networks can naturally form through a self-organising process using local random walk-based attachment, applicable to various models and producing weighted networks with power-law distributions.

Contribution

It introduces a local, self-organising growth mechanism for scale-free networks using random walks for attachment, extending to weighted networks with power-law distributions.

Findings

Scale-free degree distributions emerge from local random walk attachment.

Mean-field equations accurately model the network growth.

Weighted networks with power-law distributions are achievable.

Abstract

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of parameters. The growth mechanism is based on using local graph information only, so this is a process of self-organisation. The standard mean-field equations are an excellent approximation for network growth using these rules. We discuss the effects of finite size on the degree distribution, and compare analytical results to simulated networks. Finally, we generalise the random walk algorithm to produce weighted networks with power-law distributions of both weight and degree.