Random Processes with High Variance Produce Scale Free Networks

TL;DR

This paper proposes an alternative model for scale-free networks based on high-variance random processes, challenging the traditional growth and preferential attachment explanations.

Contribution

It introduces a new randomly stopped linking model inspired by a generalized CLT, emphasizing variance as the key factor in scale-free network formation.

Findings

High variance in linking processes leads to scale-free degree distributions.

Classical models have low variance, unlike real-world networks.

Variance, not growth or preferential attachment, explains scale-free properties.

Abstract

Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms leading to these networks and are incorporated in the Barab\'asi-Albert (BA) model. We provide an alternative model using a randomly stopped linking process inspired by a generalized Central Limit Theorem (CLT) for geometric distributions with widely varying parameters. The common characteristic of both the BA model and our randomly stopped linking model is the mixture of widely varying geometric distributions, suggesting the critical characteristic of scale free networks is high variance, not growth or preferential attachment. The limitation of classical random graph models is low variance in parameters, while scale free networks are the natural, expected result of real-world variance.