The "Cameo Principle" and the Origin of Scale-Free Graphs in Social Networks

TL;DR

This paper introduces a simple edge formation rule inspired by social behavior that results in scale-free degree distributions and high clustering in social network models, providing insights into their structural properties.

Contribution

It presents a novel edge generation rule based on an inverse like mass action principle and a local search principle to explain scale-free and highly clustered social networks.

Findings

Degree distribution follows a power law under weak assumptions

The local search principle increases clustering coefficient

Model captures key features of real social networks

Abstract

We formulate a simple edge generation rule based on an inverse like mass action principle for random graphs over a structured vertex set. We show that under very weak assumptions on the structure generating distribution we obtain a scale free distribution for the degree. We furthermore introduce and study a "my friends are your friends" local search principle which makes the clustering coefficient large.