Emergence of Soft Communities from Geometric Preferential Attachment

TL;DR

This paper introduces a geometric preferential attachment model that explains the simultaneous emergence of scale-free degree distributions, clustering, and community structure in networks, validated on Internet data.

Contribution

The paper proposes the geometric preferential attachment (GPA) model as a simple mechanism to generate networks with key structural properties and explores its implications.

Findings

GPA reproduces scale-free, clustered, and community structures in networks.

Validation of GPA on Internet topology data.

Discussion of links between GPA and cosmological models.

Abstract

All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate it against the Internet. GPA gives rise to soft communities that provide a different perspective on the community structure in networks. The connections between GPA and cosmological models, including inflation, are also discussed.