Emergence of Clustering in an Acquaintance Model without Homophily

TL;DR

This paper presents an agent-based acquaintance model demonstrating that high clustering can emerge without homophily, driven by variable transitive interactions, and shows how the model can replicate Facebook-like networks.

Contribution

The study introduces a novel acquaintance model with variable transitive interactions that explains clustering without homophily and matches real-world social network properties.

Findings

High clustering arises without homophily due to transitive interactions.

A clustering transition occurs as the transitive interaction rate varies.

The model can replicate Facebook network properties with a soft cutoff variant.

Abstract

We introduce an agent-based acquaintance model in which social links are created by processes in which there is no explicit homophily. In spite of the homogeneous nature of the social interactions, highly-clustered social networks can arise. The crucial feature of our model is that of variable transitive interactions. Namely, when an agent introduces two unconnected friends, the rate at which a connection actually occurs between them depends on the number of their mutual acquaintances. As this transitive interaction rate is varied, the social network undergoes a dramatic clustering transition. Close to the transition, the network consists of a collection of well-defined communities. As a function of time, the network can also undergo an \emph{incomplete} gelation transition, in which the gel, or giant cluster, does not constitute the entire network, even at infinite time. Some of the clustering properties of our model also arise, but in a more gradual manner, in Facebook networks. Finally, we discuss a more realistic variant of our original model in which there is a soft cutoff in the rate of transitive interactions. With this variant, one can construct network realizations that quantitatively match Facebook networks.