Properties of highly clustered networks

TL;DR

This paper introduces an exactly solvable network model with adjustable degree distribution and clustering, revealing how increased clustering impacts network connectivity and epidemic dynamics, including epidemic size and threshold.

Contribution

It provides a novel exactly solvable model linking clustering with network properties and epidemic outcomes, advancing understanding of complex network behavior.

Findings

Higher clustering reduces the size of the giant component.

Clustering decreases epidemic size and threshold.

Epidemics saturate faster in highly clustered networks.

Abstract

We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the giant component of the network. We also study SIR-type epidemic processes within the model and find that clustering decreases the size of epidemics, but also decreases the epidemic threshold, making it easier for diseases to spread. In addition, clustering causes epidemics to saturate sooner, meaning that they infect a near-maximal fraction of the network for quite low transmission rates.