Cascades on clique-based graphs

TL;DR

This paper introduces an analytical method for predicting cascade sizes and conditions for global cascades on highly-clustered random graphs, with applications to percolation, Watts's model, and social network in-group bias effects.

Contribution

It provides a novel analytical framework for analyzing cascades on clustered graphs, extending previous models to include in-group bias effects.

Findings

Derived conditions for global cascades.

Applicable to percolation and Watts's model.

Analyzed effects of in-group bias on social networks.

Abstract

We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly-clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.