A generating-function approach to modelling complex contagion on clustered networks with multi-type branching processes

TL;DR

This paper extends multi-type branching process models to clustered networks, enabling detailed analysis of cascade distributions in complex contagion processes on real-world and synthetic networks.

Contribution

It introduces a new inversion method for probability generating functions and applies it to model cascade distributions in clustered networks, advancing beyond average behavior analysis.

Findings

Accurate distribution predictions for cascade sizes in clustered networks

Validation of theoretical models with numerical simulations

Application to both synthetic and real-world networks

Abstract

Understanding cascading processes on complex network topologies is paramount for modelling how diseases, information, fake news and other media spread. In this paper, we extend the multi-type branching process method developed in Keating et al., 2022, which relies on homogenous network properties, to a more general class of clustered networks. Using a model of socially-inspired complex contagion we obtain results, not just for the average behaviour of the cascades but for full distributions of the cascade properties. We introduce a new method for the inversion of probability generating functions to recover their underlying probability distributions; this derivation naturally extends to higher dimensions. This inversion technique is used along with the multi-type branching process to obtain univariate and bivariate distributions of cascade properties. Finally, using clique cover methods, we apply the methodology to synthetic and real-world networks and compare the theoretical distribution of cascade sizes with the results of extensive numerical simulations.