A multi-type branching process method for modelling complex contagion on clustered networks

TL;DR

This paper introduces a multi-type branching process approach to model complex contagion dynamics on clustered networks, enabling efficient analysis of cascade sizes and critical behavior.

Contribution

It develops a novel discrete-time model using clique motifs to approximate contagion on clustered networks, improving analytical and simulation efficiency.

Findings

Accurate analytical calculation of cascade sizes

Identification of critical contagion thresholds

Faster Monte Carlo simulations compared to network-based methods

Abstract

Complex contagion adoption dynamics are characterised by a node being more likely to adopt after multiple network neighbours have adopted. We show how to construct multi-type branching processes to approximate complex contagion adoption dynamics on networks with clique-based clustering. This involves tracking the evolution of a cascade via different classes of clique motifs that account for the different numbers of active, inactive and removed nodes. This discrete-time model assumes that active nodes become immediately and certainly removed in the next time step. This description allows for extensive Monte Carlo simulations (which are faster than network-based simulations), accurate analytical calculation of cascade sizes, determination of critical behaviour and other quantities of interest.