Clustering determines the dynamics of complex contagions in multiplex networks

TL;DR

This paper provides a mathematical framework for understanding how clustering and multiplex network structures influence the spread of complex contagions, revealing phase transitions and the importance of considering link types.

Contribution

It introduces a generalized model for complex contagions in clustered multiplex networks, accounting for content-dependent thresholds and multiple link types, extending previous approaches.

Findings

Increasing clustering generally reduces global cascade probability and size.

There exists a threshold average degree where clustering begins to promote contagion.

Ignoring link types in multiplex networks can lead to inaccurate contagion predictions.

Abstract

We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other spreading process implying a threshold dynamics, in setups of interconnected networks with significant clustering. The contagion is assumed to be general enough to account for a content-dependent linear threshold model, where each link type has a different weight (for spreading influence) that may depend on the content (e.g., product, rumor, political view) that is being spread. Using the generating functions formalism, we determine the conditions, probability, and expected size of the emergent global cascades. This analysis provides a generalization of previous approaches and is specially useful in problems related to spreading and percolation. The results present non trivial dependencies between the clustering coefficient of the networks and its average degree. In particular, several phase transitions are shown to occur depending on these descriptors. Generally speaking, our findings reveal that increasing clustering decreases the probability of having global cascades and their size, however this tendency changes with the average degree. There exists a certain average degree from which on clustering favours the probability and size of the contagion. By comparing the dynamics of complex contagions over multiplex networks and their monoplex projections, we demonstrate that ignoring link types and aggregating network layers may lead to inaccurate conclusions about contagion dynamics, particularly when the correlation of degrees between layers is high.