Threshold driven contagion on weighted networks

TL;DR

This paper investigates how threshold-driven contagion processes behave on weighted networks, revealing complex effects of weight heterogeneity on cascade dynamics through analytical and numerical methods.

Contribution

It introduces a dynamical threshold model on weighted networks, analyzing the impact of weight heterogeneity on cascade timing and behavior, a novel approach in this context.

Findings

Cascade timing depends non-monotonously on weight heterogeneity.

Weight heterogeneity can accelerate or decelerate contagion dynamics.

The methodology applies broadly to binary state processes on weighted networks.

Abstract

Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of influence that neighbours have in determining a node's behaviour. Despite describing numerous cascading phenomena, such as neural firing or social contagion, threshold models have never been explicitly addressed on weighted networks. We fill this gap by studying a dynamical threshold model over synthetic and real weighted networks with numerical and analytical tools. We show that the time of cascade emergence depends non-monotonously on weight heterogeneities, which accelerate or decelerate the dynamics, and lead to non-trivial parameter spaces for various networks and weight distributions. Our methodology applies to arbitrary binary state processes and link properties, and may prove instrumental in understanding the role of edge heterogeneities in various natural and social phenomena.