Threshold cascade dynamics on signed random networks

TL;DR

This paper investigates how mixed positive and negative interactions in signed networks influence cascade dynamics, revealing that negative links suppress widespread cascades and introduce heterogeneity in activation patterns.

Contribution

It introduces a model for threshold cascades on signed networks and uncovers the role of negative interactions in shaping cascade behavior and variability.

Findings

Negative interactions suppress global cascades.

Negative links induce heterogeneity in activation patterns.

Negative interactions contribute to variability in cascading dynamics.

Abstract

Relationships between individuals in a social network, genes in biological systems, and spins in magnetic systems often reflect a mixture of positive (friendly) and negative (antagonistic) interactions. However, most studies of complex networks have focused on networks consisting of solely positive interactions. Here, we study threshold cascades on signed networks composed of both positive and negative connections, focusing on when a pair of nodes connected by a negative link can only be activated exclusively to each other. We found that the negative interactions not only suppress global cascades, but also induce the heterogeneity in activation patterns manifesting from single-node to network levels. Our results suggest that negative interactions may be an important source of the variability in cascading dynamics.