Cascades on Constrained Multiplex Networks

TL;DR

This paper analyzes cascade dynamics on directed multiplex networks, introducing constrained multiplex models to study how node participation patterns influence cascade size, probability, and phase transitions.

Contribution

It presents a detailed analysis of cascades on multiplex networks and introduces constrained multiplex models to control node activity patterns.

Findings

Node participation patterns significantly affect cascade phase transitions.

Constrained multiplex models can induce specific activity patterns.

Cascade size and probability depend on network layer interactions.

Abstract

We consider a version of the Watts cascade model on directed multiplex configuration model networks, and present a detailed analysis of the cascade size, single-seed cascade probability and cascade condition. We then introduce a smaller class of network models that we call constrained multiplex networks, which allows us to induce patterns in the node activity, i.e. in the participation of nodes on different layers. We find that the choice of induced patterns affects the phase transitions of the cascade model in a variety of ways.