Cascades on Constrained Multiplex Networks

2025-05-30

AI Summary

This work investigates the cascade dynamics of Watts-type models on constrained multilayer networks, focusing on cascade size distribution, single-seed triggering probability, and phase transition conditions. To address the limitation of existing models in capturing heterogeneous cross-layer node activity, we propose a class of constrained multiplex configuration models that explicitly characterize and systematically tune interlayer participation patterns—such as the number of active layers and layer-specific connection preferences. Leveraging random graph theory and generating function techniques, we derive analytical expressions for the cascade size distribution and exact phase transition thresholds. Results demonstrate that node-level activity patterns enable targeted control of network robustness and propagation criticality: strengthening interlayer coupling lowers the critical threshold, whereas sparse interlayer participation enhances robustness. This study establishes a novel mechanistic framework and rigorous theoretical criteria for cascade control in multilayer networks.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Multiagent Systems under Uncertainty
• Game Theory and Economic Paradigms: Cooperative Game Theory

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Analyzes cascade dynamics in directed multiplex networks
• Introduces constrained networks to model node activity patterns
• Examines how patterns influence cascade phase transitions

Innovation

• Watts cascade model on multiplex networks
• Constrained multiplex networks induce patterns
• Patterns affect cascade phase transitions