Robustness of One-to-Many Interdependent Higher-order Networks Against Cascading Failures

2025-09-28

AI Summary

Real-world interdependent networks often exhibit intra-layer higher-order interactions and inter-layer one-to-many dependencies; however, existing studies either neglect higher-order structures or assume oversimplified one-to-one inter-layer couplings, lacking a unified modeling framework. To address this, we propose a coupled hypergraph model that jointly captures intra-layer higher-order interactions and inter-layer one-to-many dependencies, establishing a unified theoretical framework encompassing both full and partial dependency scenarios. Leveraging percolation theory, we develop a cascade failure analysis method and validate it through simulations on synthetic and real-world networks, characterizing phase transitions and connectivity evolution. Our results reveal a non-monotonic regulatory mechanism whereby higher-order structure and coupling strength jointly govern system robustness. Theoretical predictions are empirically confirmed across diverse network topologies, significantly advancing the understanding of failure propagation in complex interdependent systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Reasoning under Uncertainty: Graphical Models
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Social Networks and Social Media: Social media analysis through the lenses of networks
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex one-to-many dependency relationship. Meanwhile, there may also be higher-order interactions between multiple nodes within a layer, which increases the connectivity within the layer. However, existing research on one-to-many interdependence often neglects intra-layer higher-order structures and lacks a unified theoretical framework for inter-layer dependencies. Moreover, current research on interdependent higher-order networks typically assumes idealized one-to-one inter-layer dependencies, which does not reflect the complexity of real-world systems. These limitations hinder a comprehensive understanding of how such networks withstand failures. Therefore, this paper investigates the robustness of one-to-many interdependent higher-order networks under random attacks. Depending on whether node survival requires at least one dependency edge or multiple dependency edges, we propose four inter-layer interdependency conditions and analyze the network's robustness after cascading failures induced by random attacks. Using percolation theory, we establish a unified theoretical framework that reveals how higher-order interaction structures within intra-layers and inter-layer coupling parameters affect network reliability and system resilience. Additionally, we extend our study to partially interdependent hypergraphs. We validate our theoretical analysis on both synthetic and real-data-based interdependent hypergraphs, offering insights into the optimization of network design for enhanced reliability.

Problem

• Analyzing robustness of one-to-many interdependent networks against cascading failures
• Establishing unified framework for higher-order intra-layer and inter-layer dependencies
• Investigating how network structures affect reliability under random attacks

Innovation

• Proposed four inter-layer interdependency conditions for robustness
• Established unified theoretical framework using percolation theory
• Extended study to partially interdependent hypergraphs for validation