Scale-Free Cascading Failures: Generalized Approach for All Simple, Connected Graphs

• 成果类型: Article; Early Access
• 署名作者: Janicka, Agnieszka; Sloothaak, Fiona; Vlasiou, Maria
• 署名单位: Eindhoven University of Technology; University of Twente
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0465
• 发表日期: 2026-06-08
• 关键词: cascading failures; heavy-tailed failures; overload failures; principle of a single big jump; scale-free failures; self-organized criticality; FREE NETWORKS; ATTACK VULNERABILITY; city size; MODEL

摘要

Cascading failures, wherein the failure of one component triggers subsequent failures in complex interconnected systems, pose a significant risk of disruptions and emerge across various domains. Understanding and mitigating the risk of such failures is crucial to minimize their impact and ensure the resilience of these systems. In multiple applications, the failure processes exhibit scale-free behavior in terms of their total failure sizes. Various models have been developed to explain the origin of this scale-free behavior. A recent study proposed a novel hypothesis, suggesting that scale-free failure sizes might be inherited from scale-free input characteristics in power networks. However, the scope of this study excluded certain network topologies. Here, motivated by power networks, we strengthen this hypothesis by generalizing to a broader range of graph topologies where this behavior is manifested. Our approach yields a universal theorem applicable to all simple, connected graphs, revealing that when a cascade leads to network disconnections, the total cascade size exhibits a scale-free tail inherited from the input characteristics. We do so by characterizing cascade sequences of failures in the asymptotic regime.