Scale-Free Cascading Failures: Generalized Approach for All Simple, Connected Graphs
研究级联失效中总失效规模的无标度特性，将先前只适用于部分网络拓扑的假说推广到所有简单连通图，证明级联导致断网时失效尾部由输入特征决定。适合关心级联失效机理的复杂网络研究者。
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. Funding: This work was funded by the Dutch Research Council (NWO) through Gravitation NETWORKS [Grant 024.002.003]