Advancing vulnerability assessment in critical infrastructure systems through higher-order cycles and community structures

Ensuring the stability of Critical Infrastructure Systems (CIS) is paramount for modern societies. Represented as complex networks, these systems require robust disintegration strategies to identify critical vulnerabilities and prevent systemic failures. However, existing algorithms often oversimplify interactions, assume rarely observed fully connected higher-order structures, and overlook strong community formations and indirect connections. To overcome these limitations, this study develops the Higher-Order Cycle Disintegration Framework, leveraging higher-order cycles and community structures to capture both direct and indirect interactions. Extensive experiments on synthetic and empirical networks confirm that the strategy developed within the framework dramatically outperforms existing state-of-the-art algorithms, particularly demonstrating superior early-stage disintegration capability. Specifically, it achieves improvements of up to 63.41 % and 23.83 % in R and fc respectively, with average of 40.16 % and 16.87 % across 12 empirical networks. Unlike conventional methods, which often display a rich-club effect with tightly clustered critical nodes, our algorithm identifies a more dispersed distribution of vulnerabilities. Furthermore, Kendall's Tau analysis reveals consistently low correlations (below 0.52) with baselines, underscoring the distinctiveness and enhanced discriminative capability of our framework. These findings provide valuable insights into vulnerability assessment and the development of targeted protection strategies, advancing the long-term reliability and robustness of CIS.