Network Robustness against Vertex Removal Based on Cycle-Redundancy Score

Complex infrastructure, as well as economic and social systems, are often represented as networks. The continuedoperation of most networks is threatened by random failures and targeted attacks. Therefore, quantifying andimproving network robustness remains a fundamental challenge in network science. The optimal percolation probleminvolves identifying the smallest set of nodes whose removal would most rapidly fragment the network. Recent evidencesuggests that the presence of redundant cycles significantly restricts optimal solutions. Building on this insight,we propose the Cycle-Redundancy Score (CRS), a purely local metric that estimates the number of independent cyclessupported by a node. We also design a CRS-guided attack algorithm. We tested the robustness of networks againstCRS-guided attacks on both synthetic and empirical networks. On synthetic networks, CRS dismantles networks asquickly as CoreHD. However, on empirical networks with pronounced clustering, CRS systematically underperformscompared to CoreHD and Collective-Influence attacks. A comparative analysis reveals that strong local clustering effectivelyprotects important nodes from early removal, thereby limiting the effectiveness of CRS. These results clarifythe circumstances in which cycle-based dismantling is advantageous and emphasize the necessity of attack strategiesthat can adapt to mesoscale clustering.