Impact of seed node position on network robustness under localized attacks.

Localized attacks (LAs), where damage propagates from a single seed node to its neighbors, pose significant threats to the robustness of complex networks. Although previous studies have extensively analyzed network vulnerability under such attacks, they typically assume random seed node placement and evaluate average robustness. However, the structural position of the seed node can significantly impact the extent of damage. This study proposes the Localized Attack Vulnerability Index (LAVI), a node-level metric that quantifies the potential impact of a LA initiated at a specific node. LAVI quantifies the cumulative number of severed links during attack progression, capturing how local connectivity and topological position amplify the resulting damage. Numerical experiments on synthetic and real-world networks demonstrate that LAVI correlates more strongly with network robustness degradation than standard centrality measures, such as degree, closeness, and betweenness. Our findings highlight that classical centrality metrics fail to capture key dynamics of spatially localized failures, while LAVI provides an accurate and generalizable indicator of node vulnerability under such disruptions.