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.

💡 Research Summary

This paper addresses a critical gap in the study of network robustness under localized attacks (LAs). While prior work has extensively examined how networks fragment when damage spreads outward from a single point, it has largely assumed that the seed node is chosen uniformly at random and has focused on average robustness measures. The authors argue that the structural position of the seed node can dramatically alter the severity of an LA, and they introduce a novel node‑level metric, the Localized Attack Vulnerability Index (LAVI), to quantify this effect.

LAVI is defined for a given seed node i in an undirected graph G = (V, E). First, a breadth‑first search computes the shortest‑path distance d_i(v) from i to every other node, grouping nodes into concentric shells S_d of equal distance. The attack proceeds shell by shell, removing all nodes in S_0 (the seed), then S_1, and so on, until the desired number of nodes has been eliminated. Within each shell two removal orders are considered: (a) a random permutation (modeling stochastic local damage) and (b) a descending‑degree order (modeling an adversary that first disables the most connected nodes). As nodes are removed, the cumulative number of half‑links severed up to step k is C_k = Σ_{j=1}^k deg_G(v_j), where v_j is the j‑th node in the removal sequence. The LAVI value for seed i is then

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