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Impact of seed node position on network robustness under localized attacks

Masaki Chujyo, Shu Liu, Fujio Toriumi

TL;DR

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, capturing how local connectivity and topological position amplify the resulting damage.

Abstract

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.

Impact of seed node position on network robustness under localized attacks

TL;DR

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, capturing how local connectivity and topological position amplify the resulting damage.

Abstract

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.
Paper Structure (10 sections, 6 equations, 4 figures, 5 tables)

This paper contains 10 sections, 6 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Materials and methods
  3. Results
  4. Discussion
  5. Conclusion
  6. Acknowledgments

Figures (4)

  • Figure 1: Random-case cumulative half-link removals $C_k$ versus removal index $k$ on a $3\times3$ lattice. The blue curve shows the average over 10 runs when the seed node is placed at the center, while the red curve corresponds to placement at a corner. The shaded areas under each curve correspond to the LAVI $\mathcal{L}(i)$. A larger shaded area (center seed) indicates more rapid link removal and hence greater vulnerability.
  • Figure 2: Correlation between the robustness index $R$ and various indices characterizing the choice of the seed node in a Barabási--Albert network with $N = 100$ and $m = 2$. The panels show correlations between $R$ and $\mathcal{L}_{\text{random}}$, $\mathcal{L}_{\text{worst}}$, degree, closeness, and betweenness centrality of the seed node, as well as the mutual correlation between $\mathcal{L}_{\text{worst}}$ and $\mathcal{L}_{\text{random}}$. Spearman and Pearson correlation coefficients are reported in each panel.
  • Figure 3: Correlation between the robustness index $R$ and various indices characterizing the choice of the seed node in the power-494-bus network. The panels demonstrate correlations between $R$ and $\mathcal{L}_{\text{random}}$, $\mathcal{L}_{\text{worst}}$, degree, closeness, and betweenness centrality of the seed node, as well as the mutual correlation between $\mathcal{L}_{\text{worst}}$ and $\mathcal{L}_{\text{random}}$. Spearman and Pearson correlation coefficients are reported in each panel.
  • Figure 4: Example from the bio-diseasome network illustrating a case where LAVI fails to distinguish robustness against localized attack. (a) Cumulative half-link removals $C_k$ and (b) largest connected component fraction $s_\mathrm{LA}$ for two seed nodes with similar LAVI values. (c) Network visualization highlighting the positions of the two seeds.