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Topological persistence pinpoints higher-order network vulnerabilities.

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We developed a new method to identify critical nodes in complex networks by analyzing higher-order topological features. This approach enhances network analysis and robustness assessment, outperforming traditional methods.

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Area of Science:

  • Network Science
  • Complex Systems Analysis
  • Topological Data Analysis

Background:

  • Conventional graph models struggle with multi-node interactions and multi-scale connectivity in complex systems.
  • Understanding structural influence and robustness in networks with higher-order dependencies is challenging.

Purpose of the Study:

  • To introduce a novel metric, the persistent structural influence indicator, for quantifying node influence in complex networks.
  • To capture latent higher-order topological features and localized structural sensitivities.

Main Methods:

  • Integration of persistent homology with local geometric perturbation analysis.
  • Extraction of multi-scale topological features and node influence quantification.
  • Evaluation on synthetic and real-world networks against baseline methods.

Main Results:

  • The proposed model accurately identifies structurally critical nodes, leading to faster network disintegration.
  • Achieved a reduction in giant component size to 0.12 (vs. 0.23 for degree-based attacks) after 20% node removal.
  • Improved correlation with ground-truth spreading dynamics by up to 25.1% compared to existing measures.

Conclusions:

  • The persistent structural influence indicator provides a robust and generalizable framework for complex network analysis.
  • The method offers improved interpretability, computational tractability, and structural fidelity without domain-specific priors.
  • This approach enhances the understanding of structural robustness and influence in networked systems.