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Identifying Vulnerable Nodes to Cascading Failures: Optimization-Based Approach

  • Richard J. LaEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)

Abstract

A key challenge to ensuring robustness of complex systems is to correctly identify component systems, which we simply call nodes, that are more likely to trigger cascading failures. A recent approach takes advantage of the relationship between the cascading failure probability and the non-backtracking centrality of nodes when the Perron-Frobenius (P-F) eigenvalue of the associated non-backtracking matrix is close to one. However, this assumption is not guaranteed to hold in practice. Motivated by this observation, we propose a new approach that does not require the P-F eigenvalue to be close to one, and demonstrate that it offers good accuracy and outperforms the non-backtracking centrality-based approach for both synthetic and real networks.

Keywords

Cascading failures Optimization Robustness 

Notes

Acknowledgment

This work was supported in part by contract 70NANB16H024 from National Institute of Standards and Technology (NIST).

References

  1. 1.
    Stanford Large Network Dataset Collection. http://snap.stanford.edu/data/
  2. 2.
    Albert, R., Jeong, H., Barabasi, A.L.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000)CrossRefGoogle Scholar
  3. 3.
    Bollobas, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 24(1), 5–34 (2004)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  5. 5.
    Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1994)zbMATHGoogle Scholar
  6. 6.
    La, R.J.: Identifying vulnerable nodes to cascading failures: centrality to the rescue. In: Proceedings of the 7th International Conference on Complex Networks and Their Applications (2018)Google Scholar
  7. 7.
    La, R.J.: Influence of clustering on cascading failures in interdependent systems. IEEE Trans. Netw. Sci. Eng. 6(3), 351–363 (2019)CrossRefGoogle Scholar
  8. 8.
    Martin, T., Zhang, X., Newman, M.E.J.: Localization and centrality in networks. Phys. Rev. E 90(5), 052808 (2014)CrossRefGoogle Scholar
  9. 9.
    Molloy, M., Reed, B.: A critical point for random graphs with a given degree sequence. Random Struct. Algorithms 6(2–3), 161–180 (1995)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Molloy, M., Reed, B.: The size of the largest component of a random graph on a fixed degree sequence. Comb. Probab. Comput. 7(3), 295–305 (1998)CrossRefGoogle Scholar
  11. 11.
    Newman, M.E.J.: Assortative mixing in networks. Phys. Rev. Lett. 89(20), 208701 (2002)CrossRefGoogle Scholar
  12. 12.
    Newman, M.E.J.: Mixing patterns in networks. Phys. Rev. E 67(2), 026126 (2003)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yang, Y., Nishikawa, T., Motter, A.E.: Small vulnerable sets determine large network cascades in power grids. Science 358(6365), eaan3184 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of MarylandCollege ParkUSA

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