Comparative Network Robustness Evaluation of Link Attacks

  • Clara PizzutiEmail author
  • Annalisa Socievole
  • Piet Van Mieghem
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)


Existing link attack strategies in networks differ in the importance or robustness metric, that quantifies the effect of a link removal upon the network’s vulnerability. In this paper, we investigate the role of the effective resistance matrix in the removal of links on a graph and compare this removal strategy with other state-of-the-art attack strategies over synthetic networks. The results of the analysis show that the effective resistance and the link-betweenness strategies behave similarly and are more harmful than the degree based strategies when evaluating robustness with different performance measures.


Complex networks Robustness Graph resistance 


  1. 1.
    Abbas, W., Egerstedt, M.: Robust graph topologies for networked systems. In: 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems, pp. 85–90 (2012)CrossRefGoogle Scholar
  2. 2.
    Albert, R., Jeong, H., Barabási, A.L.: Error and attack tolerance of complex networks. Nature 406, 378–381 (2000)CrossRefGoogle Scholar
  3. 3.
    Cetinay, H., Devriendt, K., Van Mieghem, P.: Nodal vulnerability to targeted attacks in power grids. Appl. Netw. Sci. 3, 34 (2018)CrossRefGoogle Scholar
  4. 4.
    Chandra, A.K., Raghavan, P., Ruzzo, W.L., Smolensky, R.: The electrical resistance of a graph captures its commute and cover times. In: Proceedings of the Twenty-First Annual ACM Symposium on Theory of Computing, STOC ’89, pp. 574–586. ACM, New York (1989)Google Scholar
  5. 5.
    Devriendt, K., Van Mieghem, P.: The simplex geometry of graphs. J. Complex Netw. 7(4), 469–490 (2019)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Doyle, P.G., Snell, J.L.: Random Walks and Electric Networks. The Mathematical Association of America, Washington, D.C. (1984)zbMATHGoogle Scholar
  7. 7.
    Ellens, W., Spieksm, F.M., Van Mieghem, P., Jamakovic, A., Kooij, R.E.: Effective graph resistance. Linear Algebra Appl. 435(10), 2491–2506 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Erdös, P., Renyi, A.: On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci 5, 17–61 (1960)Google Scholar
  9. 9.
    Fiedler, M.: Algebraic connectivity of graphs. Czech. Math. J. 23(2), 298–305 (1973)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Frank, H., Frish, I.: Analysis and design of survivable networks. IEEE Trans. Commun. Technol. 8(5), 501–519 (1970)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ghosh, A., Boyd, S., Saberi, A.: Minimizing effective resistance of a graph. SIAM Rev. 50(1), 37–66 (2008)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Holme, P., Kim, B.J., Yoon, C.N., Han, S.K.: Attack vulnerability of complex networks. Phys. Rev. E 65(5), 056109 (2002)CrossRefGoogle Scholar
  13. 13.
    Klein, D.J., Randić, M.: Resistance distance. J. Math. Chem. 12, 81–95 (1993)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Li, X., Shi, Y.T.: A survey on the Randić index. Commun. Math. Comput. Chem. 59(1), 127–156 (2008)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Ranjan, G., Zhang, Z.L., Boley, D.: Incremental computation of pseudo-inverse of Laplacian. In: Combinatorial Optimization and Applications, COCOA, pp. 730–749. Springer, Switzerland (2014)CrossRefGoogle Scholar
  16. 16.
    Van Mieghem, P.: Graph Spectra for Complex Networks. Cambridge University Press, Cambridge (2011)zbMATHGoogle Scholar
  17. 17.
    Van Mieghem, P., Devriendt, K., Cetinay, H.: Pseudo-inverse of the Laplacian and best spreader node in a network. Phys. Rev. E 96(3), 032311 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Van Mieghem, P., Doerr, C., Wang, H., Martin Hernandez, J., Hutchison, D., Karaliopoulos, M., Kooij, R.E.: A framework for computing topological network robustness. Delft University of Technology, Report 20101218 (2010). (
  19. 19.
    Van Mieghem, P.: Graph eigenvectors, fundamental weights and centrality metrics for nodes in networks. arXiv preprint arXiv:1401.4580 (2014)
  20. 20.
    Wang, X., Pournaras, E., Kooij, R.E., Van Mieghem, P.: Improving robustness of complex networks via the effective graph resistance. Eur. Phys. J. B 87(9), 221 (2014)CrossRefGoogle Scholar
  21. 21.
    Wu, J., Barahona, M., Tan, Y.J., Deng, H.Z.: Spectral measure of structural robustness in complex networks. Trans. Sys. Man Cyber. Part A 41(6), 1244–1252 (2011)CrossRefGoogle Scholar
  22. 22.
    Zeng, A., Liu, W.: Enhancing network robustness for malicious attacks. Phys. Rev. E 85(6), 066130 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Clara Pizzuti
    • 1
    Email author
  • Annalisa Socievole
    • 1
  • Piet Van Mieghem
    • 2
  1. 1.National Research Council of Italy (CNR), Institute for High Performance Computing and Networking (ICAR)RendeItaly
  2. 2.Faculty of Electrical Engineering, Mathematics and Computer ScienceDelft University of TechnologyDelftThe Netherlands

Personalised recommendations