Skip to main content

Attack induced cascading breakdown in complex networks

Abstract

The possibility that a complex network can be brought down by attack on a single or very few nodes through the process of cascading failures is of significant concern. In this paper, we investigate cascading failures in complex networks and uncover a phase-transition phenomenon in terms of the key parameter characterizing the node capacity. For parameter value below the phase-transition point, cascading failures can cause the network to disintegrate almost entirely. Then we show how to design networks of finite capacity that are safe against cascading breakdown. Our theory yields estimates for the maximally achievable network integrity via controlled removal of a small set of low-degree nodes.

References

  1. A.-L. Barabási e R. Albert, Emergence of scaling in random networks,Science, 286:509–512, 1999.

    Article  MathSciNet  Google Scholar 

  2. R. Albert e A.-L. Barabási, Statistical mechanics of complex networks,Rev. Mod. Phys., 74:47–97, 2002.

    Article  Google Scholar 

  3. Newman, M. E. J., The structure and function of complex networks,SIAM Review, 45(2):167–256, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Albert, H. Jeong, and A.-L. Barabási, Diameter of the World-Wide Web,Nature, 401:130–131, 1999.

    Article  Google Scholar 

  5. G. Siganos, M. Faloutsos, P. Faloutsos, and C. Faloutsos, Power Laws and the AS-Level Internet Topology,IEEE/ACM Trans. Networking, 11:514–524, 2003.

    Article  Google Scholar 

  6. X. F., Wang and G.-R. Chen, Complex Networks: Small-World, Scale-Free and Beyond,IEEE Circuit and System Magzine, First Quarter:6–20, 2003.

  7. K. Sun, Complex networks theory: A new method of research in power grid, 2005IEEE/PES Transmission and Distribution Conference and Exhibition: Asia and Pacific, pages 1–6, 2005.

  8. A. E. Motter and Y.-C. Lai, Cascade-based attacks on complex networks,Phys. Rev. E, 66:065102(1–4), 2002.

    Google Scholar 

  9. M. E. J. Newman, The structure of scientific collaboration networks,Proc. Natl. Acad. Sci. U.S.A., 98:404–409, 2001.

    Article  MATH  Google Scholar 

  10. P. Erdös e A. Rényi, On the strength of connectedness of a random graph,Acta Math. Acad. Sci. Hungar., 12:261–267, 1961.

    Article  MATH  MathSciNet  Google Scholar 

  11. D. J. Watts e S. H. Strogatz, Collective dynamics of “small-world” networks,Nature, 393:440–442, 1998.

    Article  Google Scholar 

  12. M. Kurant and P. Thiran, Layered complex networks,Phys. Rev. Letts., 96:138701(1–4), 2006.

    Google Scholar 

  13. K. Bömer, J. T. Maru and R. L. Goldstone, The simultaneous evolution of author and paper networks,Proc. Natl. Acad. Sci. U.S.A., 101:5266–5273, 2004.

    Article  Google Scholar 

  14. C. L. DeMarco, A phase transition model for cascading network failure,IEEE Control Systems Magazine, 21:40–51, 2001.

    Article  Google Scholar 

  15. B. A. Carreras, V. E., Lynch, I. Dobson, and D. E. Newman, Critical points and transitions in an electric power transmission model for cascading failure blackouts,Chaos, 12:985–994, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  16. M. A. Rios, D. S. Kirschen, D. Jayaweera, D. P. Nedic, and R. N. Allan, Value of Security: Modeling Time-Dependent Phenomena and Weather Conditions,IEEE Trans. Power Systems, 17:543–548, 2002.

    Article  Google Scholar 

  17. M. Ni, J. D. McCalley, V. Vittal, and T. Tayyib, Online Risk-Based Security Assessment,IEEE Trans. Power Systems, 18:258–265, 2003.

    Article  Google Scholar 

  18. B. A. Carreras, D. E. Newman, I. Dobson, and A. B. Poole, Evidence for Self-Organized Criticality in a Time Series of Electric Power System Blackouts,IEEE Trans. Circuit and Systems — I, 51:1733–1740, 2004.

    Article  Google Scholar 

  19. I. Dobson, B. A. Carreras, D. E. Newman, A loading-dependent model of probabilistic cascading failure,Probability in the Engineering and Informational Sciences, 19:15–32, 2005.

    MATH  MathSciNet  Google Scholar 

  20. A. Arenas, A. Díaz-Guilera, e R. Guimerà, Communication in networks with hierarchical branching,Phys. Rev. Letts., 86(14), pp. 3196–3199, 2001.

    Article  Google Scholar 

  21. R. Albert, H. Jeong and A.-L. Barabási, Error and attack tolerance of complex networks”,Nature (London) 406:378–382, 2000.

    Article  Google Scholar 

  22. R. Cohen, K. Erez, D. b-Avraham, and S. Havlin, Resilience of the Internet to Random Breakdowns,Phys. Rev. Letts., 85:4626–4628, 2000.

    Article  Google Scholar 

  23. R. Cohen, K. Erez, D. b-Avraham, and S. Havlin, Breakdown of the Internet under Intentional Attack,Phys. Rev. Letts., 86:3682–3685, 2001.

    Article  Google Scholar 

  24. D. J., Watts, A simple model of global cascades on random networks,Proc. Natl. Acad. Sci. U.S.A., 99:5766–5771, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  25. P. Holme, Congestion and centrality in traffic flow on complex networks,Advances in Complex Systems, 6:163–176, 2003.

    Article  MATH  Google Scholar 

  26. L. Zhao, K. Park, and Y.-C. Lai, Attack vulnerability of scale-free networks due to cascading breakdown,Phys. Rev. E, 70:035101(1–4), 2004.

    Article  Google Scholar 

  27. A. E. Motter, Cascade Control and Defense in Complex Networks,Phys. Rev. Letts., 93:098701(1–4), 2004.

    Google Scholar 

  28. L. Zhao, K.-H. Park, e Y.-C. Lai, Tolerance of scale-free networks against attack-induced cascades,Phys. Rev. E, 72:025104(1–4), 2005.

    Article  Google Scholar 

  29. M. E. J. Newman, Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality,Phys. Rev. E, 64:016132(1–7), 2001.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Zhao, L., Park, K., Lai, YC. et al. Attack induced cascading breakdown in complex networks. J Braz Comp Soc 13, 67–76 (2007). https://doi.org/10.1007/BF03192546

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03192546

Keywords

  • complex networks
  • scale-free networks
  • power grids
  • computer networks
  • degree distribution
  • cascading
  • breakdown