Vulnerability analysis of interdependent network via integer programming approaches

  • Shanshan Hou
  • Andres Garrido
  • Neng FanEmail author
Original Paper


The interdependent network can be applied to model two or more infrastructure systems with mutual reliance. The failure of elements in one system may lead to failure of dependent elements in other systems, and this may happen recursively leading to a cascade of failures. In this paper, integer programming models are proposed to identify the most vulnerable network elements (nodes and edges), whose removal can maximally destroy the interdependent network, with minimum functional components survived after the cascading failure process. Numerical experiments are performed on several interdependent networks consisting of power grid and control communication network, to validate the proposed models and to identify the vulnerable network elements.


Interdependent network Vulnerability analysis Cascading failure Connected component 



  1. 1.
    Sforna, M., Delfanti, M.: Overview of the events and causes of the 2003 Italian blackout. Power Syst. Conf. Expos. 2006, 301–308 (2007)Google Scholar
  2. 2.
    Buldyrev, S., Parshani, R., Paul, G., Stanley, H., Havlin, S.: Catastrophic cascade of failures in interdependent networks. Nature 464, 1025–1028 (2010)CrossRefGoogle Scholar
  3. 3.
    Stokes-Draut, J., Taptich, M., Kavvada, O., Horvath, A.: Evaluating the electricity intensity of evolving water supply mixes: the case of California’s water network. Environ. Res. Lett. 12, 114005 (2017)CrossRefGoogle Scholar
  4. 4.
    Zhang, Y., Yang, N., Lall, U.: Modeling and simulation of the vulnerability of interdependent power-water infrastructure networks to cascading failures. J. Syst. Sci. Syst. Eng. 25(1), 102–118 (2016)CrossRefGoogle Scholar
  5. 5.
    Parshani, R., Rozenblat, C., Ietri, D., Ducruet, C., Havlin, S.: Inter-similarity between coupled networks. Europhys. Lett. 92, 68002–68006 (2010)CrossRefGoogle Scholar
  6. 6.
    U.S. Department of Transportation: An objectives- and performance-based approach for improving the design, operations, and maintenance of traffic signal systems. Traffic Signal Management Plans (2015)Google Scholar
  7. 7.
    Yang, Y., Motter, A.: Cascading failures as continuous phase–space transitions. Phys. Rev. Lett. 119, 248302 (2017)CrossRefGoogle Scholar
  8. 8.
    Duenas-Osorio, L., Vemuru, S.: Cascading failures in complex infrastructure systems. Struct. Saf. 31(2), 157–167 (2009)CrossRefGoogle Scholar
  9. 9.
    Wang, Z., Scaglione, A., Thomas, R.: Electrical centrality measures for electric power grid vulnerability analysis. In: The 49th IEEE Conference on Decision and Control, pp. 5792–5797 (2010)Google Scholar
  10. 10.
    Jenelius, E., Petersen, T., Mattsson, L.: Importance and exposure in road network vulnerability analysis. Transp. Res. A Policy Pract. 40(7), 537–560 (2005)CrossRefGoogle Scholar
  11. 11.
    Abedin, M., Nessa, S., Al-Shaer, E., Khan, L.: Vulnerability analysis for evaluating quality of protection of security policies. In: The 2nd ACM Workshop on Quality of Protection, pp. 49–52 (2006)Google Scholar
  12. 12.
    Wang, S., Hong, L., Ouyang, M., Zhang, J., Chen, X.: Vulnerability analysis of interdependent infrastructure systems under edge attack strategies. Saf. Sci. 51(1), 328–337 (2013)CrossRefGoogle Scholar
  13. 13.
    Sen, A., Mazumder, A., Banerjee, J., Das, A., Compton, R.: Identification of k most vulnerable nodes in multi-layered using a new model of interdependency. In: IEEE Conference on Computer Communications Workshops, pp. 831–836 (2014)Google Scholar
  14. 14.
    Nguyen, D., Shen, Y., Thai, M.: Detecting critical nodes in interdependent power networks for vulnerability assessment. IEEE Trans. Smart Grid 4(1), 151–158 (2013)CrossRefGoogle Scholar
  15. 15.
    Li, Y., Ma, D., Zhang, H., Sun, Q.: Critical node identification of power systems based on controllability of complex networks. Appl. Sci. 5(3), 622–636 (2015)CrossRefGoogle Scholar
  16. 16.
    Veremyev, A., Boginski, V., Pasiliao, E.: Exact identification of critical nodes in sparse networks via new compact formulations. Optim. Lett. 8(4), 1245–1259 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Veremyev, A., Sorokin, A., Boginski, V., Pasiliao, E.L.: Minimum vertex cover problem for coupled interdependent networks with cascading failures. Eur. J. Oper. Res. 232(3), 499–511 (2014)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Nguyen, H., Sharkey, T.: A computational approach to determine damage in infrastructure networks from outage reports. Optim. Lett. 11(4), 753–770 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Zhang, J., Modiano, E.: Connectivity in interdependent networks. arXiv:1709.03034 (2017)
  20. 20.
    Yu, Z., Huang, S., Ma, Z., Chen, G.: Identification of critical lines in power grid based on electric betweenness entropy. In: The 2015 IEEE PES Asia-Pacific Power and Energy Engineering Conference (2016)Google Scholar
  21. 21.
    Sun, X., Zhang, T., Zhang, B.: Identification of critical lines in power grid based on active power flow betweenness. In: The 5th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, pp. 1283–1287 (2016)Google Scholar
  22. 22.
    Liu, M., Zhao, L., Huang, L., Zhang, X., Deng, C., Long, Z.: Identification of critical lines in power system based on optimal load shedding. Energy Power Eng. 9, 261–269 (2017)CrossRefGoogle Scholar
  23. 23.
    Qiang, Q., Nagurney, A.: A unified network performance measure with importance identification and the ranking of network components. Optim. Lett. 2(1), 127–142 (2008)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Gao, J., Buldyrev, S.V., Stanley, H., Havlin, S.: Networks formed from interdependent networks. Nat. Phys. 8, 40–48 (2012)CrossRefGoogle Scholar
  25. 25.
    Parandehgheibi, M., Modiano, E., Hay, D.: Mitigating cascading failures in interdependent power grids and communication networks. In: 2014 IEEE International Conference on Smart Grid Communications, pp. 242–247 (2014)Google Scholar
  26. 26.
    Parandehgheibi, M., Modiano, E.: Robustness of interdependent networks: the case of communication networks and the power grid. In: IEEE Global Communications Conference, pp. 2164–2169 (2013)Google Scholar
  27. 27.
    Buldyrev, S., Shere, N., Cwilich, G.: Interdependent networks with identical degree of mutually dependent nodes. Phys. Rev. Lett. 83, 016112 (2011)MathSciNetGoogle Scholar
  28. 28.
    Bianconi, G., Dorogovtsev, S., Mendes, J.: Mutually connected component of networks of networks with replica nodes. Phys. Rev. Lett. 91, 012804 (2015)Google Scholar
  29. 29.
    Hwang, S., Choi, S., Lee, D., Kahng, B.: Efficient algorithm to compute mutually connected components in interdependent networks. Phys. Rev. Lett. 91, 022814 (2015)Google Scholar
  30. 30.
    Fan, N., Watson, J.: On integer programming models for the multi-channel PMU placement problem and their solution. Energy Syst. 6(1), 1–19 (2015)CrossRefGoogle Scholar
  31. 31.
    Huang, Z., Zheng, Q.P., Pasiliao, E.L., Simmons, D.: Exact algorithms on reliable routing problems under uncertain topology using aggregation techniques for exponentially many scenarios. Ann. Oper. Res. 249(1), 141–162 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Systems and Industrial EngineeringUniversity of ArizonaTucsonUSA
  2. 2.Departamento de Ingenieria de SistemasUniversidad de La FronteraTemucoChile

Personalised recommendations