Discovering Vulnerabilities in Heterogeneous Interconnected Systems

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11260)


The identification of vulnerabilities in critical infrastructure networks, especially in the event of an intentional attack, is a fundamental task to comprehend the behavior of such networks and to implement protection strategies with the purpose of raising their robustness and resilience. In this work, we characterize the network vulnerability with respect to an attacker that aims at destroying subsystems in a way that guarantees, at the same time, the maximization of the damage dealt and the minimization of the effort spent in the attack. To this end, we follow a topological approach and we characterize each subsystem as a node, while dependencies are modeled in terms of a directed edges. Moreover, each node is characterized by an intrinsic degree of importance and by the effort required to attack it. Such a differentiation of the nodes allows to capture the heterogeneous essence of the different subsystems in a Critical Infrastructure network. In this setting, we model the damage dealt by the attacker in terms of a weighted version of the pairwise connectivity, where the weights correspond to the nodes’ importance; moreover we model the overall attack effort in terms of the effort required to attack the nodes. The proposed methodology aims at computing a criticality metric based on a multi-objective optimization formulation. Specifically, the criticality metric represents the frequency with which a given subsystem is attacked in the hypothetical attack plans belonging to the Pareto front. Finally, we complement our methodology by introducing upper and lower bounds on the overall attacker’s effort, in order to specialize the proposed methodology to different classes of attackers. The feasibility of the proposed solution is tested on the US Airline Network as in 1997.


Critical infrastructure Connectivity measure Critical nodes 


  1. 1.
    Arulselvan, A., Commander, C.W., Elefteriadou, L., Pardalos, P.M.: Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36(7), 2193–2200 (2009)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Faramondi, L., et al: Network structural vulnerability: a multiobjective attacker perspective. IEEE Trans. Syst. Man Cybern. Syst. (99), 1–14 (2018)Google Scholar
  3. 3.
    Fiol, M.A., Garriga, E.: Number of walks and degree powers in a graph. Discrete Math. 309(8), 2613–2614 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Censor, Y.: Pareto optimality in multiobjective problems. Appl. Math. Optim. 4(1), 41–59 (1977)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Rossi, R., Ahmed, N.: The network data repository with interactive graph analytics and visualization. In: AAAI, vol. 15, pp. 4292–4293, January 2015Google Scholar
  6. 6.
    Arulselvan, A., Commander, C.W., Elefteriadou, L., Pardalos, P.M.: Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36(7), 2193–2200 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Shen, Y., Nguyen, N.P., Xuan, Y., Thai, M.T.: On the discovery of critical links and nodes for assessing network vulnerability. IEEE/ACM Trans. Networking (TON) 21(3), 963–973 (2013)CrossRefGoogle Scholar
  8. 8.
    Di Summa, M., Grosso, A., Locatelli, M.: Branch and cut algorithms for detecting critical nodes in undirected graphs. Comput. Optim. Appl. 53(3), 649–680 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Sun, F., Shayman, M.A.: On pairwise connectivity of wireless multihop networks. Int. J. Secur. Netw. 2(1–2), 37–49 (2007)CrossRefGoogle Scholar
  10. 10.
    Lalou, M., Tahraoui, M.A., Kheddouci, H.: The critical node detection problem in networks: a survey. Comput. Sci. Rev. 28, 92–117 (2018)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Faramondi, L., Oliva, G., Setola, R., Pascucci, F., Esposito Amideo, A., Scaparra, M.P.: Performance analysis of single and multi-objective approaches for the critical node detection problem. In: Sforza, A., Sterle, C. (eds.) Optimization and Decision Science: Methodologies and Applications, ODS 2017. Springer Proceedings in Mathematics & Statistics, vol. 217, pp. 315–324. Springer, Cham (2017).
  12. 12.
    Lu, Z.M., Li, X.F.: Attack vulnerability of network controllability. PloS one 11(9), e0162289 (2016)CrossRefGoogle Scholar
  13. 13.
    Dorigo, M., Birattari, M.: Ant colony optimization. In: Sammut, C., Webb, G.I. (eds.) Encyclopedia of Machine Learning, pp. 36–39. Springer, Boston (2011). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Campus Bio-Medico UniversityRomeItaly
  2. 2.University Roma TreRomeItaly

Personalised recommendations