Dependency-based targeted attacks in interdependent networks.

Abstract

Modern large engineered network systems normally work in cooperation and incorporate dependencies between their components for purposes of efficiency and regulation. Such dependencies may become a major risk since they can cause small-scale failures to propagate throughout the system. Thus, the dependent nodes could be a natural target for malicious attacks that aim to exploit these vulnerabilities. Here we consider a type of targeted attack that is based on the dependencies between the networks. We study strategies of attacks that range from dependency-first to dependency-last, where a fraction 1-p of the nodes with dependency links, or nodes without dependency links, respectively, are initially attacked. We systematically analyze, both analytically and numerically, the percolation transition of partially interdependent networks, where a fraction q of the nodes in each network are dependent on nodes in the other network. We find that for a broad range of dependency strength q, the "dependency-first" attack strategy is actually less effective, in terms of lower critical percolation threshold p_{c}, compared with random attacks of the same size. In contrast, the "dependency-last" attack strategy is more effective, i.e., higher p_{c}, compared with a random attack. This effect is explained by exploring the dynamics of the cascading failures initiated by dependency-based attacks. We show that while "dependency-first" strategy increases the short-term impact of the initial attack, in the long term the cascade slows down compared with the case of random attacks and vice versa for "dependency-last." Our results demonstrate that the effectiveness of attack strategies over a system of interdependent networks should be evaluated not only by the immediate impact but mainly by the accumulated damage during the process of cascading failures. This highlights the importance of understanding the dynamics of avalanches that may occur due to different scenarios of failures in order to design resilient critical infrastructures.