Underestimated cost of targeted attacks on complex networks

TL;DR

This paper reveals that targeted attack algorithms on complex networks are less effective when attack costs are considered and introduces an efficient edge removal strategy, HPI-Ncut, that outperforms existing methods under cost constraints.

Contribution

The paper demonstrates the inefficiency of existing targeted attack algorithms with cost considerations and proposes a novel, efficient edge removal strategy called HPI-Ncut for complex networks.

Findings

HPI-Ncut outperforms existing attack algorithms when costs are considered.

The complexity of HPI-Ncut is $O(n ext{log}^{2+ extepsilon}(n))$ on sparse networks.

Targeted attack effectiveness decreases significantly when attack costs are incorporated.

Abstract

The robustness of complex networks under targeted attacks is deeply connected to the resilience of complex systems, i.e., the ability to make appropriate responses to the attacks. In this article, we investigated the state-of-the-art targeted node attack algorithms and demonstrate that they become very inefficient when the cost of the attack is taken into consideration. In this paper, we made explicit assumption that the cost of removing a node is proportional to the number of adjacent links that are removed, i.e., higher degree nodes have higher cost. Finally, for the case when it is possible to attack links, we propose a simple and efficient edge removal strategy named Hierarchical Power Iterative Normalized cut (HPI-Ncut).The results on real and artificial networks show that the HPI-Ncut algorithm outperforms all the node removal and link removal attack algorithms when the cost of the attack is taken into consideration. In addition, we show that on sparse networks, the complexity of this hierarchical power iteration edge removal algorithm is only $O(n\log^{2+\epsilon}(n))$.