Attacking the Core Structure of Complex Network

Abstract

The concept of <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core in complex networks plays a key role in many applications, e.g., understanding the global structure or identifying central/critical nodes, of a network. A malicious attacker with a jamming ability can exploit the vulnerability of the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core structure to attack the network and invalidate the network analysis methods, e.g., reducing the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-shell values of nodes can deceive graph algorithms, leading to the wrong decisions. In this article, we investigate the robustness of the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core structure under adversarial attacks by deleting edges, for the first time. First, we give the general definition of the targeted <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core attack, map it to the set cover problem, which is NP-hard, and further introduce a series of evaluation metrics to measure the performance of attack methods. Then, we propose the <inline-formula> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> index theoretically as the probability that the terminal node of an edge does not belong to the innermost core, which is further used to guide the design of our heuristic attack methods, namely, COREATTACK and GreedyCOREATTACK. The experiments on a variety of real-world networks demonstrate that our methods behave much better than a series of baselines, in terms of much smaller edge change rate (ECR) and false attack rate (FAR), achieving state-of-the-art attack performance. More impressively, for certain real-world networks, only deleting one edge from the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core may lead to the collapse of the innermost core, even if this core contains dozens of nodes. Such a phenomenon indicates that the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core structure could be extremely vulnerable under adversarial attacks, and its robustness, thus, should be carefully addressed to ensure the security of many graph algorithms. An open-source implementation is available at https://github.com/Yocenly/COREATTACCK.