The Robustness of Graph k-Shell Structure Under Adversarial Attacks

The
${k}$
-shell decomposition plays an important role in unveiling the structural properties of a network. However, there arises concern about the robustness of the
${k}$
-shell structure when networks suffer from adversarial attacks. Here, we introduce and formalize the problem of
${k}$
-shell attack and develop an efficient strategy to attack the
${k}$
-shell structure by rewiring a small number of links. In particular, we propose a Simulated Annealing (SA) based
${k}$
-shell attack method and testify it on five real-world networks. The extensive experiments validate that the
${k}$
-shell structure of a network is robust under random perturbation, but it is quite vulnerable under adversarial attack. Therefore, it could be an interesting topic to improve the robustness of various network properties against adversarial attack in the future.