Mitigation of malicious attacks on structural balance of signed networks

The studies of malicious attacks have received great attention due to their catastrophic damages on potential functions of complex networks. An initial attack first causes the failures of the attacked elements (like nodes and edges), and then those failures may trigger a cascade of failures, resulting in the catastrophic damages on the functions (like the largest connected topology and the community structures) of the networks. Previous methods, however, mainly focus on the impacts of malicious attacks on unsigned networks, and signed networks with conflicting relationships have more complex functions than unsigned counterparts. In this paper, we study the impacts of malicious attacks on the structural balance of signed networks which reflects the potentially functional conflicts and tensions in the networks. First, we model malicious attacks as a two-level targeted one: the small-scale node attacks and large-scale cluster attacks, and analyze the failures of the structural balance of signed networks during the attacks. Second, we propose a balance robustness index to evaluate the functional resilience of signed networks to those failures. Finally, to mitigate the balance failures, we present a protection technique with six strategies to protect a small fraction of influential nodes from malicious attacks. Experiments on synthetic data and real signed networks show that their structural balance is fragile to targeted attacks, but their robustness can be improved greatly by protecting a small fraction of influential nodes.