We study the robustness of scale-free networks against attack with grey information, which means that one can obtain the information of all nodes, but the attack information may be imprecise. The known random failure and intentional attack are two extreme scenarios of our robustness model. By introducing two attack information parameters α and β, where α governs negative deviation of one's observation while β governs positive deviation of the observation, we demonstrate tunable equilibrium of degree, which accommodates abundant observation mechanisms. We derive the exact solution of the critical removal fraction of nodes for the disintegration of networks. Increasing the precision of attack information can reduce the robustness of scale-free networks. Our main finding is that the attack robustness of scale-free networks is more sensitive to the parameter α than to the parameter β. Moreover, if α and β for a node having degree k are proportional to k~γ, where -∞<γ<+∞, we find that increasing γ enhances the robustness of scale-free networks when γ> 0 and that the network seems rather fragile for any γ<0. Our model provides insight into the investigation of attack and defence strategies of complex networks.
展开▼
