Attack Robustness of Scale-Free Networks Based on Grey Information

We introduce an attack robustness model of scale-free networks based on 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 the intentional attack are two extreme cases of our investigation. Using the generating function method, we derive the analytical value of the critical removal fraction of nodes for the disintegration of networks, which agree with the simulation results well. We also investigate the effect of grey information on the attack robustness of scale-free networks and find that decreasing the precision of attack information can remarkably enhance the attack robustness of scale-free networks.