Stability and topology of scale-free networks under attack and defense strategies

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree $k$ of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge on the network. We determine, for all strategies, the critical fraction $p_c$ of nodes that must be removed for disintegrating the network. We find that for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce $p_c$. At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.