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. 
Lazaros K. Gallos, Reuven Cohen, Panos Argyrakis, Armin Bunde, Shlomo   Havlin