Robustness of interdependent networks under targeted attack

When an initial failure of nodes occurs in interdependent networks, a cascade of failure between the networks occurs. Earlier studies focused on random initial failures. Here we develop a theoretical framework for understanding the robustness of interdependent networks under targeted attack on high or low degree nodes. We find that interdependent networks are significantly more vulnerable under targeted attack, i.e. the percolation threshold $p_c$ increases compared to random attack. We also find that when the highly connected nodes are protected and have lower probability to fail, in contrast to single scale free (SF) networks where the percolation threshold $p_c=0$, coupled SF networks are significantly more vulnerable with $p_c$ significantly higher than zero. These results imply that interdependent networks are difficult to defend by strategies such as protecting the high degree nodes that have been found useful to significantly improve robustness of single networks.