Robustness of Controllability for Networks Based on Edge-Attack

We study the controllability of networks in the process of cascading failures under two different attacking strategies, random and intentional attack, respectively. For the highest-load edge attack, it is found that the controllability of Erd？s-Rényi network, that with moderate average degree, is less robust, whereas the Scale-free network with moderate power-law exponent shows strong robustness of controllability under the same attack strategy. The vulnerability of controllability under random and intentional attacks behave differently with the increasing of removal fraction, especially, we find that the robustness of control has important role in cascades for large removal fraction. The simulation results show that for Scale-free networks with various power-law exponents, the network has larger scale of cascades do not mean that there will be more increments of driver nodes. Meanwhile, the number of driver nodes in cascading failures is also related to the edges amount in strongly connected components.