New Measure for Network Controllability Robustness Based on Controllable Subspace

In this paper, we propose a new criteria to measure network controllability robustness based on generic dimension of controllable subspace given a network. Generic dimension curve and controllabillity robustness index are introduced to show network controllability robustness from different aspects. 12 different attack methods are carried out for six network models. It is found that the multiloop structure is useful to maintain network robustness under attacks. Moreover, the networks with single backbone structure are fragile under attacks. Besides, both the increase and protection of driver nodes can enhance the controllability robustness of networks.