Quantitatively computational controllability of complex networks

At present, people are paying more attention to exploring the ultimate goal of complex networks, that is, how to control complex networks, while the existing research on complex networks is qualitative. In this paper, a new problem of quantification controllability for complex networks is discussed. We obtain a controllability quantitative index by using the condition number of controllability matrix and control centrality of complex networks. The effect of this index is observed and discussed by a series of simulations on various types of complex networks, namely ER networks, WS small-world networks, and BA scale-free networks. The results show that the performance index can truly reflect the controllability of the complex networks.