Controllability of deterministic complex networks

Recently, the controllability of complex networks has attracted wide attention of researchers. The main contribution comes from Liu et al. who proposed the structural controllability as an analytical framework for making predictions regarding the control of directed networks in Nature. Since then, the controllability of many model and real networks has been deeply investigated except deterministic complex networks. In this paper, we focus on studying the controllability of deterministic complex networks. We examine six typical deterministic networks, the simulation results show that the minimum number of driver nodes grows linearly with network size. When the network size is large enough, the controllability approximates to a constant not more than 0.4, indicating that the deterministic networks are relatively easy to control. Furthermore, we investigate the characteristics of driver nodes in deterministic complex networks, finding that the driver nodes tend to avoid high degree nodes but to have high clustering coefficients.