Controllability and modularity of complex networks

Two primary properties of complex networks, controllability and modularity not only are closely related to each other, but also play an important role in understanding the networks' characteristics. In this paper, we discuss an elastic model to enhance the control of undirected networks and study the controllability of random networks with built-in gradually varied modularity as well as real-world networks to elaborate the correlation between the networks' controllability and modularity. The results show that it is easier to control the networks with stronger modularity than that of weaker modularity, and the networks with larger size communities probably need more driver nodes to control than that of smaller size communities when we fix both the number of nodes and the number of links of the networks. In addition, the robustness analysis indicates that the model enhances the resistance of networks against link failure. This work shows that the controllability of complex networks is highly associated with the networks' degree distribution as well as the networks' modularity, which gives a new insight into the understanding of controllability and modularity of complex networks.