Target control of edge dynamics in complex networks

Controlling edge dynamics in complex networks, which is relevant to many real systems, is significant in network science. However, the full control of the edge dynamics may be neither feasible nor necessary in some real systems with huge size and complexity. This practical situation motivates us to explore target control, that is, the full control of a preselected subset of edges. In this paper, an effective method is proposed to approximate the minimum number of driver nodes sufficient for target control of the edge dynamics in complex networks. The method allows us not only to analyze the target control efficiency, i.e., a unified metric of the propensity of an edge dynamics to be target controllable, but also to show the structural property of driver nodes. Evaluation of real networks indicates that the target control efficiency is determined mainly by the network's degree distribution. Simulation results and analytic calculations show that the edge dynamics in dense and homogeneous networks tend to have higher target control efficiency. Also, the target edge set selected by the random scheme is easier to control than that by the local scheme and the critical scheme. Furthermore, the analysis of the local structure of driver nodes shows that spare and inhomogeneous networks, which emerge in many real systems, tend to choose high-degree and divergent nodes as driver nodes.