Driver edges analysis for network controllability

Using fewer control inputs and links to drive the dynamics on complex networks toward some desired state is a basic issue in the field of network controllability. The links between control inputs and controlled objects are defined as driver edges, and the minimum links theorem is proposed to determine the minimum set of driver edges for full controllability of a complex directed network with arbitrary structures. Simulations with different influence factors of the driver edges number are performed. The results based on model and real networks show the following conclusions. The sparse and heterogeneous networks require more driver edges, while the dense and homogeneous networks can be controlled easily. The driver edges number equals almost to the number of the driver nodes. Moreover, the driver edges number is determined mainly by the networks degree distribution.