Enhancing pinning controllability of complex networks through link rewiring

In this paper, we propose a method to optimize topology of networks to enhance their pinning controllability while the locations of the drivers and their associated feedback gains are fixed. Inspired by the master stability function approach, the pinning controllability is measured by the eigenratio of the augmented Laplacian matrix. A perturbation mechanism is used to approximate the influence of adding/removing edges on the pinning controllability, which leads to a criterion for efficient rewirings. Simulation results on model scale-free networks show that the proposed rewiring-based topology optimization strategy can successfully optimize the pinning controllability. The optimized networks show significantly different topological properties as compared to the original networks. Furthermore, regardless of the initial choice of drivers, they become hubs in the optimized networks.