Augmenting complex networked systems under improved pinning controllability condition

In this paper we introduce a method for efficient augmentation of networked systems provided that the pinning controllability of the final network is improved. The problem is how to connect a sub-network to an already existing network such that the controllability is maximised. We consider the eigenratio of the augmented Laplacian matrix as a pinning controllability metric, and use graph perturbation theory to approximate influence of edge addition on the eigenratio. The resulting metric can be efficiently used to find the links connecting two disjoint networks. We also provide numerical simulations on synthetic networks and show that the proposed method is more effective than heuristics such as connecting nodes with high degrees or betweenness centrality values.