Finding the Most Influential Nodes in Pinning Controllability of Complex Networks

Abstract

Identifying the best drivers (i.e., the nodes to apply the control signals in a large complex network), which gives the fastest synchronization to the reference state, is a challenge in pinning control of a network. There is not yet a method that exactly predicts a set of best drivers. In this brief, we introduce a novel method that gives first-order approximation for the importance of nodes in pinning control. A spectral measure (the largest eigenvalue of the augmented Laplacian matrix divided by the smallest eigenvalue) is considered as a pinning controllability metric. We develop this method based on the sensitivity analysis of the Laplacian eigenratio, resulting in the scoring of nodes based on their importance in pinning control. The method is rather simple to compute and needs a single eigendecomposition of the Laplacian matrix of the connection graph. Applying this technique on a number of model networks reveals its effectiveness over heuristic approaches.