CONTROL CONTRIBUTION IDENTIFIES TOP DRIVER NODES IN COMPLEX NETWORKS

Abstract

We propose a new measure to quantify the impact of a node [Formula: see text] in controlling a directed network. This measure, called “control contribution” [Formula: see text], combines the probability for node [Formula: see text] to appear in a set of driver nodes and the probability for other nodes to be controlled by [Formula: see text]. To calculate [Formula: see text], we propose an optimization method based on random samples of minimum sets of drivers. Using real-world and synthetic networks, we find very broad distributions of [Formula: see text]. Ranking nodes according to their [Formula: see text] values allows us to identify the top driver nodes that can control most of the network. We show that this ranking is superior to rankings based on other control-based measures. We find that control contribution indeed contains new information that cannot be traced back to degree, control capacity or control range of a node.