Sensitivity of network controllability to weight-based edge thresholding

Abstract

In this study we investigate the change in network controllability, the ability to fully control the state of a network by applying external inputs, as edges of a network are removed according to their edge weight. A significant challenge to analyzing real-world networks is that surveys to capture network structure are almost always incomplete. While strong connections may be easy to detect, weak interactions, modeled by small edge weights are the most likely to be omitted. The incompleteness of network data leads to biasing calculated network statistics—including network controllability—away from the true values [16]. To get at the sensitivity of network control to these inaccuracies, we investigate the evolution of the minimum number of independent inputs needed to fully control the system as links are removed based on their weights. We find that the correlation between edge weight and the degrees of their adjacent nodes dominates the change in network controllability. In our surveyed real networks, this correlation is positive, meaning the number of controls increases quickly when weaker links are targeted first. We confirm this result with synthetic networks from both the scale-free and the Erdös-Rényi types. We also look at the evolution of the control profile, a network statistic that captures the ratio of the different functional types of controls.