Effect of correlations on network controllability

TL;DR

This paper investigates how network features like correlations influence the number of driver nodes needed for controllability, revealing that certain symmetries and correlations significantly affect control requirements.

Contribution

It uncovers the specific impact of degree correlations and symmetries on network controllability, clarifying factors affecting the minimal driver nodes needed.

Findings

Clustering and modularity do not affect controllability.

Symmetries in the matching problem influence the dependence on degree correlations.

Numerical simulations support the theoretical predictions.

Abstract

A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network characteristics on the minimal number of driver nodes required to control a network. We find that clustering and modularity have no discernible impact, but the symmetries of the underlying matching problem can produce linear, quadratic or no dependence on degree correlation coefficients, depending on the nature of the underlying correlations. The results are supported by numerical simulations and help narrow the observed gap between the predicted and the observed number of driver nodes in real networks.