Effect of correlations on controllability transition in network control

TL;DR

This paper investigates how degree correlations affect the controllability transition in networks, revealing that correlations influence the minimal number of driver nodes needed, especially in sparse networks, with effects diminishing in dense networks.

Contribution

It provides new insights into the role of degree correlations on controllability transition points across different network types and densities.

Findings

Degree correlation causes local maxima in controllability transition points in sparse networks.

In dense ER networks, degree correlation and distribution do not significantly affect controllability.

Numerical simulations support the impact of degree correlation on the minimal driver nodes needed.

Abstract

The numerical controllability transition makes the success of control can be achieved by increasing the number of driver nodes to a certain point. Motivated by the fact that the degree correlation has vast role in the dynamics on networks, we study the impact of various degree correlations of different networks on the controllability transition point and find that the transition point depicts local maximum in sparse networks as degree correlation r around 0.1 and 0 in ER and SF networks respectively. With the increasing of average degree, the local maximum disappear and the controllability transition cannot be influenced by degree correlation and degree distribution in dense ER networks. The results are supported by numerical simulations and provide more details to estimate the minimal driver nodes in large networks.