On the Role of Network Centrality in the Controllability of Complex Networks

TL;DR

This paper investigates the controllability of complex networks with a focus on energy requirements, revealing a connection between controllability and network centrality measures like PageRank, especially in reversible networks.

Contribution

It introduces a novel analysis linking network controllability energy to eigenvector centrality and PageRank, providing insights into control feasibility in stable networks.

Findings

Eigenvectors influence control energy requirements.

Controllability relates to PageRank in reversible networks.

Results apply to random graph models.

Abstract

In recent years complex networks have gained increasing attention in different fields of science and engineering. The problem of controlling these networks is an interesting and challenging problem to investigate. In this paper we look at the controllability problem focusing on the energy needed for the control. Precisely not only we want to analyze whether a network can be controlled, but we also want to establish whether the control can be performed using a limited amount of energy. We restrict our study to irreducible and (marginally) stable networks and we find that the leading right and left eigenvectors of the network matrix play a crucial role in this analysis. Interestingly, our results suggest the existence of a connection between controllability and network centrality, a well-known concept in network science. In case the network is reversible, the latter connection involves the PageRank, an extensively studied type of centrality measure. Finally, the proposed results are applied to examples concerning random graphs.