Control centrality and hierarchical structure in complex networks

TL;DR

This paper introduces control centrality as a measure of a node's influence in directed networks, linking it to hierarchical structure and proposing an attack strategy to disrupt network controllability.

Contribution

It defines control centrality, establishes its relation to hierarchy in directed networks, and develops an attack method to impair network controllability.

Findings

Control centrality distribution depends on degree distribution.

In loopless directed networks, control centrality is determined by node hierarchy.

An effective attack strategy reduces network controllability.

Abstract

We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the network's degree distribution. We rigorously prove that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.