Controlling edge dynamics in complex networks

TL;DR

This paper introduces a new edge-based dynamical process on complex networks, revealing that real-world networks, especially transcriptional regulatory networks, are more controllable than randomized ones, with scale-free and degree correlations enhancing control.

Contribution

It presents a novel edge-based control process and analyzes its controllability, contrasting it with node-based dynamics and highlighting properties of real-world networks.

Findings

Most real-world networks are more controllable than randomized versions.

Transcriptional regulatory networks are particularly easy to control.

Scale-free degree distributions and degree correlations improve controllability.

Abstract

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degrees enhance the controllability of the proposed dynamics.