Energy Scaling with Control Distance in Complex Networks

TL;DR

This paper investigates how the energy needed to control complex networks depends on the distance between driver and target nodes, proposing an improved scaling law that accounts for this distance.

Contribution

It introduces a refined energy scaling law that incorporates control distance and self-regulation effects to better predict control energy in complex networks.

Findings

Energy scaling law can include node distance for better predictions

Control energy varies significantly with driver-target node distance

Self-regulation influences the energy required for control

Abstract

It has recently been shown that the expected energy requirements of a control action applied to a complex network scales exponentially with the number of nodes that are targeted. While the exponential scaling law provides an adequate prediction of the mean required energy, it has also been shown that the spread of energy values for a particular number of targets is large. Here, we explore more closely the effect distance between driver nodes and target nodes and the magnitude of self-regulation has on the energy of the control action. We find that the energy scaling law can be written to include information about the distance between driver nodes and target nodes to more accurately predict control energy.