Value of peripheral nodes in controlling multilayer networks

TL;DR

This study investigates how selecting peripheral nodes with low importance values as driver nodes in a two-layer scale-free network enhances controllability and cost-efficiency, offering new insights into network control strategies.

Contribution

It introduces a novel approach of using peripheral nodes for control and interconnection in multilayer networks, demonstrating their effectiveness and cost benefits.

Findings

Controlling with peripheral nodes is as effective as using central nodes.

Peripheral nodes lead to more cost-efficient control strategies.

Connecting layers through peripheral nodes improves overall controllability.

Abstract

We analyze the controllability of a two-layer network, where driver nodes can be chosen randomly only from one layer. Each layer contains a scale-free network with directed links and the node dynamics depends on the incoming links from other nodes. We combine the in-degree and out-degree values to assign an importance value $w$ to each node, and distinguish between peripheral nodes with low $w$ and central nodes with high $w$. Based on numerical simulations, we find that the controllable part of the network is larger when choosing low $w$ nodes to connect the two layers. The control is as efficient when peripheral nodes are driver nodes as it is for the case of more central nodes. However, if we assume a cost to utilize nodes that is proportional to their overall degree, utilizing peripheral nodes to connect the two layers or to act as driver nodes is not only the most cost-efficient solution, it is also the one that performs best in controlling the two-layer network among the different interconnecting strategies we have tested.