Communication coordination in network controllability

TL;DR

This paper critically examines the assumptions underlying node and edge controllability in network science, highlighting their limitations in social systems and proposing principles for more realistic communication models.

Contribution

It reveals the communication assumptions in existing controllability methods and offers guidelines for selecting suitable approaches in socioeconomic contexts.

Findings

Node controllability assumes a single message, no heterogeneity in communication.

Edge controllability relaxes this assumption but focuses on edge states.

Comparing node and edge controllability results is often invalid due to different assumptions.

Abstract

Better understanding our ability to control an interconnected system of entities has been one of the central challenges in network science. The theories of node and edge controllability have been the main methodologies suggested to find the minimal set of nodes enabling control over the whole system's dynamics. While the focus is traditionally mostly on physical systems, there has been an increasing interest in control questions involving socioeconomic systems. However, surprisingly little attention has been given to the methods' underlying assumptions on control propagation, or communication assumptions, a crucial aspect in social contexts. In this paper, we show that node controllability contains a single message assumption, allowing no heterogeneity in communication to neighbouring nodes in a network. Edge controllability is shown to relax this communication assumption but aims to control the dynamics of the edge states and not the node states, thus answering a fundamentally different question. This makes comparisons of the results from the two methods nonsensical. To increase the applicability of controllability methodology to socioeconomic contexts, we provide guiding principles to choose the appropriate methodology and suggest new avenues for future theoretical work to encode more realistic communication assumptions.