Communication coordination in network controllability

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.