  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.
