  Many real-world systems are composed of many individual components that
interact with one another in a complex pattern to produce diverse behaviors.
Understanding how to intervene in these systems to guide behaviors is
critically important to facilitate new discoveries and therapies in systems
biology and neuroscience. A promising approach to optimizing interventions in
complex systems is network control theory, an emerging conceptual framework and
associated mathematics to understand how targeted input to nodes in a network
system can predictably alter system dynamics. While network control theory is
currently being applied to real-world data, the practical performance of these
measures on simple networks with pre-specified structure is not well
understood. In this study, we benchmark measures of network controllability on
canonical graph models, providing an intuition for how control strategy, graph
topology, and edge weight distribution mutually depend on one another. Our
numerical studies motivate future analytical efforts to gain a mechanistic
understanding of the relationship between graph topology and control, as well
as efforts to design networks with specific control profiles.
