Benchmarking measures of network controllability on canonical graph models

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.