Role of graph architecture in controlling dynamical networks with applications to neural systems

Networked systems display complex patterns of interactions between components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology, supporting a variety of system-wide dynamical behaviours such as synchronization. Although descriptions of these behaviours are important, they are only a first step towards understanding and harnessing the relationship between network topology and system behaviour. Here, we use linear network control theory to derive accurate closed-form expressions that relate the connectivity of a subset of structural connections (those linking driver nodes to non-driver nodes) to the minimum energy required to control networked systems. To illustrate the utility of the mathematics, we apply this approach to high-resolution connectomes recently reconstructed from Drosophila, mouse, and human brains. We use these principles to suggest an advantage of the human brain in supporting diverse network dynamics with small energetic costs while remaining robust to perturbations, and to perform clinically accessible targeted manipulation of the brain’s control performance by removing single edges in the network. Generally, our results ground the expectation of a control system’s behaviour in its network architecture, and directly inspire new directions in network analysis and design via distributed control. The energy needed to control a network is related to the links between driver and non-driver nodes, a linear control theory suggests. Applying the theory to connectome data reveals that diverse dynamics in brain networks incur small energetic cost.