Path-dependent connectivity, not modularity, consistently predicts controllability of structural brain networks

The human brain displays rich communication dynamics that are thought to be particularly well-reflected in its marked community structure. Yet, the precise relationship between community structure in structural brain networks and the communication dynamics that can emerge therefrom is not well understood. In addition to offering insight into the structure-function relationship of networked systems, such an understanding is a critical step toward the ability to manipulate the brain's large-scale dynamical activity in a targeted manner. We investigate the role of community structure in the controllability of structural brain networks. At the region level, we find that certain network measures of community structure are sometimes statistically correlated with measures of linear controllability. However, we then demonstrate that this relationship depends on the distribution of network edge weights. We highlight the complexity of the relationship between community structure and controllability by performing numerical simulations using canonical graph models with varying mesoscale architectures and edge weight distributions. Finally, we demonstrate that weighted subgraph centrality, a measure rooted in the graph spectrum, and which captures higher order graph architecture, is a stronger and more consistent predictor of controllability. Our study contributes to an understanding of how the brain's diverse mesoscale structure supports transient communication dynamics. Author Summary A central question in network neuroscience is how the structure of the brain constrains the patterns of communication dynamics that underlie function. At the mesoscale of network organization, this question has been examined through the lens of modularity. Recent work has demonstrated a diversity in the mesoscale architecture of the human connectome. Further diversity in the characterization of structural brain networks is introduced by the fact that the distribution of edge weights in a network depends on the precise empirical measurement whose value is assigned to an edge. This paper explores network controllability in light of the variety of community interaction motifs and edge weight distributions that may be used to characterize structural brain networks.