Persistent homology broadens brain network control in 70 connectomes

A new arXiv paper by Carter Sale, Marco Coraggio, Mengsen Zhang, and Michael J. Richardson asks whether standard network control theory captures the full picture of how driver-node selection shapes brain dynamics. Instead of ranking brain regions purely by structural connectivity strength, they introduce a criterion based on persistent homology—a topological technique that identifies stable cycles in connectivity patterns at multiple scales. The researchers applied this approach to 70 human structural connectomes across three parcellation scales, comparing topology-informed driver sets against traditional degree-based selection.

Surprisingly, both methods achieved nearly identical scalar control energy, differing by only ~0.2%. However, the geometry of the controllable subspace differed substantially: topology-informed sets distributed controllability across more dimensions of state space and produced better-conditioned controllability matrices. This geometric advantage held even when high-degree hub nodes were removed. The two criteria also placed driver nodes in different cortical territories, meaning each most efficiently reached different classes of target brain states. The results show that persistent topology captures information about brain network control that simple energy summaries miss, offering a new way to think about how brain structure constrains possible state transitions.