Persistent homology broadens the controllable subspace in human structural connectomes

Abstract

Network control theory applied to structural connectomes typically ranks brain regions as candidate driver nodes by their structural connectivity strength, and evaluates performance through scalar control energy. We test whether this framing captures the most relevant information about how driver-node selection shapes brain network control. We introduce an alternative criterion based on the persistent topological cycles in which each node participates---a measure of mesoscale integration that captures features beyond local connectivity---and compare it to standard degree-based selection across 70 human structural connectomes at three parcellation scales. Topology- and degree-informed driver sets achieve nearly identical scalar control energy, differing by approximately 0.2%. The geometry of the controllable subspace, however, differs substantially: topology-informed sets distribute controllability across more dimensions of state space and produce better-conditioned controllability matrices. This geometric advantage is preserved when high-degree hub nodes are removed, and it carries a functional signature: because the two criteria place driver nodes in different cortical territory, each most efficiently reaches a different class of target state. The choice of node-ranking criterion therefore shapes which brain-state transitions are energetically favored even when average control cost is unchanged. The results reveal a dissociation between control cost and control geometry, and demonstrate that persistent topology captures information about brain network control that scalar energy summaries miss.