The complex network dynamics that arise from the interaction of the brain’s structural and functional architectures give rise to mental/nfunction. Theoretical models demonstrate that the structure–function relation is maximal when the global network dynamics operate at/na critical point of state transition. In the present work, we used a dynamic mean-field neural model to fit empirical structural connectivity/n(SC) and functional connectivity (FC) data acquired in humans and macaques and developed a new iterative-fitting algorithm to optimize/nthe SC matrix based on the FC matrix. A dramatic improvement of the fitting of the matrices was obtained with the addition of a small/nnumber of anatomical links, particularly cross-hemispheric connections, and reweighting of existing connections. We suggest that the/nnotion of a critical working point, where the structure–function interplay is maximal, may provide a new way to link behavior and/ncognition, and a new perspective to understand recovery of function in clinical conditions.

G.D. was supported by the European Research Council Advanced Grant DYSTRUCTURE (n.295129), by the Spanish/nResearch Project SAF2010-16085, and by the CONSOLIDER-INGENIO 2010 Programme CSD2007-00012. V.K.J. and/nG.D. are supported by FP7-ICT BrainScales. The research reported herein was supported by Collaborative Research/nGrant 220020255 from the James S. McDonnell Foundation. P.H. is supported by the Leenaards Foundation