Barzon, G.; Allegra, M.; Aarabi, M. H.; Pini, L.; De Domenico, M.; Corbetta, M.; Suweis, S.

The structural connectome serves as the foundation for neural information signaling, playing a primary constraint on brain functionality. Yet, its influence on emergent dynamical properties is not fully understood. Generally, a key measure of a system\'s structural impact on dynamical phenomena is its dimension. By tracking the temporal evolution of diffusive perturbations, we estimate a scale-dependent measure of dimension of empirical connectomes. At the local scale, it is highly heterogeneous and follows a gradient from sensory-motor to executive areas. At the global scale, it encapsulates mesoscale topological information related to the balance between segregation and integration. Furthermore, by comparing connectomes from stroke patients, we find that dimension captures the local effects of lesions and, at a global level, is linked to impaired critical patterns and decreased cognitive performance. Overall, the dimension of the connectome may serve as a powerful descriptor for bridging the gap between structure and function in the human brain.