Coarse-graining effect in axonal wiring databases confirms the exponential distance rule

Abstract: Axonal connections in the mouse brain show exponential scaling in the number of connections with their length, recently referred to as the exponential distance rule (EDR). This work investigates the theoretical and experimental background for extending this rule to the brain connectomes of other species, including drosophila, mouse, macaque and human. Our mathematical formulation of brain region level coarse-graining observed in the experimental data indicates the existence of the EDR rule for all species. We find that the simplest distance minimization scheme reproduces the EDR rule. Our results may suggest that some general properties of the brain's structural connectivity can be interpreted by simple statistical and/or geometrical considerations with no relation to the complex network organization of the brain.