  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.
