  To determine the precise link between form and function, brain studies
primarily concentrate on the anatomical wiring of the brain and its topological
properties. In this work, we investigate the weighted degree and connection
length distributions of the KKI-113 and KKI-18 human connectomes, the fruit
fly, and of the mouse retina. We found that the node strength (weighted degree)
distribution behavior differs depending on the considered scale. On the global
scale, the distributions are found to follow a power-law behavior, with a
roughly universal exponent close to 3. However, this behavior breaks at the
local scale as the node strength distributions of the KKI-18 follow a stretched
exponential, and the fly and mouse retina follow the log-normal distribution,
respectively which are indicative of underlying random multiplicative processes
and underpins non-locality of learning in a brain close to the critical state.
However, for the case of the KKI-113 and the H01 human (1mm$^3$) datasets, the
local weighted degree distributions follow an exponentially truncated
power-law, which may hint at the fact that the critical learning mechanism may
have manifested at the node level too.
