To determine the precise link between anatomical structure 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 the mouse retina.
We find 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 nonlocality of learning in a brain close to the critical state.
However, for the case of the KKI-113 and the H01 human ( 1 mm 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.
