A scale-free network is one whose degree distribution follows a power law. [0]

Self-organized criticality describes a phenomenon where certain complex systems naturally evolve toward a critical state where they exhibit power-law behavior and scale invariance. [1]

The power laws observed in such systems suggest they are at the edge between order and chaos. In intelligent systems, such as the brain, this edge-of-chaos behavior is thought to enable maximal adaptability, information processing, and optimization.

The brain has been proposed to operate near critical points, with neural avalanches following power laws. This allows a very small amount of energy to have an outsized impact, the key feature of scale-free networks. This phenomenon is a natural extension of the stationary action principle.

[0] https://en.wikipedia.org/wiki/Scale-free_network

[1] https://www.researchgate.net/publication/235741761_Self-Orga...