In our new paper, we replicate the statistics of brain network structure using a sandpile model that introduces Hebbian learning on a hierarchical modular network (HMN).

• M.T. Cirunay, R.C. Batac, and G. Ódor, Learning and criticality in a self-organizing model of connectome growth, Scientific Reports 15, 31890 (2025). https://doi.org/10.1038/s41598-025-16377-8 

Empirical studies of brain networks, or connectomes, of various species reveal log-normal degree distributions and power-law edge weight distributions between functional elements. We attribute these statistical signatures to the brain criticality hypothesis, allowing the brain to operate at an optimal configuration.

To model how the brain rewires itself into such a configuration, we impose a sandpile model on baseline hierarchical modular networks (HMN). Sandpiles are the paradigm models of self-organized criticality (SOC), while HMNs have been shown to mimic some features of brain operation. Hebbian learning is imposed during avalanche events, as toppled sites are rewired to have stronger connections. Random prunings are also introduced during instances without avalanches.

Our results recover the power-laws observed in neuronal avalanches, with scaling exponents close to 3/2. The resulting rewired network also exhibits similar statistical behaviors as the observed brain structure: we observed log-normal distributions of node degrees, and power-law distributions of edge weights with exponents close to 3.

The model therefore provides a simple model that explains these structural properties through the lens of (self-organized) criticality.