Heavy-tailed neuronal connectivity arises from Hebbian self-organization

The connections in networks of neurons are heavy-tailed, with a small number of neurons connected much more strongly than the vast majority of pairs. However, it remains unclear whether this heavy-tailed connectivity emerges from simple underlying mechanisms. Here we propose a minimal model of synaptic self-organization: connections are pruned at random, and the synaptic strength rearranges under a mixture of preferential and random dynamics. Under these generic rules, networks evolve to produce distributions of connectivity strength that are asymptotically scale-free, with a power-law exponent that depends only on the probability of preferential (rather than random) growth. Extending our model to include neuronal activity and Hebbian plasticity, we find that clustering in the network also emerges naturally. We confirm these predictions in the connectomes of several animals, suggesting that heavy-tailed and clustered connectivity may arise from general principles of network self-organization rather than mechanisms specific to individual species or systems.