Heavy-tailed neuronal connectivity arises from Hebbian self-organization

In networks of neurons, the connections are heavy-tailed, with a small number of neurons connected much more strongly than the vast majority of pairs.1-6 Yet it remains unclear whether, and how, such 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 Hebbian and random dynamics. Under these generic rules, networks evolve to produce scale-free distributions of connectivity strength, with a power-law exponent [Formula] that depends only on the probability p of Hebbian (rather than random) growth. By extending our model to include correlations in neuronal activity, we find that clustering--another ubiquitous feature of neuronal networks6-9--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 self-organization, rather than the biophysical particulars of individual neural systems.