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Spontaneous emergence of neuronal activity avalanches characterized by power-law distributions is known to occur in different types of nervous tissues suggesting that nervous systems may operate at a critical regime. Here, we explore the possible relation of this dynamical state with the underlying topology in a small-size network of interconnected Morris-Lecar neurons. Studying numerically different topological configurations, we find that, very close to the efficient small-world situation, the system self-organizes near to a critical branching process with observable distributions in the proximity of a power law with exponents similar to those reported in the experimental literature. Therefore, we conclude that the observed scaling is intimately related only with the small-world topology

A Small Morris-Lecar Neuron Network Gets Close to Critical Only in the Small-World Regimen