Statistical characterization of an ensemble of functional neural networks

Abstract

This work uses a complex network approach to analyze temporal sequences of electrophysiological signals of brain activity from freely behaving rats. A network node represents a neuron and a network link is included between a pair of nodes whenever their firing rates are correlated. The framework of time varying graph (TVG) is used to deal with a very large number (>30 000) of time dependent networks, which are set up by taking into account correlations between neuron firing rates in a moving time lag window of suitable width. Statistical distributions for the following network measures are obtained: size of the largest connected cluster, number of edges, average node degree, and average minimal path. We find that the number of networks with highly correlated activity in distinct brain areas has a fat-tailed distribution, irrespective of the behavioral state of the animal. This contrasts with short-tailed distributions for surrogates obtained by shuffling the original data, and reflects the fact that neurons in the neocortex and hippocampus often act in precise temporal coordination. Our results also suggest that functional neuronal networks at the millimeter scale undergo statistically nontrivial rearrangements over time, thus delimitating an empirical constraint for models of brain activity.