On the effect of neuronal spatial subsampling in small-world networks.

The analysis of real-world networks of neurons is biased by the current ability to measure just a subsample of the entire network. It is thus relevant to understand if the information gained in the subsamples can be extended to the global network to improve functional interpretations. Here we showed how average clustering coefficient (CC), average path length (PL), and small-world propensity (SWP) scale when spatial sampling is applied to small-world networks. This extraction mimics the measurement of physical neighbors by means of electrical and optical techniques, both used to study neuronal networks. We applied this method to in silico and in vivo data and we found that the analyzed properties scale with the size of the sampled network and the global network topology. By means of mathematical manipulations, the topology dependence was reduced during scaling. We highlighted the behaviors of the descriptors that, qualitatively, are shared by all the analyzed networks and that allowed an approximated prediction of those descriptors in the global graph using the subgraph information. In contrast, below a spatial threshold, any extrapolation failed; the subgraphs no longer contain enough information to make predictions. In conclusion, the size of the chosen subgraphs is critical to extend the findings to the global network.