Supplementary material from "A statistical model for brain networks inferred from large-scale electrophysiological signals"

Network science has been extensively developed to characterize structural properties of complex systems, including brain networks inferred from neuroimaging data. As a result of the inference process, networks estimated from experimentally obtained biological data, represent one instance of a larger number of realizations with similar intrinsic topology. A modelling approach is therefore needed to support statistical inference on the bottom-up local connectivity mechanisms influencing the formation of the estimated brain networks. Here, we adopted a statistical model based on exponential random graphs (ERGM) to reproduce brain networks, or connectomes, estimated by spectral coherence between high-density electroencephalographic (EEG) signals. ERGMs are made up by different local graph metrics, whereas the parameters weight the respective contribution in explaining the observed network. We validated this approach in a dataset of N = 108 healthy subjects during eyes-open (EO) and eyes-closed (EC) resting-state conditions. Results showed that the tendency to form triangles and stars, reflecting clustering and node centrality, better explained the global properties of the EEG connectomes as compared to other combinations of graph metrics. In particular, the synthetic networks generated by this model configuration replicated the characteristic differences found in the real brain networks, with EO eliciting significantly higher segregation in the alpha frequency band (8–13 Hz) as compared to EC. Furthermore, the fitted ERGM parameter values provided complementary information showing that clustering connections are significantly more represented from EC to EO in the alpha range, but also in the beta band (14–29 Hz), which is known to play a crucial role in cortical processing of visual input and externally oriented attention. Taken together, these findings support the current view of the brain functional segregation and integration in terms of modules and hubs, and provide a statistical approach to extract new information on the (re)organizational mechanisms in healthy and diseased brains.