  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 modeling
approach is therefore needed to support statistical inference on the bottom-up
local connectivity mechanisms influencing the formation of the estimated brain
networks. 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. We
validated this approach in a dataset of 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. Synthetic networks generated
by this model configuration replicated the characteristic differences found in
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.
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.
