  We investigate scaling properties of human brain functional networks in the
resting-state. Analyzing network degree distributions, we statistically test
whether their tails scale as power-law or not. Initial studies, based on
least-squares fitting, were shown to be inadequate for precise estimation of
power-law distributions. Subsequently, methods based on maximum-likelihood
estimators have been proposed and applied to address this question.
Nevertheless, no clear consensus has emerged, mainly because results have shown
substantial variability depending on the data-set used or its resolution. In
this study, we work with high-resolution data (10K nodes) from the Human
Connectome Project and take into account network weights. We test for the
power-law, exponential, log-normal and generalized Pareto distributions. Our
results show that the statistics generally do not support a power-law, but
instead these degree distributions tend towards the thin-tail limit of the
generalized Pareto model. This may have implications for the number of hubs in
human brain functional networks.
