# Scaling Properties of Human Brain Functional Networks

## TL;DR

This study analyzes high-resolution human brain functional networks to determine their degree distribution, finding they generally do not follow a power-law but tend towards a generalized Pareto distribution, impacting understanding of brain hubs.

## Contribution

It provides a comprehensive analysis using high-resolution data and multiple distribution models, clarifying the nature of brain network degree distributions.

## Key findings

- Degree distributions tend towards the generalized Pareto model.
- Results do not support power-law distribution in brain networks.
- Implications for the number of hubs in brain networks.

## Abstract

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.