# Geometric renormalization unravels self-similarity of the multiscale human connectome

## TL;DR

This study reveals that the human brain's structural connectivity exhibits self-similarity across multiple scales, and a geometric renormalization model effectively predicts these multiscale properties, suggesting simple underlying organizing principles.

## Contribution

The paper introduces a geometric renormalization approach that uncovers self-similarity in multiscale human connectomes, advancing understanding of brain architecture across resolutions.

## Key findings

- Brain connectomes are self-similar across multiple resolutions.
- A geometric network model predicts multiscale connectome properties.
- Simple organizing principles underlie the brain's multiscale structure.

## Abstract

Structural connectivity in the brain is typically studied by reducing its observation to a single spatial resolution. However, the brain possesses a rich architecture organized over multiple scales linked to one another. We explored the multiscale organization of human connectomes using datasets of healthy subjects reconstructed at five different resolutions. We found that the structure of the human brain remains self-similar when the resolution of observation is progressively decreased by hierarchical coarse-graining of the anatomical regions. Strikingly, a geometric network model, where distances are not Euclidean, predicts the multiscale properties of connectomes, including self-similarity. The model relies on the application of a geometric renormalization protocol which decreases the resolution by coarse-graining and averaging over short similarity distances. Our results suggest that simple organizing principles underlie the multiscale architecture of human structural brain networks, where the same connectivity law dictates short- and long-range connections between different brain regions over many resolutions. The implications are varied and can be substantial for fundamental debates, such as whether the brain is working near a critical point, as well as for applications including advanced tools to simplify the digital reconstruction and simulation of the brain.