## The hyperbolic brain

2021/06/01 | academic

Recent advances in network science include the discovery that complex networks have a hidden geometry and that this geometry is hyperbolic. Studying complex networks through the lens of their effective hyperbolic geometry has led to valuable insights on the organization of a variety of complex systems ranging from the Internet to the metabolism of *E. coli* and humans. This methodology can also be used to infer high-quality maps of connectomes, where brain regions are given coordinates in hyperbolic space such that the closer they are the more likely that they are connected. Even if Euclidean space is typically assumed as the natural geometry of the brain, distances in hyperbolic space offer a more accurate interpretation of the structure of connectomes, which suggests a new perspective for the mapping of the organization of the brain’s neuroanatomical regions.

In humans, this approach has been able to explain the multiscale organization of connectomes in healthy subjects at five anatomical resolutions. Zoomed-out connectivity maps remain self-similar and our geometric network model, where distances are not Euclidean but hyperbolic, predicts the observations by application of a renormalization protocol. Our results prove that the same principles organize brain con-nectivity at different scales and lead to efficient decentralized communication.

If you want to see more:

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

PNAS 117 20244-20253 (2020)

## Navigable maps of structural brain networks across species

PLoS Computational Biology 16 e1007584 (2020)