Navigable maps of structural brain networks across species

TL;DR

This study demonstrates that hyperbolic space effectively models the structure of brain connectomes across species, enabling nearly perfect navigation and offering a new geometric perspective on brain network organization.

Contribution

It introduces hyperbolic geometry as a universal framework for representing and analyzing connectomes across species, surpassing Euclidean models.

Findings

Hyperbolic space provides near-perfect navigability of connectomes.

Euclidean distances fail to fully explain connectome organization in mammals.

Hyperbolic maps reveal a common geometric structure across diverse species.

Abstract

Connectomes are spatially embedded networks whose architecture has been shaped by physical constraints and communication needs throughout evolution. Using a decentralized navigation protocol, we investigate the relationship between the structure of the connectomes of different species and their spatial layout. As a navigation strategy, we use greedy routing where nearest neighbors, in terms of geometric distance, are visited. We measure the fraction of successful greedy paths and their length as compared to shortest paths in the topology of connectomes. In Euclidean space, we find a striking difference between the navigability properties of mammalian and non-mammalian species, which implies the inability of Euclidean distances to fully explain the structural organization of their connectomes. In contrast, we find that hyperbolic space, the effective geometry of complex networks, provides almost perfectly navigable maps of connectomes for all species, meaning that hyperbolic distances are exceptionally congruent with the structure of connectomes. Hyperbolic maps therefore offer a quantitative meaningful representation of connectomes that suggests a new cartography of the brain based on the combination of its connectivity with its effective geometry rather than on its anatomy only. Hyperbolic maps also provide a universal framework to study decentralized communication processes in connectomes of different species and at different scales on an equal footing.