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.
Highlights
The human brain is arguably one of the most complex systems known to humankind and understanding its inner workings is one of the great scientific challenges of the 21st century [1]
Previous work showed that the combination of topology and anatomical geometry in mammalian cortical networks allows for near-optimal decentralized communication under greedy routing, in addition to explaining significant variation in functional connectivity [26]
Navigable maps of structural brain networks across species investigated this question by computing the success rate and stretch of greedy routing, a decentralized routing protocol typically used to explore the navigability properties of networks
Summary
The human brain is arguably one of the most complex systems known to humankind and understanding its inner workings is one of the great scientific challenges of the 21st century [1]. There is, mounting evidence that most connectomes share universal topological properties with other networked complex systems They are modular [16], small-world [17], their distribution of number of connections per node is heavy-tailed [18], and their most connected nodes form a rich-club [19]. Euclidean distances alone cannot explain the observed connectivity between brain regions and other factors are necessarily at play [22, 27, 28] This opens the possibility to investigate the relationship between the topology of connectomes and their effective geometry [29, 30], i.e. a geometrical representation that encodes all factors guiding the existence of connections
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