Brains are spatially embedded networks whose architecture has been shaped by physical and biochemical constraints throughout evolution. While these networks provide global connectivity and sustain the broad spectrum of the functions of the brain, the underlying routing strategies for communication between the different areas and their control remain to be elucidated. Here, we investigate the flow of information in connectomes of several species using greedy routing as a distributed navigation protocol . In Euclidean space, in which brains have evolved, our results unveil that the navigability of brains vary highly across species. On the one hand, this result may suggest that the more evolved URLanism is, the more the structure of the connectome is encoded in the URLanization of the brain. On the other hand, conclusions obtained using coarse-grained connectomes, where nodes correspond to areas instead of individual neurones, may not apply to connectomes obtained at the microscopic, neuronal level. Moreover, we prove that the effective geometry of the brain is better described as hyperbolic rather than Euclidean. This indicates that other factors besides degrees and Euclidean distance play a significant role in the existence of connections. On a more practical perspective, hyperbolic embeddings offer a universal and meaningful representations to compare brain networks across species on an equal footing.
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 URLanization 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.
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Brains
Connectomes
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and biochemical constraints
constraints and communication needs
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While these networks provide global connectivity and sustain the broad spectrum of the functions of the brain, the underlying routing strategies for communication between the different areas and their control remain to be elucidated. Here, we investigate the flow of information in connectomes of several species using greedy routing as a distributed navigation protocol
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
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in which brains have evolved, our results unveil that the navigability
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 URLanization
R
brains vary highly across species. On the one hand, this result may suggest that the more evolved URLanism is, the more the structure of
their connectomes. In contrast, we find that hyperbolic space,
D
connectome is encoded in the URLanization of the brain. On the other hand, conclusions obtained using coarse-grained connectomes, where nodes correspond to areas instead of individual neurones, may not apply to connectomes obtained at the microscopic, neuronal level. Moreover, we prove that the
R
the brain is better described as hyperbolic rather than Euclidean. This indicates that other factors besides degrees and Euclidean distance play a significant role in the existence of connections. On a more practical perspective, hyperbolic embeddings offer a universal and meaningful representations to compare brain networks across species
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