Before revision:  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.
After revision:  Moreover, we prove that 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.