Structural connectivity in the brain is typically studied by reducing its observation to a single spatial resolution. However, the brain poses a rich URLanized in multiple scales linked to one another. We explored the URLanization of the human connectome using a dataset of healthy subjects reconstructed at five different resolutions. We find that the structure of the human brain remains self-similar when the resolution length is progressively decreased by hierarchical coarse-graining of the anatomical regions. Strikingly, geometric renormalization of connectome maps in hyperbolic space, which decreases the resolution by coarse-graining and averaging over short similarity distances , predicts the properties of connectomes including self-similarity . Our results suggest that the same principles regulate connectivity between brain regions at different length scales and that the multiscale self-similarity of brain connectomes may offer an advantageous architecture for  navigation purposes. The implications are varied and can affect fundamental debates, like whether the brain is working near a critical point, and lead to applications including advanced tools to simplify the digital reconstruction and simulation of the brain.
Structural connectivity in the brain is typically studied by reducing its observation to a single spatial resolution. However, the brain possesses a rich URLanized in multiple scales linked to one another. We explored the URLanization of the human connectome using datasets of healthy subjects reconstructed at five different resolutions. We found that the structure of the human brain remains self-similar when the resolution length is progressively decreased by hierarchical coarse-graining of the anatomical regions. Strikingly, a geometric network model, where distances are not Euclidean, predicts the multiscale properties of connectomes, including self-similarity. The model relies on the application of a geometric renormalization protocol which decreases the resolution by coarse-graining and averaging over short similarity distances . Our results prove that simplicity is one of URLanizing principles of the large-scale self-similar architecture of human structural brain networks, with the same connectivity law ruling short and long range connections and operating between brain regions at different length scales . Moreover, the multiscale self-similarity of brain connectomes may offer an advantageous architecture for decentralized navigation purposes. The implications are varied and can be substantial for fundamental debates, like whether the brain is working near a critical point, and for applications including advanced tools to simplify the digital reconstruction and simulation of the brain.
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