Geometric renormalization unravels the multiscale structure of complex networks
26th June 2020, 3:30 pm – 4:30 pm
The renormalization group allows a systematic investigation of physical systems when observed at different length scales. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Network geometry offers now a powerful framework where similarity distances between nodes in a latent space allow a geometric renormalization (GR) method for exploring the structure of real networks at lower resolutions. The technique is based on network maps that are progressively coarse-grained and rescaled to unfold real networks into a multilayer shell that shows statistical self-similarity. Interestingly, self-similarity of the GR multiscale shell holds for human brain connectomes, in agreement with the self-similarity observed when the resolution length is progressively decreased by hierarchical coarse-graining of anatomical regions, suggesting that the same principles organize connectivity between brain regions at different length scales. Finally, self-similarity is also found in the evolution of some growing real networks, suggesting that evolutionary processes can be modeled by reversing GR.