Towards multiscale network science

Network geometry offers a powerful framework for solving network problems which have important features at multiple length scales. Within this paradigm, we have been developing methods for exploring real networks at different resolutions on the basis of similarity distances between nodes in a latent hyperbolic space. The core method is a geometric renormalization technique that coarse-grains and rescales the network to unfold it into a multilayer shell. We found that the multiscale shells of real networks, including connectomes of the human brain, show self-similarity, which is also found in the evolution of some growing real networks. This suggests that evolutionary processes can be modeled by a reverse renormalization process, meaning that the same principles that shape connectivity in networks at different length scales also remain over time. Multiscale unfolding has also practical applications. For instance, it can be used to produce scaled down and scaled up replicas of real networks, a useful tool for the study of processes where network size is relevant, or in the optimization of dynamical processes.