# Multiscale unfolding of real networks by geometric renormalization

## TL;DR

This paper introduces a geometric renormalization group for complex networks, revealing their multiscale structure and self-similarity, which enables better understanding, modeling, and navigation of large-scale networks.

## Contribution

It develops a novel geometric renormalization method to analyze and unfold real networks across multiple scales, highlighting their self-similar properties and practical applications.

## Key findings

- Real networks exhibit geometric scaling consistent with underlying models.
- Multiscale unfolding reveals coexisting scales and their interactions.
- The approach improves network modeling and navigation in hyperbolic space.

## Abstract

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group for complex networks and use the technique to investigate networks as viewed at different scales. We find that real networks embedded in a hidden metric space show geometric scaling, in agreement with the renormalizability of the underlying geometric model. This allows us to unfold real scale-free networks in a self-similar multilayer shell which unveils the coexisting scales and their interplay. The multiscale unfolding offers a basis for a new approach to explore critical phenomena and universality in complex networks, and affords us immediate practical applications, like high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space which boosts the success of single-layer versions.