Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature

TL;DR

This paper introduces a dynamic curvature measure for networks that captures multiscale community structures and bottlenecks, outperforming previous methods in detecting communities and understanding information flow.

Contribution

It proposes a novel dynamic edge curvature based on network processes, enabling multiscale community detection and analysis of network bottlenecks.

Findings

Curvature gaps indicate bottleneck edges affecting information spread.

The method robustly detects communities even with degree fluctuations.

It outperforms existing community detection techniques in real-world networks.

Abstract

Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to specific classes of networks because incompatible metric spaces generally result in information loss. Here, we study arbitrary networks geometrically by defining a dynamic edge curvature measuring the similarity between pairs of dynamical network processes seeded at nearby nodes. We show that the evolution of the curvature distribution exhibits gaps at characteristic timescales indicating bottleneck-edges that limit information spreading. Importantly, curvature gaps are robust to large fluctuations in node degrees, encoding communities until the phase transition of detectability, where spectral and node-clustering methods fail. Using this insight, we derive geometric modularity to find multiscale communities based on deviations from constant network curvature in generative and real-world networks, significantly outperforming most previous methods. Our work suggests using network geometry for studying and controlling the structure of and information spreading on networks.