Hyperbolic embedding of multilayer networks

TL;DR

This paper presents a hyperbolic embedding framework for multilayer networks that captures complex interdependencies and preserves community structures, enabling detailed intra- and inter-layer analysis in a unified geometric space.

Contribution

It introduces a novel hyperbolic embedding method supporting heterogeneous nodes and inter-layer connections, outperforming existing approaches in multilayer network analysis.

Findings

Effectively preserves community structure in synthetic multilayer models.

Successfully clusters disease-related brain regions in real brain networks.

Outperforms layer-independent embedding methods in experiments.

Abstract

Multilayer networks offer a powerful framework for modeling complex systems across diverse domains, effectively capturing multiple types of connections and interdependent subsystems commonly found in real world scenarios. To analyze these networks, embedding techniques that project nodes into a lower-dimensional geometric space are essential. This paper introduces a novel hyperbolic embedding framework that advances the state of the art in multilayer network analysis. Our method, which supports heterogeneous node sets across networks and inter-layer connections, generates layer-specific hyperbolic embeddings, enabling detailed intra-layer analysis and inter-layer comparisons, while simultaneously preserving the global multilayer structure within hyperbolic space, a capability that sets it apart from existing approaches, which typically rely on independent embedding of layers. Through experiments on synthetic multilayer stochastic block models, we demonstrate that our approach effectively preserves community structure, even when layers consist of different node sets. When applied to real brain networks, the method successfully clusters disease-related brain regions from different patients, outperforming layer-independent approaches and highlighting its relevance for comparative analysis. Overall, this work provides a robust tool for multilayer network analysis, enhancing interpretability and offering new insights into the structure and function of complex systems.