Symmetry-driven embedding of networks in hyperbolic space

Abstract Hyperbolic models are known to produce networks with properties observed empirically in most network datasets, including heavy-tailed degree distribution, high clustering, and hierarchical structures. As a result, several embedding algorithms have been proposed to invert these models and as...

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Bibliographic Details
Main Authors: Simon Lizotte, Jean-Gabriel Young, Antoine Allard
Format: Article
Language:English
Published: Nature Portfolio 2025-05-01
Series:Communications Physics
Online Access:https://doi.org/10.1038/s42005-025-02122-0
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Summary:Abstract Hyperbolic models are known to produce networks with properties observed empirically in most network datasets, including heavy-tailed degree distribution, high clustering, and hierarchical structures. As a result, several embedding algorithms have been proposed to invert these models and assign hyperbolic coordinates to network data. Current algorithms for finding these coordinates, however, do not quantify uncertainty in the inferred coordinates. We present BIGUE, a Markov chain Monte Carlo (MCMC) algorithm that samples the posterior distribution of a Bayesian hyperbolic random graph model. We show that the samples are consistent with current algorithms while providing added credible intervals for the coordinates and all network properties. We also show that some networks admit two or more plausible embeddings, a feature that an optimization algorithm can easily overlook.
ISSN:2399-3650