# Symmetry-driven embedding of networks in hyperbolic space

arXiv: https://arxiv.org/abs/2406.10711 · HTML: https://mlsanity.com/paper/2406.10711/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 101 references that are in the map.
- First posted on arXiv 15 Jun 2024.

## Builds on (most cited first, 30 of 32)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [Network Geometry](https://mlsanity.com/paper/2001.03241/) (2020)
- [Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors](https://mlsanity.com/paper/2006.12335/) (2020)
- [Bayesian stochastic blockmodeling](https://mlsanity.com/paper/1705.10225/) (2017)
- [Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space](https://mlsanity.com/paper/1602.06522/) (2016)
- [A Framework for Adaptive MCMC Targeting Multimodal Distributions](https://mlsanity.com/paper/1812.02609/) (2018)
- [Hypergraph reconstruction from network data](https://mlsanity.com/paper/2008.04948/) (2020)
- [Network structure from rich but noisy data](https://mlsanity.com/paper/1703.07376/) (2017)
- [Reconstructing networks with unknown and heterogeneous errors](https://mlsanity.com/paper/1806.07956/) (2018)
- [Hydra: A method for strain-minimizing hyperbolic embedding of network- and distance-based data](https://mlsanity.com/paper/1903.08977/) (2019)
- [Systematic comparison of graph embedding methods in practical tasks](https://mlsanity.com/paper/2106.10198/) (2021)
- [Mercator: uncovering faithful hyperbolic embeddings of complex networks](https://mlsanity.com/paper/1904.10814/) (2019)
- [Emergence of Soft Communities from Geometric Preferential Attachment](https://mlsanity.com/paper/1501.06835/) (2015)
- [Network Geometry Inference using Common Neighbors](https://mlsanity.com/paper/1502.05578/) (2015)
- [Embedding Graphs in Lorentzian Spacetime](https://mlsanity.com/paper/1602.03103/) (2016)
- [Link prediction with hyperbolic geometry](https://mlsanity.com/paper/1903.08810/) (2019)
- [Geometric renormalization unravels self-similarity of the multiscale human connectome](https://mlsanity.com/paper/1904.11793/) (2019)
- [Adaptive Path Sampling in Metastable Posterior Distributions](https://mlsanity.com/paper/2009.00471/) (2020)
- [Feature-aware ultra-low dimensional reduction of real networks](https://mlsanity.com/paper/2401.09368/) (2024)
- [Clustering implies geometry in networks](https://mlsanity.com/paper/1604.01575/) (2016)
- [Latent Space Network Modelling with Hyperbolic and Spherical Geometries](https://mlsanity.com/paper/2109.03343/) (2021)
- [Exact and rapid linear clustering of networks with dynamic programming](https://mlsanity.com/paper/2301.10403/) (2023)
- [Geometric description of clustering in directed networks](https://mlsanity.com/paper/2302.09055/) (2023)

## Built on by (most cited first, 1 of 1)

- [Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors](https://mlsanity.com/paper/2605.18927/) (2026)

## Abstract (arXiv)

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 embeddings 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.