# Identifying the latent space geometry of network models through analysis of curvature

arXiv: https://arxiv.org/abs/2012.10559 · HTML: https://mlsanity.com/paper/2012.10559/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2020.

## Built on by (most cited first, 11 of 11)

- [Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature](https://mlsanity.com/paper/2309.09384/) (2023)
- [Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimization](https://mlsanity.com/paper/2309.04810/) (2023)
- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [Wrapped Distributions on homogeneous Riemannian manifolds](https://mlsanity.com/paper/2204.09790/) (2022)
- [Continuous Latent Position Models for Instantaneous Interactions](https://mlsanity.com/paper/2103.17146/) (2021)
- [Toward a Taxonomy of Trust for Probabilistic Machine Learning](https://mlsanity.com/paper/2112.03270/) (2021)
- [Bayesian Hyperbolic Multidimensional Scaling](https://mlsanity.com/paper/2210.15081/) (2022)
- [Reconstruction of Random Geometric Graphs: Breaking the Omega(r) distortion barrier](https://mlsanity.com/paper/2107.14323/) (2021)
- [Automated Manifold Learning for Reduced Order Modeling](https://mlsanity.com/paper/2506.01741/) (2025)
- [Spectral goodness-of-fit tests for complete and partial network data](https://mlsanity.com/paper/2106.09702/) (2021)
- [Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors](https://mlsanity.com/paper/2605.18927/) (2026)

## Abstract (arXiv)

A common approach to modeling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter communities; negative curvature induces repulsion. We consistently estimate manifold type, dimension, and curvature from simply connected, complete Riemannian manifolds of constant curvature. We represent the graph as a noisy distance matrix based on the ties between cliques, then develop hypothesis tests to determine whether the observed distances could plausibly be embedded isometrically in each of the candidate geometries. We apply our approach to data-sets from economics and neuroscience.