# The Geometry of Continuous Latent Space Models for Network Data

arXiv: https://arxiv.org/abs/1712.08641 · HTML: https://mlsanity.com/paper/1712.08641/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2017.

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

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- [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)
- [Continuous-time Graph Representation with Sequential Survival Process](https://mlsanity.com/paper/2312.13068/) (2023)
- [Entropic Optimal Transport in Random Graphs](https://mlsanity.com/paper/2201.03949/) (2022)
- [A group-theoretic framework for machine learning in hyperbolic spaces](https://mlsanity.com/paper/2501.06934/) (2025)
- [Bayesian Hyperbolic Multidimensional Scaling](https://mlsanity.com/paper/2210.15081/) (2022)
- [Latent structure blockmodels for Bayesian spectral graph clustering](https://mlsanity.com/paper/2107.01734/) (2021)
- [Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors](https://mlsanity.com/paper/2605.18927/) (2026)

## Abstract (arXiv)

We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to be conditionally independent given the dyads? unobserved positions in a latent space. In this way, these models provide a probabilistic framework for embedding network nodes in a continuous space equipped with a geometry that facilitates the description of dependence between random dyadic ties. Specifically, these models naturally capture homophilous tendencies and triadic clustering, among other common properties of observed networks. In addition to reviewing the literature on continuous latent space models from a geometric perspective, we highlight the important role the geometry of the latent space plays on properties of networks arising from these models via intuition and simulation. Finally, we discuss results from spectral graph theory that allow us to explore the role of the geometry of the latent space, independent of network size. We conclude with conjectures about how these results might be used to infer the appropriate latent space geometry from observed networks.