# Manifold structure in graph embeddings

arXiv: https://arxiv.org/abs/2006.05168 · HTML: https://mlsanity.com/paper/2006.05168/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 17 of 17)

- [Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach](https://mlsanity.com/paper/2106.04941/) (2021)
- [Hardness of Learning Neural Networks under the Manifold Hypothesis](https://mlsanity.com/paper/2406.01461/) (2024)
- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [Matrix factorisation and the interpretation of geodesic distance](https://mlsanity.com/paper/2106.01260/) (2021)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Frameless Graph Knowledge Distillation](https://mlsanity.com/paper/2307.06631/) (2023)
- [SALMAN: Stability Analysis of Language Models Through the Maps Between Graph-based Manifolds](https://mlsanity.com/paper/2508.18306/) (2025)
- [Implications of sparsity and high triangle density for graph representation learning](https://mlsanity.com/paper/2210.15277/) (2022)
- [Hermitian Symmetric Spaces for Graph Embeddings](https://mlsanity.com/paper/2105.05275/) (2021)
- [Latent structure blockmodels for Bayesian spectral graph clustering](https://mlsanity.com/paper/2107.01734/) (2021)
- [Spectral embedding and the latent geometry of multipartite networks](https://mlsanity.com/paper/2202.03945/) (2022)
- [Graph-theoretical approach to robust 3D normal extraction of LiDAR data](https://mlsanity.com/paper/2205.11460/) (2022)
- [Semisupervised regression in latent structure networks on unknown manifolds](https://mlsanity.com/paper/2305.02473/) (2023)
- [Signal Recovery from Random Dot-Product Graphs Under Local Differential Privacy](https://mlsanity.com/paper/2504.17274/) (2025)
- [Self-Reinforced Graph Contrastive Learning](https://mlsanity.com/paper/2505.13650/) (2025)
- [Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embedding](https://mlsanity.com/paper/2603.11965/) (2026)
- [Learning Submanifolds for Subsequent Inference on Random Dot Product Graphs, Part 1: Theory](https://mlsanity.com/paper/2609.19357/) (2026)

## Abstract (arXiv)

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is often available. In spectral embedding, this dimension may be very high. However, this paper shows that existing random graph models, including graphon and other latent position models, predict the data should live near a much lower-dimensional set. One may therefore circumvent the curse of dimensionality by employing methods which exploit hidden manifold structure.