# One-Hot Graph Encoder Embedding

arXiv: https://arxiv.org/abs/2109.13098 · HTML: https://mlsanity.com/paper/2109.13098/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 27 Sep 2021.

## Builds on (most cited first, 10 of 10)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [Achieving Optimal Misclassification Proportion in Stochastic Block Model](https://mlsanity.com/paper/1505.03772/) (2015)
- [On a 'Two Truths' Phenomenon in Spectral Graph Clustering](https://mlsanity.com/paper/1808.07801/) (2018)
- [Subsampling bootstrap of count features of networks](https://mlsanity.com/paper/1312.2645/) (2013)
- [Bootstrapping Exchangeable Random Graphs](https://mlsanity.com/paper/1711.00813/) (2017)
- [Robust Vertex Classification](https://mlsanity.com/paper/1311.5954/) (2013)
- [Network Dependence Testing via Diffusion Maps and Distance-Based Correlations](https://mlsanity.com/paper/1703.10136/) (2017)

## Built on by (most cited first, 16 of 16)

- [From Local to Global: Spectral-Inspired Graph Neural Networks](https://mlsanity.com/paper/2209.12054/) (2022)
- [Graph Encoder Ensemble for Simultaneous Vertex Embedding and Community Detection](https://mlsanity.com/paper/2301.11290/) (2023)
- [Synergistic Graph Fusion via Encoder Embedding](https://mlsanity.com/paper/2303.18051/) (2023)
- [Discovering Communication Pattern Shifts in Large-Scale Labeled Networks using Encoder Embedding and Vertex Dynamics](https://mlsanity.com/paper/2305.02381/) (2023)
- [Refined Graph Encoder Embedding via Self-Training and Latent Community Recovery](https://mlsanity.com/paper/2405.12797/) (2024)
- [Encoder Embedding for General Graph and Node Classification](https://mlsanity.com/paper/2405.15473/) (2024)
- [Principal Graph Encoder Embedding and Principal Community Detection](https://mlsanity.com/paper/2501.14939/) (2025)
- [Detection of Model-based Planted Pseudo-cliques in Random Dot Product Graphs by the Adjacency Spectral Embedding and the Graph Encoder Embedding](https://mlsanity.com/paper/2312.11054/) (2023)
- [Edge-Parallel Graph Encoder Embedding](https://mlsanity.com/paper/2402.04403/) (2024)
- [Efficient Graph Encoder Embedding for Large Sparse Graphs in Python](https://mlsanity.com/paper/2406.03726/) (2024)
- [A Graph Sufficiency Perspective for Neural Networks](https://mlsanity.com/paper/2507.10215/) (2025)
- [Fast and Scalable Multi-Kernel Encoder Classifier](https://mlsanity.com/paper/2406.02189/) (2024)
- [Explaining Categorical Feature Interactions Using Graph Covariance and LLMs](https://mlsanity.com/paper/2501.14932/) (2025)
- [Graph Transformer with Disease Subgraph Positional Encoding for Improved Comorbidity Prediction](https://mlsanity.com/paper/2503.03046/) (2025)
- [Graph Neural Networks Powered by Encoder Embedding for Improved Node Learning](https://mlsanity.com/paper/2507.11732/) (2025)
- [Adjacency Spectral Embeddings of Correlation Networks](https://mlsanity.com/paper/2602.21055/) (2026)

## Abstract (arXiv)

In this paper we propose a lightning fast graph embedding method called one-hot graph encoder embedding. It has a linear computational complexity and the capacity to process billions of edges within minutes on standard PC -- making it an ideal candidate for huge graph processing. It is applicable to either adjacency matrix or graph Laplacian, and can be viewed as a transformation of the spectral embedding. Under random graph models, the graph encoder embedding is approximately normally distributed per vertex, and asymptotically converges to its mean. We showcase three applications: vertex classification, vertex clustering, and graph bootstrap. In every case, the graph encoder embedding exhibits unrivalled computational advantages.