# Simple and Effective Graph Autoencoders with One-Hop Linear Models

arXiv: https://arxiv.org/abs/2001.07614 · HTML: https://mlsanity.com/paper/2001.07614/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2020.

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

- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [Variational Graph Normalized Auto-Encoders](https://mlsanity.com/paper/2108.08046/) (2021)
- [Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2202.00961/) (2022)
- [Cold Start Similar Artists Ranking with Gravity-Inspired Graph Autoencoders](https://mlsanity.com/paper/2108.01053/) (2021)
- [Homophily-enhanced Structure Learning for Graph Clustering](https://mlsanity.com/paper/2308.05309/) (2023)
- [Logiformer: A Two-Branch Graph Transformer Network for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.00731/) (2022)
- [Learning Graph Representations](https://mlsanity.com/paper/2102.02026/) (2021)
- [Finding MNEMON: Reviving Memories of Node Embeddings](https://mlsanity.com/paper/2204.06963/) (2022)
- [A Comprehensive Survey on Graph Summarization with Graph Neural Networks](https://mlsanity.com/paper/2302.06114/) (2023)
- [On Generalization of Graph Autoencoders with Adversarial Training](https://mlsanity.com/paper/2107.02658/) (2021)
- [Sparsifying the Update Step in Graph Neural Networks](https://mlsanity.com/paper/2109.00909/) (2021)
- [Relating graph auto-encoders to linear models](https://mlsanity.com/paper/2211.01858/) (2022)
- [Norm Augmented Graph AutoEncoders for Link Prediction](https://mlsanity.com/paper/2502.05868/) (2025)
- [New Frontiers in Graph Autoencoders: Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2211.08972/) (2022)
- [Learning Network Representations with Disentangled Graph Auto-Encoder](https://mlsanity.com/paper/2402.01143/) (2024)
- [Disentangled and Self-Explainable Node Representation Learning](https://mlsanity.com/paper/2410.21043/) (2024)
- [To Share or Not to Share: Investigating Weight Sharing in Variational Graph Autoencoders](https://mlsanity.com/paper/2502.16724/) (2025)

## Abstract (arXiv)

Over the last few years, graph autoencoders (AE) and variational autoencoders (VAE) emerged as powerful node embedding methods, with promising performances on challenging tasks such as link prediction and node clustering. Graph AE, VAE and most of their extensions rely on multi-layer graph convolutional networks (GCN) encoders to learn vector space representations of nodes. In this paper, we show that GCN encoders are actually unnecessarily complex for many applications. We propose to replace them by significantly simpler and more interpretable linear models w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph, involving fewer operations, fewer parameters and no activation function. For the two aforementioned tasks, we show that this simpler approach consistently reaches competitive performances w.r.t. GCN-based graph AE and VAE for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE. Based on these results, we also question the relevance of repeatedly using these datasets to compare complex graph AE and VAE.