# USER: Unsupervised Structural Entropy-based Robust Graph Neural Network

arXiv: https://arxiv.org/abs/2302.05889 · HTML: https://mlsanity.com/paper/2302.05889/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 12 Feb 2023.

## Builds on (most cited first, 20 of 20)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)
- [Attributed Graph Clustering via Adaptive Graph Convolution](https://mlsanity.com/paper/1906.01210/) (2019)
- [Adaptive Graph Encoder for Attributed Graph Embedding](https://mlsanity.com/paper/2007.01594/) (2020)
- [Learning Graph Embedding with Adversarial Training Methods](https://mlsanity.com/paper/1901.01250/) (2019)
- [A Survey of Adversarial Learning on Graphs](https://mlsanity.com/paper/2003.05730/) (2020)
- [Graph InfoClust: Leveraging cluster-level node information for unsupervised graph representation learning](https://mlsanity.com/paper/2009.06946/) (2020)

## Built on by (most cited first, 5 of 5)

- [Hierarchical State Abstraction Based on Structural Information Principles](https://mlsanity.com/paper/2304.12000/) (2023)
- [Unsupervised Graph Clustering with Deep Structural Entropy](https://mlsanity.com/paper/2505.14040/) (2025)
- [Toward Data-centric Directed Graph Learning: An Entropy-driven Approach](https://mlsanity.com/paper/2505.00983/) (2025)
- [Robustness of Graph Self-Supervised Learning to Real-World Noise: A Case Study on Text-Driven Biomedical Graphs](https://mlsanity.com/paper/2605.05463/) (2026)
- [Rethinking Generalization in Graph Neural Networks: A Structural Complexity Perspective](https://mlsanity.com/paper/2605.13597/) (2026)

## Abstract (arXiv)

Unsupervised/self-supervised graph neural networks (GNN) are vulnerable to inherent randomness in the input graph data which greatly affects the performance of the model in downstream tasks. In this paper, we alleviate the interference of graph randomness and learn appropriate representations of nodes without label information. To this end, we propose USER, an unsupervised robust version of graph neural networks that is based on structural entropy. We analyze the property of intrinsic connectivity and define intrinsic connectivity graph. We also identify the rank of the adjacency matrix as a crucial factor in revealing a graph that provides the same embeddings as the intrinsic connectivity graph. We then introduce structural entropy in the objective function to capture such a graph. Extensive experiments conducted on clustering and link prediction tasks under random-noises and meta-attack over three datasets show USER outperforms benchmarks and is robust to heavier randomness.