# Graph Coarsening via Supervised Granular-Ball for Scalable Graph Neural Network Training

arXiv: https://arxiv.org/abs/2412.13842 · HTML: https://mlsanity.com/paper/2412.13842/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 58 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Builds on (most cited first, 25 of 25)

- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [Condensing Graphs via One-Step Gradient Matching](https://mlsanity.com/paper/2206.07746/) (2022)
- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [Hierarchical Graph Transformer with Adaptive Node Sampling](https://mlsanity.com/paper/2210.03930/) (2022)
- [Spectrally approximating large graphs with smaller graphs](https://mlsanity.com/paper/1802.07510/) (2018)
- [TwiBot-22: Towards Graph-Based Twitter Bot Detection](https://mlsanity.com/paper/2206.04564/) (2022)
- [Graph Coarsening with Preserved Spectral Properties](https://mlsanity.com/paper/1802.04447/) (2018)
- [Learning Graph Neural Networks with Noisy Labels](https://mlsanity.com/paper/1905.01591/) (2019)
- [Graph coarsening: From scientific computing to machine learning](https://mlsanity.com/paper/2106.11863/) (2021)
- [Granular-ball computing: an efficient, robust, and interpretable adaptive multi-granularity representation and computation method](https://mlsanity.com/paper/2304.11171/) (2023)
- [A Multiscale Pyramid Transform for Graph Signals](https://mlsanity.com/paper/1308.4942/) (2013)
- [Faster Graph Embeddings via Coarsening](https://mlsanity.com/paper/2007.02817/) (2020)
- [Graph Pooling via Coarsened Graph Infomax](https://mlsanity.com/paper/2105.01275/) (2021)
- [Granular-ball Representation Learning for Deep CNN on Learning with Label Noise](https://mlsanity.com/paper/2409.03254/) (2024)

## Built on by (most cited first, 9 of 9)

- [Granular Ball Guided Masking: Structure-aware Data Augmentation](https://mlsanity.com/paper/2512.21011/) (2025)
- [Efficient Time Series Clustering from Multiscale Reservoir Dynamics with Granular-Ball Anchoring Graph Optimization](https://mlsanity.com/paper/2606.12077/) (2026)
- [Adaptive Graph Coarsening for Efficient GNN Training](https://mlsanity.com/paper/2509.25706/) (2025)
- [Granular Ball Guided Stable Latent Domain Discovery for Domain-General Crowd Counting](https://mlsanity.com/paper/2603.24106/) (2026)
- [Efficient and Scalable Granular-ball Graph Coarsening Method for Large-scale Graph Node Classification](https://mlsanity.com/paper/2603.29148/) (2026)
- [Square Superpixel Generation and Representation Learning via Granular Ball Computing](https://mlsanity.com/paper/2603.29460/) (2026)
- [Towards Faithful Graph Explanations with Synergistic Edge Effects via Granular Balls](https://mlsanity.com/paper/2607.21381/) (2026)
- [Remedying Coarsening-Based GNN Training under Heterophily via Adaptive Complementary Enhancement](https://mlsanity.com/paper/2607.21885/) (2026)
- [3DGBGS: 3D Granular Ball Gaussian Splatting for Compact Novel View Synthesis](https://mlsanity.com/paper/2607.26578/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have demonstrated significant achievements in processing graph data, yet scalability remains a substantial challenge. To address this, numerous graph coarsening methods have been developed. However, most existing coarsening methods are training-dependent, leading to lower efficiency, and they all require a predefined coarsening rate, lacking an adaptive approach. In this paper, we employ granular-ball computing to effectively compress graph data. We construct a coarsened graph network by iteratively splitting the graph into granular-balls based on a purity threshold and using these granular-balls as super vertices. This granulation process significantly reduces the size of the original graph, thereby greatly enhancing the training efficiency and scalability of GNNs. Additionally, our algorithm can adaptively perform splitting without requiring a predefined coarsening rate. Experimental results demonstrate that our method achieves accuracy comparable to training on the original graph. Noise injection experiments further indicate that our method exhibits robust performance. Moreover, our approach can reduce the graph size by up to 20 times without compromising test accuracy, substantially enhancing the scalability of GNNs.