# GBGC: Efficient and Adaptive Graph Coarsening via Granular-ball Computing

arXiv: https://arxiv.org/abs/2506.19224 · HTML: https://mlsanity.com/paper/2506.19224/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 56 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Builds on (most cited first, 24 of 24)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [Knowledge Transfer for Out-of-Knowledge-Base Entities: A Graph Neural Network Approach](https://mlsanity.com/paper/1706.05674/) (2017)
- [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)
- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [Spectrally approximating large graphs with smaller graphs](https://mlsanity.com/paper/1802.07510/) (2018)
- [A Comprehensive Study on Large-Scale Graph Training: Benchmarking and Rethinking](https://mlsanity.com/paper/2210.07494/) (2022)
- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [Graph Coarsening with Preserved Spectral Properties](https://mlsanity.com/paper/1802.04447/) (2018)
- [Online Graph Dictionary Learning](https://mlsanity.com/paper/2102.06555/) (2021)
- [Graph coarsening: From scientific computing to machine learning](https://mlsanity.com/paper/2106.11863/) (2021)
- [EXGC: Bridging Efficiency and Explainability in Graph Condensation](https://mlsanity.com/paper/2402.05962/) (2024)
- [Granular-ball computing: an efficient, robust, and interpretable adaptive multi-granularity representation and computation method](https://mlsanity.com/paper/2304.11171/) (2023)
- [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)
- [A Gromov--Wasserstein Geometric View of Spectrum-Preserving Graph Coarsening](https://mlsanity.com/paper/2306.08854/) (2023)
- [A Unified Granular-ball Learning Model of Pawlak Rough Set and Neighborhood Rough Set](https://mlsanity.com/paper/2201.03349/) (2022)
- [Parallel Graph Partitioning for Complex Networks](https://mlsanity.com/paper/1404.4797/) (2014)
- [Solution of Large-Scale Supply Chain Models using Graph Sampling & Coarsening](https://mlsanity.com/paper/2111.01249/) (2021)

## Built on by (most cited first, 2 of 2)

- [Efficient and Scalable Granular-ball Graph Coarsening Method for Large-scale Graph Node Classification](https://mlsanity.com/paper/2603.29148/) (2026)
- [3DGBGS: 3D Granular Ball Gaussian Splatting for Compact Novel View Synthesis](https://mlsanity.com/paper/2607.26578/) (2026)

## Abstract (arXiv)

The objective of graph coarsening is to generate smaller, more manageable graphs while preserving key information of the original graph. Previous work were mainly based on the perspective of spectrum-preserving, using some predefined coarsening rules to make the eigenvalues of the Laplacian matrix of the original graph and the coarsened graph match as much as possible. However, they largely overlooked the fact that the original graph is composed of subregions at different levels of granularity, where highly connected and similar nodes should be more inclined to be aggregated together as nodes in the coarsened graph. By combining the multi-granularity characteristics of the graph structure, we can generate coarsened graph at the optimal granularity. To this end, inspired by the application of granular-ball computing in multi-granularity, we propose a new multi-granularity, efficient, and adaptive coarsening method via granular-ball (GBGC), which significantly improves the coarsening results and efficiency. Specifically, GBGC introduces an adaptive granular-ball graph refinement mechanism, which adaptively splits the original graph from coarse to fine into granular-balls of different sizes and optimal granularity, and constructs the coarsened graph using these granular-balls as supernodes. In addition, compared with other state-of-the-art graph coarsening methods, the processing speed of this method can be increased by tens to hundreds of times and has lower time complexity. The accuracy of GBGC is almost always higher than that of the original graph due to the good robustness and generalization of the granular-ball computing, so it has the potential to become a standard graph data preprocessing method.