# Faster Graph Embeddings via Coarsening

arXiv: https://arxiv.org/abs/2007.02817 · HTML: https://mlsanity.com/paper/2007.02817/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2020.

## Built on by (most cited first, 15 of 15)

- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [Geometric Knowledge Distillation: Topology Compression for Graph Neural Networks](https://mlsanity.com/paper/2210.13014/) (2022)
- [Graph coarsening: From scientific computing to machine learning](https://mlsanity.com/paper/2106.11863/) (2021)
- [Graph Coarsening via Convolution Matching for Scalable Graph Neural Network Training](https://mlsanity.com/paper/2312.15520/) (2023)
- [A Topology-aware Graph Coarsening Framework for Continual Graph Learning](https://mlsanity.com/paper/2401.03077/) (2024)
- [Graph Coarsening via Supervised Granular-Ball for Scalable Graph Neural Network Training](https://mlsanity.com/paper/2412.13842/) (2024)
- [HyperSF: Spectral Hypergraph Coarsening via Flow-based Local Clustering](https://mlsanity.com/paper/2108.07901/) (2021)
- [Efficient Large-Scale Urban Parking Prediction: Graph Coarsening Based on Real-Time Parking Service Capability](https://mlsanity.com/paper/2410.04022/) (2024)
- [GBGC: Efficient and Adaptive Graph Coarsening via Granular-ball Computing](https://mlsanity.com/paper/2506.19224/) (2025)
- [FIT-GNN: Faster Inference Time for GNNs that 'FIT' in Memory Using Coarsening](https://mlsanity.com/paper/2410.15001/) (2024)
- [Boosting Graph Embedding on a Single GPU](https://mlsanity.com/paper/2110.10049/) (2021)
- [Learning node embeddings via summary graphs: a brief theoretical analysis](https://mlsanity.com/paper/2207.01189/) (2022)
- [Randomized Schur Complement Views for Graph Contrastive Learning](https://mlsanity.com/paper/2306.04004/) (2023)
- [Understanding Community Bias Amplification in Graph Representation Learning](https://mlsanity.com/paper/2312.04883/) (2023)
- [Remedying Coarsening-Based GNN Training under Heterophily via Adaptive Complementary Enhancement](https://mlsanity.com/paper/2607.21885/) (2026)

## Abstract (arXiv)

Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we are interested only in a small subset of relevant vertices. To address this, we present an efficient graph coarsening approach, based on Schur complements, for computing the embedding of the relevant vertices. We prove that these embeddings are preserved exactly by the Schur complement graph that is obtained via Gaussian elimination on the non-relevant vertices. As computing Schur complements is expensive, we give a nearly-linear time algorithm that generates a coarsened graph on the relevant vertices that provably matches the Schur complement in expectation in each iteration. Our experiments involving prediction tasks on graphs demonstrate that computing embeddings on the coarsened graph, rather than the entire graph, leads to significant time savings without sacrificing accuracy.