# Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks

arXiv: https://arxiv.org/abs/1905.07953 · HTML: https://mlsanity.com/paper/1905.07953/

## Key facts

- Cited by 541 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2019.

## Built on by (most cited first, 30 of 541)

- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Exploring the Potential of Large Language Models (LLMs) in Learning on Graphs](https://mlsanity.com/paper/2307.03393/) (2023)
- [NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification](https://mlsanity.com/paper/2306.08385/) (2023)
- [LLaGA: Large Language and Graph Assistant](https://mlsanity.com/paper/2402.08170/) (2024)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [Equivariant Subgraph Aggregation Networks](https://mlsanity.com/paper/2110.02910/) (2021)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Graph Unlearning](https://mlsanity.com/paper/2103.14991/) (2021)
- [Node Feature Extraction by Self-Supervised Multi-scale Neighborhood Prediction](https://mlsanity.com/paper/2111.00064/) (2021)
- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [Harnessing Explanations: LLM-to-LM Interpreter for Enhanced Text-Attributed Graph Representation Learning](https://mlsanity.com/paper/2305.19523/) (2023)
- [SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations](https://mlsanity.com/paper/2306.10759/) (2023)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [A Unified Lottery Ticket Hypothesis for Graph Neural Networks](https://mlsanity.com/paper/2102.06790/) (2021)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Robustness of Graph Neural Networks at Scale](https://mlsanity.com/paper/2110.14038/) (2021)
- [Decoupling the Depth and Scope of Graph Neural Networks](https://mlsanity.com/paper/2201.07858/) (2022)
- [GNNAutoScale: Scalable and Expressive Graph Neural Networks via Historical Embeddings](https://mlsanity.com/paper/2106.05609/) (2021)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion](https://mlsanity.com/paper/2301.09474/) (2023)
- [Graph Attention Multi-Layer Perceptron](https://mlsanity.com/paper/2206.04355/) (2022)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [When Do Flat Minima Optimizers Work?](https://mlsanity.com/paper/2202.00661/) (2022)

## Abstract (arXiv)

Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16]. Our codes are publicly available at https://github.com/google-research/google-research/tree/master/cluster_gcn.