# GraphHop: An Enhanced Label Propagation Method for Node Classification

arXiv: https://arxiv.org/abs/2101.02326 · HTML: https://mlsanity.com/paper/2101.02326/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 100 references that are in the map.
- First posted on arXiv 7 Jan 2021.

## Builds on (most cited first, 30 of 45)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Label Propagation for Deep Semi-supervised Learning](https://mlsanity.com/paper/1904.04717/) (2019)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)

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

- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [Toward Robust Graph Semi-Supervised Learning against Extreme Data Scarcity](https://mlsanity.com/paper/2208.12422/) (2022)
- [E-PixelHop: An Enhanced PixelHop Method for Object Classification](https://mlsanity.com/paper/2107.02966/) (2021)
- [Multi-View Subgraph Neural Networks: Self-Supervised Learning with Scarce Labeled Data](https://mlsanity.com/paper/2404.12569/) (2024)
- [Rethinking Independent Cross-Entropy Loss For Graph-Structured Data](https://mlsanity.com/paper/2405.15564/) (2024)
- [Label Efficient Regularization and Propagation for Graph Node Classification](https://mlsanity.com/paper/2204.08646/) (2022)
- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [Graph Your Own Prompt](https://mlsanity.com/paper/2509.23373/) (2025)
- [Learning Optimal Graph Filters for Clustering of Attributed Graphs](https://mlsanity.com/paper/2211.04634/) (2022)
- [Propagation with Adaptive Mask then Training for Node Classification on Attributed Networks](https://mlsanity.com/paper/2206.10142/) (2022)
- [When LLM Agents Meet Graph Optimization: An Automated Data Quality Improvement Approach](https://mlsanity.com/paper/2510.08952/) (2025)
- [ModSSC: A Modular Framework for Semi-Supervised Classification on Heterogeneous Data](https://mlsanity.com/paper/2512.13228/) (2025)
- [Learning from Limited Labels: Transductive Graph Label Propagation for Indian Music Analysis](https://mlsanity.com/paper/2601.03626/) (2026)
- [OpenRTAG: A Comprehensive Benchmark for Robust Text-Attributed Graph Learning under Data Quality Degradation](https://mlsanity.com/paper/2607.19108/) (2026)

## Abstract (arXiv)

A scalable semi-supervised node classification method on graph-structured data, called GraphHop, is proposed in this work. The graph contains attributes of all nodes but labels of a few nodes. The classical label propagation (LP) method and the emerging graph convolutional network (GCN) are two popular semi-supervised solutions to this problem. The LP method is not effective in modeling node attributes and labels jointly or facing a slow convergence rate on large-scale graphs. GraphHop is proposed to its shortcoming. With proper initial label vector embeddings, each iteration of GraphHop contains two steps: 1) label aggregation and 2) label update. In Step 1, each node aggregates its neighbors' label vectors obtained in the previous iteration. In Step 2, a new label vector is predicted for each node based on the label of the node itself and the aggregated label information obtained in Step 1. This iterative procedure exploits the neighborhood information and enables GraphHop to perform well in an extremely small label rate setting and scale well for very large graphs. Experimental results show that GraphHop outperforms state-of-the-art graph learning methods on a wide range of tasks (e.g., multi-label and multi-class classification on citation networks, social graphs, and commodity consumption graphs) in graphs of various sizes. Our codes are publicly available on GitHub (https://github.com/TianXieUSC/GraphHop).