# Unifying Graph Convolutional Neural Networks and Label Propagation

arXiv: https://arxiv.org/abs/2002.06755 · HTML: https://mlsanity.com/paper/2002.06755/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2020.

## Built on by (most cited first, 30 of 98)

- [Graph Unlearning](https://mlsanity.com/paper/2103.14991/) (2021)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Simple and Efficient Heterogeneous Graph Neural Network](https://mlsanity.com/paper/2207.02547/) (2022)
- [Extract the Knowledge of Graph Neural Networks and Go Beyond it: An Effective Knowledge Distillation Framework](https://mlsanity.com/paper/2103.02885/) (2021)
- [Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoods](https://mlsanity.com/paper/2111.04840/) (2021)
- [Topology-Imbalance Learning for Semi-Supervised Node Classification](https://mlsanity.com/paper/2110.04099/) (2021)
- [A Comprehensive Study on Large-Scale Graph Training: Benchmarking and Rethinking](https://mlsanity.com/paper/2210.07494/) (2022)
- [Scalable and Adaptive Graph Neural Networks with Self-Label-Enhanced training](https://mlsanity.com/paper/2104.09376/) (2021)
- [A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2212.10701/) (2022)
- [p-Laplacian Based Graph Neural Networks](https://mlsanity.com/paper/2111.07337/) (2021)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [Alleviating Structural Distribution Shift in Graph Anomaly Detection](https://mlsanity.com/paper/2401.14155/) (2024)
- [Graph Positional Encoding via Random Feature Propagation](https://mlsanity.com/paper/2303.02918/) (2023)
- [Self-supervised Heterogeneous Graph Pre-training Based on Structural Clustering](https://mlsanity.com/paper/2210.10462/) (2022)
- [Grain: Improving Data Efficiency of Graph Neural Networks via Diversified Influence Maximization](https://mlsanity.com/paper/2108.00219/) (2021)
- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [Imbalanced Graph Classification via Graph-of-Graph Neural Networks](https://mlsanity.com/paper/2112.00238/) (2021)
- [Graph Few-shot Learning with Task-specific Structures](https://mlsanity.com/paper/2210.12130/) (2022)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [RIM: Reliable Influence-based Active Learning on Graphs](https://mlsanity.com/paper/2110.14854/) (2021)
- [Rethinking and Accelerating Graph Condensation: A Training-Free Approach with Class Partition](https://mlsanity.com/paper/2405.13707/) (2024)
- [FeatureNorm: L2 Feature Normalization for Dynamic Graph Embedding](https://mlsanity.com/paper/2103.00164/) (2021)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks](https://mlsanity.com/paper/2201.08932/) (2022)
- [LightEA: A Scalable, Robust, and Interpretable Entity Alignment Framework via Three-view Label Propagation](https://mlsanity.com/paper/2210.10436/) (2022)
- [Interpreting Unfairness in Graph Neural Networks via Training Node Attribution](https://mlsanity.com/paper/2211.14383/) (2022)
- [Information Gain Propagation: a new way to Graph Active Learning with Soft Labels](https://mlsanity.com/paper/2203.01093/) (2022)
- [ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting](https://mlsanity.com/paper/2205.13700/) (2022)
- [MAPLE: Many-Shot Adaptive Pseudo-Labeling for In-Context Learning](https://mlsanity.com/paper/2505.16225/) (2025)

## Abstract (arXiv)

Label Propagation (LPA) and Graph Convolutional Neural Networks (GCN) are both message passing algorithms on graphs. Both solve the task of node classification but LPA propagates node label information across the edges of the graph, while GCN propagates and transforms node feature information. However, while conceptually similar, theoretical relation between LPA and GCN has not yet been investigated. Here we study the relationship between LPA and GCN in terms of two aspects: (1) feature/label smoothing where we analyze how the feature/label of one node is spread over its neighbors; And, (2) feature/label influence of how much the initial feature/label of one node influences the final feature/label of another node. Based on our theoretical analysis, we propose an end-to-end model that unifies GCN and LPA for node classification. In our unified model, edge weights are learnable, and the LPA serves as regularization to assist the GCN in learning proper edge weights that lead to improved classification performance. Our model can also be seen as learning attention weights based on node labels, which is more task-oriented than existing feature-based attention models. In a number of experiments on real-world graphs, our model shows superiority over state-of-the-art GCN-based methods in terms of node classification accuracy.