# Label-Wise Graph Convolutional Network for Heterophilic Graphs

arXiv: https://arxiv.org/abs/2110.08128 · HTML: https://mlsanity.com/paper/2110.08128/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 50 references that are in the map.
- First posted on arXiv 15 Oct 2021.

## Builds on (most cited first, 30 of 37)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [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)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Information](https://mlsanity.com/paper/2009.01454/) (2020)
- [A Semi-supervised Graph Attentive Network for Financial Fraud Detection](https://mlsanity.com/paper/2003.01171/) (2020)
- [GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networks](https://mlsanity.com/paper/2103.08826/) (2021)

## Built on by (most cited first, 17 of 17)

- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Unnoticeable Backdoor Attacks on Graph Neural Networks](https://mlsanity.com/paper/2303.01263/) (2023)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [A Unified Framework of Graph Information Bottleneck for Robustness and Membership Privacy](https://mlsanity.com/paper/2306.08604/) (2023)
- [Sign is Not a Remedy: Multiset-to-Multiset Message Passing for Learning on Heterophilic Graphs](https://mlsanity.com/paper/2405.20652/) (2024)
- [Spatial Heterophily Aware Graph Neural Networks](https://mlsanity.com/paper/2306.12139/) (2023)
- [Robustness Inspired Graph Backdoor Defense](https://mlsanity.com/paper/2406.09836/) (2024)
- [Shape-aware Graph Spectral Learning](https://mlsanity.com/paper/2310.10064/) (2023)
- [The Heterophilic Snowflake Hypothesis: Training and Empowering GNNs for Heterophilic Graphs](https://mlsanity.com/paper/2406.12539/) (2024)
- [Clarify Confused Nodes via Separated Learning](https://mlsanity.com/paper/2306.02285/) (2023)
- [Heterophilic Graph Neural Networks Optimization with Causal Message-passing](https://mlsanity.com/paper/2411.13821/) (2024)
- [GraphSOS: Graph Sampling and Order Selection to Help LLMs Understand Graphs Better](https://mlsanity.com/paper/2501.14427/) (2025)
- [CAT: A Causally Graph Attention Network for Trimming Heterophilic Graph](https://mlsanity.com/paper/2312.08672/) (2023)
- [Edge-Splitting MLP: Node Classification on Homophilic and Heterophilic Graphs without Message Passing](https://mlsanity.com/paper/2412.08310/) (2024)
- [ElegansNet: a brief scientific report and initial experiments](https://mlsanity.com/paper/2304.13538/) (2023)
- [Poisoning the Inner Prediction Logic of Graph Neural Networks for Clean-Label Backdoor Attacks](https://mlsanity.com/paper/2603.05004/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have achieved remarkable performance in modeling graphs for various applications. However, most existing GNNs assume the graphs exhibit strong homophily in node labels, i.e., nodes with similar labels are connected in the graphs. They fail to generalize to heterophilic graphs where linked nodes may have dissimilar labels and attributes. Therefore, in this paper, we investigate a novel framework that performs well on graphs with either homophily or heterophily. More specifically, we propose a label-wise message passing mechanism to avoid the negative effects caused by aggregating dissimilar node representations and preserve the heterophilic contexts for representation learning. We further propose a bi-level optimization method to automatically select the model for graphs with homophily/heterophily. Theoretical analysis and extensive experiments demonstrate the effectiveness of our proposed framework for node classification on both homophilic and heterophilic graphs.