# Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification

arXiv: https://arxiv.org/abs/2312.04111 · HTML: https://mlsanity.com/paper/2312.04111/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 88 references that are in the map.
- First posted on arXiv 7 Dec 2023.

## Builds on (most cited first, 30 of 57)

- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [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)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Unifying Graph Convolutional Neural Networks and Label Propagation](https://mlsanity.com/paper/2002.06755/) (2020)

## Built on by (most cited first, 19 of 19)

- [FedTAD: Topology-aware Data-free Knowledge Distillation for Subgraph Federated Learning](https://mlsanity.com/paper/2404.14061/) (2024)
- [OpenGU: A Comprehensive Benchmark for Graph Unlearning](https://mlsanity.com/paper/2501.02728/) (2025)
- [Depth-Adaptive Graph Neural Networks via Learnable Bakry-'Emery Curvature](https://mlsanity.com/paper/2503.01079/) (2025)
- [Disentangling, Amplifying, and Debiasing: Learning Disentangled Representations for Fair Graph Neural Networks](https://mlsanity.com/paper/2408.12875/) (2024)
- [Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophily](https://mlsanity.com/paper/2511.06608/) (2025)
- [DiRW: Path-Aware Digraph Learning for Heterophily](https://mlsanity.com/paper/2410.10320/) (2024)
- [Improving Graph Neural Networks by Learning Continuous Edge Directions](https://mlsanity.com/paper/2410.14109/) (2024)
- [Towards Data-centric Machine Learning on Directed Graphs: a Survey](https://mlsanity.com/paper/2412.01849/) (2024)
- [Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approach](https://mlsanity.com/paper/2501.11817/) (2025)
- [OpenDDI: A Comprehensive Benchmark for DDI Prediction](https://mlsanity.com/paper/2602.00539/) (2026)
- [RIDA: A Robust Attack Framework on Incomplete Graphs](https://mlsanity.com/paper/2407.18170/) (2024)
- [Scale-aware Message Passing For Graph Node Classification](https://mlsanity.com/paper/2411.19392/) (2024)
- [Toward General Digraph Contrastive Learning: A Dual Spatial Perspective](https://mlsanity.com/paper/2510.16311/) (2025)
- [ScaleNet: Scale Invariance Learning in Directed Graphs](https://mlsanity.com/paper/2411.08758/) (2024)
- [Toward Data-centric Directed Graph Learning: An Entropy-driven Approach](https://mlsanity.com/paper/2505.00983/) (2025)
- [State Space Models over Directed Graphs](https://mlsanity.com/paper/2509.13735/) (2025)
- [Unveiling the Vulnerability of Graph-LLMs: An Interpretable Multi-Dimensional Adversarial Attack on TAGs](https://mlsanity.com/paper/2510.12233/) (2025)
- [Training Diverse Graph Experts for Ensembles: A Systematic Empirical Study](https://mlsanity.com/paper/2510.18370/) (2025)
- [Modeling Heterophily in Multiplex Graphs: An Adaptive Approach for Node Classification](https://mlsanity.com/paper/2605.12699/) (2026)

## Abstract (arXiv)

Recently, graph neural networks (GNNs) have shown prominent performance in semi-supervised node classification by leveraging knowledge from the graph database. However, most existing GNNs follow the homophily assumption, where connected nodes are more likely to exhibit similar feature distributions and the same labels, and such an assumption has proven to be vulnerable in a growing number of practical applications. As a supplement, heterophily reflects dissimilarity in connected nodes, which has gained significant attention in graph learning. To this end, data engineers aim to develop a powerful GNN model that can ensure performance under both homophily and heterophily. Despite numerous attempts, most existing GNNs struggle to achieve optimal node representations due to the constraints of undirected graphs. The neglect of directed edges results in sub-optimal graph representations, thereby hindering the capacity of GNNs. To address this issue, we introduce AMUD, which quantifies the relationship between node profiles and topology from a statistical perspective, offering valuable insights for Adaptively Modeling the natural directed graphs as the Undirected or Directed graph to maximize the benefits from subsequent graph learning. Furthermore, we propose Adaptive Directed Pattern Aggregation (ADPA) as a new directed graph learning paradigm for AMUD. Empirical studies have demonstrated that AMUD guides efficient graph learning. Meanwhile, extensive experiments on 16 benchmark datasets substantiate the impressive performance of ADPA, outperforming baselines by significant margins of 3.96.