# Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs

arXiv: https://arxiv.org/abs/2006.11468 · HTML: https://mlsanity.com/paper/2006.11468/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2020.

## Built on by (most cited first, 25 of 25)

- [Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalization](https://mlsanity.com/paper/2102.06966/) (2021)
- [Sheaf Neural Networks with Connection Laplacians](https://mlsanity.com/paper/2206.08702/) (2022)
- [Block Modeling-Guided Graph Convolutional Neural Networks](https://mlsanity.com/paper/2112.13507/) (2021)
- [Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Neural Networks](https://mlsanity.com/paper/2212.10822/) (2022)
- [Synthetic Graph Generation to Benchmark Graph Learning](https://mlsanity.com/paper/2204.01376/) (2022)
- [Structure Inducing Pre-Training](https://mlsanity.com/paper/2103.10334/) (2021)
- [Self-Pro: A Self-Prompt and Tuning Framework for Graph Neural Networks](https://mlsanity.com/paper/2310.10362/) (2023)
- [Revisiting the role of heterophily in graph representation learning: An edge classification perspective](https://mlsanity.com/paper/2205.11322/) (2022)
- [Large-Scale Spectral Graph Neural Networks via Laplacian Sparsification: Technical Report](https://mlsanity.com/paper/2501.04570/) (2025)
- [Mini-batch graphs for robust image classification](https://mlsanity.com/paper/2105.03237/) (2021)
- [Graph Feature Gating Networks](https://mlsanity.com/paper/2105.04493/) (2021)
- [Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothing](https://mlsanity.com/paper/2308.03306/) (2023)
- [DeCaf: A Causal Decoupling Framework for OOD Generalization on Node Classification](https://mlsanity.com/paper/2410.20295/) (2024)
- [FedRGL: Robust Federated Graph Learning for Label Noise](https://mlsanity.com/paper/2411.18905/) (2024)
- [GPNet: Simplifying Graph Neural Networks via Multi-channel Geometric Polynomials](https://mlsanity.com/paper/2209.15454/) (2022)
- [When Do We Need Graph Neural Networks for Node Classification?](https://mlsanity.com/paper/2210.16979/) (2022)
- [On Addressing the Limitations of Graph Neural Networks](https://mlsanity.com/paper/2306.12640/) (2023)
- [Towards Robust Graph Structural Learning Beyond Homophily via Preserving Neighbor Similarity](https://mlsanity.com/paper/2401.09754/) (2024)
- [Flow Matters: Directional and Expressive GNNs for Heterophilic Graphs](https://mlsanity.com/paper/2509.00772/) (2025)
- [AKE-GNN: Effective Graph Learning with Adaptive Knowledge Exchange](https://mlsanity.com/paper/2106.05455/) (2021)
- [On Learning the Structure of Clusters in Graphs](https://mlsanity.com/paper/2212.14345/) (2022)
- [Evolving Computation Graphs](https://mlsanity.com/paper/2306.12943/) (2023)
- [Automated Polynomial Filter Learning for Graph Neural Networks](https://mlsanity.com/paper/2307.07956/) (2023)
- [Continuous Spiking Graph Neural Networks](https://mlsanity.com/paper/2404.01897/) (2024)
- [Learning From Graph-Structured Data: Addressing Design Issues and Exploring Practical Applications in Graph Representation Learning](https://mlsanity.com/paper/2411.07269/) (2024)

## Abstract (arXiv)

We investigate the representation power of graph neural networks in the semi-supervised node classification task under heterophily or low homophily, i.e., in networks where connected nodes may have different class labels and dissimilar features. Many popular GNNs fail to generalize to this setting, and are even outperformed by models that ignore the graph structure (e.g., multilayer perceptrons). Motivated by this limitation, we identify a set of key designs -- ego- and neighbor-embedding separation, higher-order neighborhoods, and combination of intermediate representations -- that boost learning from the graph structure under heterophily. We combine them into a graph neural network, H2GCN, which we use as the base method to empirically evaluate the effectiveness of the identified designs. Going beyond the traditional benchmarks with strong homophily, our empirical analysis shows that the identified designs increase the accuracy of GNNs by up to 40% and 27% over models without them on synthetic and real networks with heterophily, respectively, and yield competitive performance under homophily.