# H3GNNs: Harmonizing Heterophily and Homophily in GNNs via Joint Structural Node Encoding and Self-Supervised Learning

arXiv: https://arxiv.org/abs/2504.11699 · HTML: https://mlsanity.com/paper/2504.11699/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Graph neural network distillation, one of 12 directions in Knowledge distillation.
- Builds on 48 of its 68 references that are in the map.
- First posted on arXiv 16 Apr 2025.

## Placed in

- Knowledge distillation / [Graph neural network distillation](https://mlsanity.com/distill/graph-neural-network-distillation/)

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (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)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [Large-Scale Representation Learning on Graphs via Bootstrapping](https://mlsanity.com/paper/2102.06514/) (2021)

## Abstract (arXiv)

Graph Neural Networks (GNNs) struggle to balance heterophily and homophily in representation learning, a challenge further amplified in self-supervised settings. We propose H3GNNs, an end-to-end self-supervised learning framework that harmonizes both structural properties through two key innovations: (i) Joint Structural Node Encoding. We embed nodes into a unified space combining linear and non-linear feature projections with K-hop structural representations via a Weighted Graph Convolution Network(WGCN). A cross-attention mechanism enhances awareness and adaptability to heterophily and homophily. (ii) Self-Supervised Learning Using Teacher-Student Predictive Architectures with Node-Difficulty Driven Dynamic Masking Strategies. We use a teacher-student model, the student sees the masked input graph and predicts node features inferred by the teacher that sees the full input graph in the joint encoding space. To enhance learning difficulty, we introduce two novel node-predictive-difficulty-based masking strategies. Experiments on seven benchmarks (four heterophily datasets and three homophily datasets) confirm the effectiveness and efficiency of H3GNNs across diverse graph types. Our H3GNNs achieves overall state-of-the-art performance on the four heterophily datasets, while retaining on-par performance to previous state-of-the-art methods on the three homophily datasets.