# Addressing Graph Heterogeneity and Heterophily from A Spectral Perspective

arXiv: https://arxiv.org/abs/2410.13373 · HTML: https://mlsanity.com/paper/2410.13373/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [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)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [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)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (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)
- [Are we really making much progress? Revisiting, benchmarking, and refining heterogeneous graph neural networks](https://mlsanity.com/paper/2112.14936/) (2021)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [Self-supervised Heterogeneous Graph Neural Network with Co-contrastive Learning](https://mlsanity.com/paper/2105.09111/) (2021)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [A Survey of Graph Neural Networks for Social Recommender Systems](https://mlsanity.com/paper/2212.04481/) (2022)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [HINormer: Representation Learning On Heterogeneous Information Networks with Graph Transformer](https://mlsanity.com/paper/2302.11329/) (2023)
- [Long-range Meta-path Search on Large-scale Heterogeneous Graphs](https://mlsanity.com/paper/2307.08430/) (2023)
- [Hetero2Net: Heterophily-aware Representation Learning on Heterogenerous Graphs](https://mlsanity.com/paper/2310.11664/) (2023)

## Built on by (most cited first, 1 of 1)

- [Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edges](https://mlsanity.com/paper/2509.13139/) (2025)

## Abstract (arXiv)

Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly hinder the performance of GNNs. Heterogeneity refers to a graph with multiple types of nodes or edges, while heterophily refers to the fact that connected nodes are more likely to have dissimilar attributes or labels. Although there have been few works studying heterogeneous heterophilic graphs, they either only consider the heterophily of specific meta-paths and lack expressiveness, or have high expressiveness but fail to exploit high-order neighbors. In this paper, we propose a Heterogeneous Heterophilic Spectral Graph Neural Network (H2SGNN), which employs two modules: local independent filtering and global hybrid filtering. Local independent filtering adaptively learns node representations under different homophily, while global hybrid filtering exploits high-order neighbors to learn more possible meta-paths. Extensive experiments are conducted on four datasets to validate the effectiveness of the proposed H2SGNN, which achieves superior performance with fewer parameters and memory consumption. The code is available at the GitHub repo: https://github.com/Lukangkang123/H2SGNN/.