# Homophily Heterogeneity Matters in Graph Federated Learning: A Spectrum Sharing and Complementing Perspective

arXiv: https://arxiv.org/abs/2502.13732 · HTML: https://mlsanity.com/paper/2502.13732/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 51 references that are in the map.
- First posted on arXiv 19 Feb 2025.

## Builds on (most cited first, 30 of 36)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [No Fear of Heterogeneity: Classifier Calibration for Federated Learning with Non-IID Data](https://mlsanity.com/paper/2106.05001/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Heterogeneous Federated Learning: State-of-the-art and Research Challenges](https://mlsanity.com/paper/2307.10616/) (2023)
- [Federated Meta-Learning with Fast Convergence and Efficient Communication](https://mlsanity.com/paper/1802.07876/) (2018)
- [Subgraph Federated Learning with Missing Neighbor Generation](https://mlsanity.com/paper/2106.13430/) (2021)
- [FedALA: Adaptive Local Aggregation for Personalized Federated Learning](https://mlsanity.com/paper/2212.01197/) (2022)
- [Federated Graph Classification over Non-IID Graphs](https://mlsanity.com/paper/2106.13423/) (2021)
- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [Federated Learning for Generalization, Robustness, Fairness: A Survey and Benchmark](https://mlsanity.com/paper/2311.06750/) (2023)
- [Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyond](https://mlsanity.com/paper/2209.06177/) (2022)
- [Personalized Subgraph Federated Learning](https://mlsanity.com/paper/2206.10206/) (2022)
- [FedGTA: Topology-aware Averaging for Federated Graph Learning](https://mlsanity.com/paper/2401.11755/) (2024)
- [Generalizable Heterogeneous Federated Cross-Correlation and Instance Similarity Learning](https://mlsanity.com/paper/2309.16286/) (2023)
- [Graph Neural Networks with Learnable and Optimal Polynomial Bases](https://mlsanity.com/paper/2302.12432/) (2023)
- [Federated Graph Semantic and Structural Learning](https://mlsanity.com/paper/2406.18937/) (2024)
- [FedFM: Anchor-based Feature Matching for Data Heterogeneity in Federated Learning](https://mlsanity.com/paper/2210.07615/) (2022)
- [FedTAD: Topology-aware Data-free Knowledge Distillation for Subgraph Federated Learning](https://mlsanity.com/paper/2404.14061/) (2024)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [Rethinking Data Heterogeneity in Federated Learning: Introducing a New Notion and Standard Benchmarks](https://mlsanity.com/paper/2209.15595/) (2022)
- [How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing](https://mlsanity.com/paper/2405.12474/) (2024)

## Built on by (most cited first, 4 of 4)

- [Heterogeneity-Aware Knowledge Sharing for Graph Federated Learning](https://mlsanity.com/paper/2601.21589/) (2026)
- [Low-pass Personalized Subgraph Federated Recommendation](https://mlsanity.com/paper/2603.20338/) (2026)
- [Graph Federated Unlearning for Privacy Preservation](https://mlsanity.com/paper/2605.02297/) (2026)
- [Beyond Rigid Alignment: Graph Federated Learning via Dual Manifold Calibration](https://mlsanity.com/paper/2605.06260/) (2026)

## Abstract (arXiv)

Since heterogeneity presents a fundamental challenge in graph federated learning, many existing methods are proposed to deal with node feature heterogeneity and structure heterogeneity. However, they overlook the critical homophily heterogeneity, which refers to the substantial variation in homophily levels across graph data from different clients. The homophily level represents the proportion of edges connecting nodes that belong to the same class. Due to adapting to their local homophily, local models capture inconsistent spectral properties across different clients, significantly reducing the effectiveness of collaboration. Specifically, local models trained on graphs with high homophily tend to capture low-frequency information, whereas local models trained on graphs with low homophily tend to capture high-frequency information. To effectively deal with homophily heterophily, we introduce the spectral Graph Neural Network (GNN) and propose a novel Federated learning method by mining Graph Spectral Properties (FedGSP). On one hand, our proposed FedGSP enables clients to share generic spectral properties (i.e., low-frequency information), allowing all clients to benefit through collaboration. On the other hand, inspired by our theoretical findings, our proposed FedGSP allows clients to complement non-generic spectral properties by acquiring the spectral properties they lack (i.e., high-frequency information), thereby obtaining additional information gain. Extensive experiments conducted on six homophilic and five heterophilic graph datasets, across both non-overlapping and overlapping settings, validate the superiority of our method over eleven state-of-the-art methods. Notably, our FedGSP outperforms the second-best method by an average margin of 3.28% on all heterophilic datasets.