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.

Federated learning (FL) is a rapidly growing privacy-preserving collaborative machine learning paradigm. In practical FL applications, local data from each data silo reflect local usage patterns. Therefore, there exists heterogeneity of data distributions among data owners (a.k.a. FL clients). If not handled properly, this can lead to model performance degradation. This challenge has inspired the research field of heterogeneous federated learning, which currently remains open. In this paper, we propose a data heterogeneity-robust FL approach, FedGSP, to address this challenge by leveraging on a novel concept of dynamic Sequential-to-Parallel (STP) collaborative training. FedGSP assigns FL clients to homogeneous groups to minimize the overall distribution divergence among groups, and increases the degree of parallelism by reassigning more groups in each round. It is also incorporated with a novel Inter-Cluster Grouping (ICG) algorithm to assist in group assignment, which uses the centroid equivalence theorem to simplify the NP-hard grouping problem to make it solvable. Extensive experiments have been conducted on the non-i.i.d. FEMNIST dataset. The results show that FedGSP improves the accuracy by 3.7% on average compared with seven state-of-the-art approaches, and reduces the training time and communication overhead by more than 90%.