Addressing Heterogeneity and Heterophily in Graphs: A Heterogeneous Heterophilic Spectral Graph Neural Network

Graph Neural Networks (GNNs) have garnered significant scholarly attention for their powerful capabilities in modeling graph structures. Despite this, two primary challenges persist: heterogeneity and heterophily. Existing studies often address heterogeneous and heterophilic graphs separately, leaving a research gap in the understanding of heterogeneous heterophilic graphs-those that feature diverse node or relation types with dissimilar connected nodes. To address this gap, we investigate the application of spectral graph filters within heterogeneous graphs. Specifically, we propose a Heterogeneous Heterophilic Spectral Graph Neural Network (H2SGNN), which employs a dual-module approach: local independent filtering and global hybrid filtering. The local independent filtering module applies polynomial filters to each subgraph independently to adapt to different homophily, while the global hybrid filtering module captures interactions across different subgraphs. Extensive empirical evaluations on four real-world datasets demonstrate the superiority of H2SGNN compared to state-of-the-art methods.

Federated Learning over Coupled Graphs

Graphs are widely used to represent the relations among entities. When one owns the complete data, an entire graph can be easily built, therefore performing analysis on the graph is straightforward. However, in many scenarios, it is impractical to centralize the data due to data privacy concerns. An organization or party only keeps a part of the whole graph data, i.e., graph data is isolated from different parties. Recently, Federated Learning (FL) has been proposed to solve the data isolation issue, mainly for Euclidean data. It is still a challenge to apply FL on graph data because graphs contain topological information which is notorious for its non-IID nature and is hard to partition. In this work, we propose a novel FL framework for graph data, FedCog, to efficiently handle coupled graphs that are a kind of distributed graph data, but widely exist in a variety of real-world applications such as mobile carriers' communication networks and banks' transaction networks. We theoretically prove the correctness and security of FedCog. Experimental results demonstrate that our method FedCog significantly outperforms traditional FL methods on graphs. Remarkably, our FedCog improves the accuracy of node classification tasks by up to 14.7%.