HFGNN: Efficient Graph Neural Networks Using Hub-Fringe Structures

Existing message passing-based and transformer-based graph neural networks (GNNs) cannot satisfy requirements for learning representative graph embeddings due to restricted receptive fields, redundant message passing, and reliance on fixed aggregations. These methods face scalability and expressivity limitations from intractable exponential growth or quadratic complexity, restricting interaction ranges and information coverage across large graphs. Motivated by the analysis of long-range graph structures, we introduce a novel Graph Neural Network called Hub-Fringe Graph Neural Network (HFGNN). Our Hub-Fringe structure, drawing inspiration from the graph indexing technique known as Hub Labeling, offers a straightforward and effective approach for learning scalable graph representations while ensuring comprehensive coverage of information. HFGNN leverages this structure to enable selective propagation of relevant embeddings through a carefully designed message function. Theoretical analysis is presented to show the expressivity and scalability of the proposed method. Empirically, HFGNN exceeds standard GNNs on tasks including classification and regression, especially for large, long-range graphs where scalability and coverage matter. Ablation studies further confirm the benefits of our hub-fringe based graph neural network, including improved expressivity and scalability. The source codes is available at https://github.com/nick12340/HFGNN.