Graph Sampling for Scalable and Expressive Graph Neural Networks on Homophilic Graphs

Graph Neural Networks (GNNs) excel in many graph machine learning tasks but face challenges when scaling to large networks. GNN transferability allows training on smaller graphs and applying the model to larger ones, but existing methods often rely on random subsampling, leading to disconnected subgraphs and reduced model expressivity. We propose a novel graph sampling algorithm that leverages feature homophily to preserve graph structure. By minimizing the trace of the data correlation matrix, our method better preserves the graph Laplacian's rank than random sampling while achieving lower complexity than spectral methods. Experiments on citation networks show improved performance in preserving graph rank and GNN transferability compared to random sampling.