Impact of converting graphs into spanning trees on node and graph classification in Graph Neural Network

Abstract

This paper investigates the impact of graph reduction to their spanning trees on Graph Neural Network (GNN) performance in node and graph classification across six GNN architectures. The proposed approach leverages spanning trees for graph sparsification while preserving critical structural information, achieving performance comparable to or better than full-graph models. A theoretical connection is established between edge sampling via determinantal point processes (DPPs) and the transfer-current matrix, showing minimum spanning trees effectively approximate DPP-selected subgraphs. Four edge-weighting schemes are analyzed such that their sparsification trade-offs are revealed. The method consistently reduces memory usage and computation while maintaining accuracy. Findings indicate that spanning tree pruning offers a scalable, theoretically grounded strategy for efficient GNN training without compromising classification accuracy. Experiments on node classification benchmarks (Cora, Citeseer, PubMed, PPI) and graph classification biological and chemical datasets (AIDS, MUTAG, PROTEINS, NCI1, IMDB-BINARY) demonstrate excellent graph classification results, notably 98.27% accuracy on AIDS, with reduced computational overhead.