Beyond PageRank in GraphHD: Centrality Metrics and Efficient Hyperdimensional Encodings

Abstract

Graph classification plays a central role in many scientific disciplines. While classical kernel-based methods and graph neural networks achieve strong predictive performance, they often require substantial computational resources. Hyperdimensional Computing (HDC) has recently emerged as an efficient and noise-resilient alternative, providing lightweight models that are attractive for resource-constrained settings. Within this context, GraphHD is a representative HDC-based approach for graph classification; however, its encoding process can become costly on large graphs and its standard configuration relies on a single centrality choice (PageRank) for node-to-hypervector assignment. In this work, we go beyond PageRank in GraphHD by systematically evaluating alternative centrality measures (degree, closeness, betweenness, Katz, and eigenvector) and by introducing two new encoding variants. GraphHD-Level preserves quantitative structural information by mapping centrality values to level-hypervectors, whereas GraphHD-Order simplifies the algorithm by eliminating edge encoding and aggregating node hypervectors directly. Experiments on six widely used benchmarks from cheminformatics and bioinformatics (MUTAG, ENZYMES, PROTEINS, DD, NCI1, and PTC\_FM) show that replacing PageRank with alternative centralities yields similar F1-scores while offering notable runtime savings, and that GraphHD-Order remains competitive with the original GraphHD baseline while providing consistent speedups in encoding time.