The successful integration of graph neural networks into recommender systems (RSs) has led to a novel paradigm in collaborative filtering (CF), graph collaborative filtering (graph CF). By representing user-item data as an undirected, bipartite graph, graph CF utilizes short- and long-range connections to extract collaborative signals that yield more accurate user preferences than traditional CF methods. Although the recent literature highlights the efficacy of various algorithmic strategies in graph CF, the impact of datasets and their topological features on recommendation performance is yet to be studied. To fill this gap, we propose a topology-aware analysis of graph CF. In this study, we (i) take some widely-adopted recommendation datasets and use them to generate a large set of synthetic sub-datasets through two state-of-the-art graph sampling methods, (ii) measure eleven of their classical and topological characteristics, and (iii) estimate the accuracy calculated on the generated sub-datasets considering four popular and recent graph-based RSs (i.e., LightGCN, DGCF, UltraGCN, and SVD-GCN). Finally, the investigation presents an explanatory framework that reveals the linear relationships between characteristics and accuracy measures. The results, statistically validated under different graph sampling settings, confirm the existence of solid dependencies between topological characteristics and accuracy in the graph-based recommendation, offering a new perspective on how to interpret graph CF.

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