By providing personalized suggestions to users, recommender systems have become essential to numerous online platforms. Collaborative filtering, particularly graph-based approaches using Graph Neural Networks (GNNs), have demonstrated great results in terms of recommendation accuracy. However, accuracy may not always be the most important criterion for evaluating recommender systems' performance, since beyond-accuracy aspects such as recommendation diversity, serendipity, and fairness can strongly influence user engagement and satisfaction. This review paper focuses on addressing these dimensions in GNN-based recommender systems, going beyond the conventional accuracy-centric perspective. We begin by reviewing recent developments in approaches that improve not only the accuracy-diversity trade-off but also promote serendipity and fairness in GNN-based recommender systems. We discuss different stages of model development including data preprocessing, graph construction, embedding initialization, propagation layers, embedding fusion, score computation, and training methodologies. Furthermore, we present a look into the practical difficulties encountered in assuring diversity, serendipity, and fairness, while retaining high accuracy. Finally, we discuss potential future research directions for developing more robust GNN-based recommender systems that go beyond the unidimensional perspective of focusing solely on accuracy. This review aims to provide researchers and practitioners with an in-depth understanding of the multifaceted issues that arise when designing GNN-based recommender systems, setting our work apart by offering a comprehensive exploration of beyond-accuracy dimensions.
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