Beyond Aggregate Recall: Degree Heterogeneity and Representation Geometry in LightGCN

Graph-based recommender systems learn representations from highly heterogeneous interaction graphs, in which a small number of popular items have many connections while most items have few. Standard aggregate metrics can obscure how this structural heterogeneity affects both model performance and learned representations. We study this relationship for LightGCN using two real-world datasets, MovieLens-1M and Amazon Beauty, together with synthetic interaction graphs whose item-degree distributions are systematically varied. Across recommendation methods, performance is substantially higher for well-connected head items than for sparsely connected tail items. In LightGCN, item degree is also reflected in the magnitude of learned embeddings, although the form of this relationship varies across datasets. Removing embedding magnitude from the scoring rule significantly reduces, but does not eliminate, the head–tail performance gap, at the cost of lower overall accuracy. Controlled simulations further show that increasing degree concentration consistently widens this gap and alters representation geometry. Our results demonstrate how graph degree distributions structure both where graph recommenders succeed and how they represent items, while aggregate evaluation obscures these effects.