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We propose a graph neural network (GNN) approach to the problem of predicting the stylistic compatibility of a set of furniture items from images. While most existing results are based on siamese networks which evaluate pairwise compatibility between items, the proposed GNN architecture exploits relational information among groups of items. We present two GNN models, both of which comprise a deep CNN that extracts a feature representation for each image, a gated recurrent unit (GRU) network that models interactions between the furniture items in a set, and an aggregation function that calculates the compatibility score. In the first model, a generalized contrastive loss function that promotes the generation of clustered embeddings for items belonging to the same furniture set is introduced. Also, in the first model, the edge function between nodes in the GRU and the aggregation function are fixed in order to limit model complexity and allow training on smaller datasets; in the second model, the edge function and aggregation function are learned directly from the data. We demonstrate state-of-the art accuracy for compatibility prediction and "fill in the blank" tasks on the Bonn and Singapore furniture datasets. We further introduce a new dataset, called the Target Furniture Collections dataset, which contains over 6000 furniture items that have been hand-curated by stylists to make up 1632 compatible sets. We also demonstrate superior prediction accuracy on this dataset.