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Visual relationship detection is fundamental for holistic image understanding. However, the localization and classification of (subject, predicate, object) triplets remain challenging tasks, due to the combinatorial explosion of possible relationships, their long-tailed distribution in natural images, and an expensive annotation process. This paper introduces a novel weakly-supervised method for visual relationship detection that relies on minimal image-level predicate labels. A graph neural network is trained to classify predicates in images from a graph representation of detected objects, implicitly encoding an inductive bias for pairwise relations. We then frame relationship detection as the explanation of such a predicate classifier, i.e. we obtain a complete relation by recovering the subject and object of a predicted predicate. We present results comparable to recent fully- and weakly-supervised methods on three diverse and challenging datasets: HICO-DET for human-object interaction, Visual Relationship Detection for generic object-to-object relations, and UnRel for unusual triplets; demonstrating robustness to non-comprehensive annotations and good few-shot generalization.