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Deep speaker embedding models have been commonly used as a building block for speaker diarization systems; however, the speaker embedding model is usually trained according to a global loss defined on the training data, which could be sub-optimal for distinguishing speakers locally in a specific meeting session. In this work we present the first use of graph neural networks (GNNs) for the speaker diarization problem, utilizing a GNN to refine speaker embeddings locally using the structural information between speech segments inside each session.