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While virtually all existing work on Automated Essay Scoring (AES) models an essay as a word sequence, we put forward the novel view that an essay can be modeled as a graph and subsequently propose GAT-AES, a graph-attention network approach to AES. A key advantage of a graph-based approach to AES is that it allows us to easily capture the interactions among essay traits directly. Experimental results show that GAT-AES has achieved the best multi-trait scoring results to date on the ASAP++ dataset.