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This paper proposes a new formulation of graph-based features for concept maps using word embeddings to evaluate the quality of ideas for Chinese compositions. The concept map derived from the student\u2019s composition is composed of the concepts appearing in the essay and the co-occurrence relationship between the concepts. By utilizing real compositions written by eighth-grade students from a large-scale assessment, the scoring accuracy of the computer evaluation system (named AECC-I: Automated Evaluation for Chinese Compositions\u2014Ideas) is higher than the baselines. 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