Nowadays, automated essay evaluation (AEE) systems play an important role in evaluating essays and have been successfully used in large-scale writing assessments. However, existing AEE systems mostly focus on grammar or shallow content measurements rather than higher-order traits such as ideas. 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’s 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—Ideas) is higher than the baselines. The results indicate that the proposed method deepens the construct-relevant coverage of automatic ideas evaluation in compositions and that it can provide constructive feedback for students.