Graph database engines stand out in the era of big data for their efficiency of modeling and processing linked data. There is a strong need of testing graph database engines. However, random testing, the most practical way of automated test generation, faces the challenges of semantic validity, non-empty result, and behavior diversity to detect bugs in graph database engines. To address these challenges, in this paper, we propose GDsmith, the first black-box approach for testing graph database engines. It ensures that each randomly generated Cypher query satisfies the semantic requirements via skeleton generation and completion. GDsmith includes our technique to increase the probability of producing Cypher queries that return non-empty results by leveraging three types of structural mutation strategies. GDsmith also includes our technique to improve the behavior diversity of the generated Cypher queries by selecting property keys according to their previous frequencies when generating new queries. Our evaluation results demonstrate that GDsmith is effective and efficient for automated query generation and substantially outperforms the baseline. GDsmith successfully detects 27 previously unknown bugs on the released versions of three popular open-source graph database engines and receive positive feedback from their developers.