Cloud computing is widely used in all walks of life today. Massive amounts of medical graph data are being outsourced to cloud servers to reduce overhead. The untrustworthiness of cloud servers puts the sensitive information of outsourced graph data at risk. To eliminate this security risk, it is an effective method to encrypt sensitive data. The adjacent queries are frequently used and highly valuable in graph data operations, and the adjacency query supporting homoionym search will enlarge the query effect and improve the query function. When the medical graph data is encrypted and stored on the cloud server, the operation of the data becomes extremely difficult.In this article, we propose a scheme to implement the adjacency query supporting homoionym search in cloud computing (AQHS), which maintains search contents privacy. We use a stem extraction algorithm and the searchable encryption mechanism to build secure index, and then achieve the adjacency query. The security of our proposed scheme is verified by formal analysis, and the effectiveness of the scheme is verified by experimental analysis.