Graph databases with the property graph model are used in multiple domains including social networks, biology, and data integration. They provide schema-exible storage for data of a different degree of a structure and support complex, expressive queries such as subgraph isomorphism queries. The exibility and expressiveness of graph databases make it difficult for the users to express queries correctly and can lead to unexpected query results, e.g. empty results. Therefore, we propose a relaxation approach for subgraph isomorphism queries that is able to automatically rewrite a graph query, such that the rewritten query is similar to the original query and returns a non-empty result set. In detail, we present relaxation operations applicable to a query, cardinality estimation heuristics, and strategies for prioritizing graph query elements to be relaxed. To determine the similarity between the original query and its relaxed variants, we propose a novel cardinality-based graph edit distance. The feasibility of our approach is shown by using real-world queries from the DBpedia query log.