Modern software applications often interface with graph-structured data managed by graph databases queried with specific graph query languages. Writing, understanding, and maintaining graph queries can be difficult and error-prone. Important decisions taken by the software application are in many cases based on the outcome of these graph queries. If test design does not account for the complexity incorporated in these queries, considerable parts of the business logic of such applications will not be tested appropriately.We aim at tackling the challenge of developing dedicated testing techniques for graph queries. In particular, we present a first model-based testing approach for read only queries supporting automated test creation, execution, and evaluation. We model queries using a well-established graph logic, being expressively equivalent to first-order logic on graphs. We develop a first coverage criterion requiring the presence of a test case returning an empty query result as well as the presence of a test case returning a non-empty result. We present the architecture of our model-based testing approach, which is supported by a first implementation. We illustrate our approach with complex read only graph queries from an industrial benchmark case study.