We investigate the problem of constructing a shape graph that describes the structure of a given graph database. We employ the framework of grammatical inference, where the objective is to find an inference algorithm that is both sound, i.e., always producing a schema that validates the input graph, and complete, i.e., able to produce any schema, within a given class of schemas, provided that a sufficiently informative input graph is presented. We identify a number of fundamental limitations that preclude feasible inference. We present inference algorithms based on natural approaches that allow to infer schemas that we argue to be of practical importance.