Comparing graph databases with traditional, e.g., relational databases, some important database features are often missing there. Particularly, a graph database schema including integrity constraints is not explicitly defined, also a conceptual modelling is not used at all. It is hard to check a consistency of the graph database, because almost no integrity constraints are defined. In the paper, we discuss these issues and present current possibilities and challenges in graph database modelling. Also a conceptual level of a graph database design is considered. We propose a sufficient conceptual model and show its relationship to a graph database model. We focus also on integrity constraints modelling functional dependencies between entity types, which reminds modelling functional dependencies known from relational databases and extend them to conditional functional dependencies.