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Graph databases are becoming more and more popular as they represent a good alternative to relational databases in some problem scenarios. Searching the graph is sometimes very convenient unlike writing complex SQL queries that require a table to be joined to itself several times. However, graph databases do not support all the constraints that are familiar and used in relational databases. In this paper we discuss integrity constraints in graph databases and technical implementation issues that prevent these constraints from being specified. However, in the end we have found a way to implement one constraint type, as we show later on.