Abstract : Graph databases have aroused a large interest in the last years thanks to their large scope of potential applications (e.g. social networks, biomedical networks, data stemming from the web). In a similar way as what has already been proposed in relational databases, defining a language allowing a flexible querying of graph databases may greatly improve usability of data. This paper focuses on the notion of fuzzy graph database and describes a fuzzy query language that makes it possible to handle such database, which may be fuzzy or not, in a flexible way. This language, called FUDGE, can be used to express preference queries on fuzzy graph databases. The preferences concern i) the content of the vertices of the graph and ii) the structure of the graph. The FUDGE language is implemented in a system, called SUGAR, that we present in this article. We also discuss implementation issues of the FUDGE language in SUGAR.