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. In this paper, we present a system called SUGAR developed for querying graph databases in a flexible way. Here, the preferences are based on fuzzy set theory and may concern i) the content of the vertices and ii) the structure of the graph.