The topological structure of a mechanism is often represented using graphs. In the field of tolerance, the graph constitutes a support for the analysis or the qualitative synthesis of dimensional and geometric tolerances. Unfortunately, the number of elementary features and relations is important even for usual mechanical systems, and they are represented by very complex graphs. In this paper, we propose to represent the mechanisms by hyper-graphs whose vertices themselves are graphs. One creates a set of different graphs, one in the other, like "nested dolls" from the low level of an elementary graph, to the highest level and the most detailed. This structure of hyper-graph is used as a support with a method of tolerances synthesis. This approach allows to deal with a complex tolerancing problem like a succession of more simple problems of tolerance synthesis. An example will illustrate this approach for the qualitative aspects. The graph allows to represent the topological structure of the mechanism and to consider the functional data such as the type of assembly and the functional requirements. Although already used by various authors, the graphs are today generally considered only as tutorial to guide the choice of the specifications. Our intention is to give to the graphs a role much more significant and even fundamental for the qualitative and quantitative analysis and synthesis of the tolerances. To our knowledge, the concept of hyper-graph is a very new approach in this field.
