This paper shows by a constructive method the existence of a diagrammatic representation called extended Euler diagrams for any collection of sets X_1,...,X_n , n<9. These diagrams are adapted for representing sets inclusions and intersections: each set X_i and each non empty intersection of a subcollection of X_1,...,X_n is represented by a unique connected region of the plane. Starting with a description of the diagram, we define the dual graph G and reason with the properties of this graph to build a planar representation of the X_1,...,X_n. These diagrams will be used to visualize the results of a complex request on any indexed video database. In fact, such a representation allows the user to perceive simultaneously the results of his query and the relevance of the database according to the query. Venn, hypergraphes, planarité de graphe, visualisation de donnée
