Recent work has used graphs to modelize expression data from microarray experiments, in view of partitioning the genes into clusters. In this paper, we introduce the use of a decomposition by clique separators. Our aim is to improve the classical clustering methods in two ways: first we want to allow an overlap between clusters, as this seems biologically sound, and second we want to be guided by the structure of the graph to define the number of clusters. We test this approach with a well-known yeast database (Saccharomyces cerevisiae). Our results are good, as the expression profiles of the clusters we find are very coherent. Moreover, we are able to organize into another graph the clusters we find, and order them in a fashion which turns out to respect the chronological order defined by the the sporulation process.