It is now widely accepted that knowledge can be learnt from networks by clustering their vertices according to connection profiles. Many deterministic and probabilistic methods have been developed. Given a network, almost all them partition the vertices into disjoint clusters. However, recent studies have shown that these methods were too restrictive and that most of the existing networks contained overlapping clusters. To tackle this issue, we present in this paper a latent logistic model, that allows each vertex to belong to multiple clusters, as well as an efficient approximate inference procedure based on global and local variational techniques. We show the results that we obtained on a transcriptional regulatory network of yeast.