In the last few years, there has been agrowing interest in studying biological networks. Many deterministic and probabilistic clustering methods have been developed. They aim at learning information from the presence or absence of links between pairs of vertices (genes or proteins). Given a network, almost all these techniques partition the vertices into disjoint clusters, according to their connection profile. However, recent studies have shown that these methods were too restrictive and that most of the existing biological 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.