Agglomerative clustering methods have been widely used by many research communities to cluster their data into hierarchical structures. These structures ease data exploration and are understandable even for non-specialists. But these methods necessarily result in a tree, since, at each agglomeration step, two clusters have to be merged. This may bias the data analysis process if, for example, a cluster is almost equally attracted by two others. In this paper we propose a new method that allows clusters to overlap until a strong cluster attraction is reached, based on a density criterion. The resulting hierarchical structure, called a quasi-dendrogram, is represented as a directed acyclic graph and combines the advantages of hierarchies with the precision of a less arbitrary clustering. We validate our work with extensive experiments on real data sets and compare it with existing tree-based methods, using a new measure of similarity between heterogeneous hierarchical structures.