Many graph clustering algorithms perform successive divisions or aggregations of subgraphs leading to a hierarchical decomposition of the network. An important question in this domain is to know if this hierarchy reflects the structure of the network or if it is only an artifice due to the conduct of the procedure. We propose a method to validate and, if necessary, to optimize the multi-scale decomposition produced by such methods. We apply our procedure to the algorithm proposed by Blondel et al. (2008) based on modularity maximization. In this context, a generalization of this quality measure in the multi-level case is introduced. We test our method on random graphs and real world examples.