Abstract : 802.15.4 proposes to use a cluster-tree hierar- chy to organize the transmissions in Wireless Sensor Networks. In this letter, we propose a framework to analyze formally the capacity and the energy consumption of this structure. We derive a Mixed Integer Linear Programming (MILP) formulation to obtain a topology compliant with the standard. This formulation provides the optimal solution for the network capacity: this con- stitutes an upper bound for any distributed algorithms permitting to construct a cluster-tree. This framework can also be used to evaluate the capacity and to compare quantitatively different cluster-tree algorithms.