Ad hoc networks are spontaneous wireless networks without any wired infrastructure, composed of mobile terminals. We assume that nodes must collaborate to set up an efficient network, such a collaboration requiring a self-organization in the network. We proposed a virtual structure to organize the network: the backbone is a connected structure helping to optimize the control traffic flooding. Clusters form services area, hierarchizing the network, electing one leader per cluster. Since the ad hoc topology is volatile, the self-stabilization of the algorithms is vital. The algorithms for both the construction and the maintenance are analytically studied to prove the self-stabilization of the proposed virtual structure. Thus, the virtual structure is efficient and very scalable, a local topology change impacting only locally the virtual structure. Finally, simulations investigate the behavior and the performances of the virtual structure according to several paremeters.