With the rapid increase in applications utilizing the current advancements of wireless sensor networks, a number of problems related to self-organization, energy-awareness and network organizations have attracted many researchers in the field. Various groups have proposed grouping the sensors into clusters and design communication routes in two levels as a way to improve communication cost and better organize networks of large sensors. In this paper, we propose a new approach to cluster wireless sensors and identify cluster heads using multi-stage graph algorithms. The approach takes advantage of the optimally associated with finding matching solutions in multi-stage graph networks. The proposed solution is designed to accommodate networks with different sizes and levels of density. We tested the algorithm using different types of networks and measure the quality of the key parameters as compared to those obtained by traditional greedy heuristics. Obtained results show that the multi-stage graph approach produces better network organization and better cluster head selection which leads to be more efficient self-organized networks.