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In this paper we present an energy efficient centralized clustering algorithm and a quantitative study, in term of messages, of necessary energy to the cluster formation. The cluster formation cost allows to combine efficiently clustering algorithm and cluster-based communication protocols. The cluster formation cost plays an important role in wireless sensor networks life span. Our clustering algorithm use the wireless network features : broadcast and methods such as power transmission control and data gathering to reduce the cluster formation cost. We show that our algorithm allows to reduce by 63% the number of necessary messages to build cluster compared to natural method and by a factor of 10 the cost of cluster formation with respect to the LEACH-C method.