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One of the most important aspects in a clustering algorithm in a wireless sensor network is the cluster head (CH) rotation mechanism. Global reclustering is the common and established method used for this purpose in many existing algorithms. This research proposes an analytical framework to investigate the average energy expenditure of the global reclustering method and a local delegation strategy in which the CH role is delegated to a member of the cluster without changing the initial cluster boundary. Further we investigate a strategy of partial local delegation within global reclustering rounds to achieve energy efficiency. Simulations are used to visualize the analytically derived results using the simulation environment MATLAB.