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A novel cluster header selection scheme in Wireless Sensor Network is proposed in this paper. Based on algebraic graph theory, the ranking of nodes is done by using the principal eigenvector of the connection matrix. The place of a node in the rank reveals the node's capability to communicate with other nodes. Thus, the top node is definitely the cluster header. This rank-based mechanism can select the most appropriate cluster header. Therefore the energy consumption of data-gathering can be reduced and the network lifetime will be extended. In general, Matrix Iteration Approach (MIA) is used to find the eigenvalue and eigenvector of a matrix by most people. As the complexity of MIA is high and a single node can not meet the requirements of space and time for calculation, a parallel computing architecture is designed to find the principal eigenvector.