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Clustering is a widely used technique to manage the essential operations such as routing and data aggregation in Wireless Sensor Networks (WSNs). The authors propose two new graph theoretic distributed clustering algorithms for WSNs that use weighted matching method for selecting strong links. To the best of the knowledge, the algorithms are the first attempts that use graph matching for clustering. The first algorithm is divided into rounds, extended weighted matching operation is executed by nodes in each round, thus the clusters are constructed synchronously. The second algorithm is the enhanced version of the first algorithm, which provides not only clustering but also backbone formation in an energy efficient and asynchronous manner.
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