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This paper presents an adaptive partitioning scheme of sensor networks for node scheduling and topology control with the aim of reducing energy consumption. Our scheme partitions sensors into groups such that a connected backbone network can be maintained by keeping only one arbitrary node from each group in active status while putting others to sleep. Unlike previous approaches that partition nodes geographically, our scheme is based on the measured connectivity between pairwise nodes and does not depend on nodes' locations. In this paper, we formulate node scheduling with topology control as a constrained optimal graph partition problem, which is NP-hard, and propose a Connectivity-based Partition Approach (CPA), which is a distributed heuristic algorithm, to approximate a good solution. We also propose a probability-based CPA algorithm to further save energy. CPA can ensure K-vertex connectivity of the backbone network, which achieves the trade-off between saving energy and preserving network quality. Moreover, simulation results show that CPA outperforms other approaches in complex environments where the ideal radio propagation model does not hold.