This paper presents a Connectivity based Partition Approach (CPA) to reduce the energy consumption of a sensor network by sleep scheduling among sensor nodes. CPA 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. Nodes within each group swap between active and sleeping status occasionally to balance the energy consumption. Unlike previous approaches that partition nodes geographically, CPA is based on the measured connectivity between pairwise nodes and does not depend on nodes’ locations. In this paper, we formulate node scheduling as a constrained optimal graph partition problem, and propose CPA as a distributed heuristic partition algorithm. CPA can ensure k-vertex connectivity of the backbone network for its partition so as to achieve the trade-off between saving energy and preserving network communication quality. Moreover, simulation results ...