Clustering is a standard approach for achieving efficient and scalable performance in wireless sensor networks (WSNs).Especially,some sensor network applications need some nodes to affiliate to more than one cluster.This paper focused on studying the impacts of a duty-cycle based connected k-neighborhood (CKN) sleep scheduling algorithm for a multi-hop overlapping clustering algorithm in WSNs.It reveals the fact that waking up more sensor nodes cannot always increase the average cluster size but can always increase the cluster overlapping degree in a given duty-cycle based WSN.