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In this paper we propose CDEEC, a Connectivity Degree-based and Energy Efficient Clustering protocol, for wireless sensor networks in order to achieve further energy conservation while extending the network lifetime. The main idea behind our proposal is to consider, in addition to the information about the nodes' residual energy, the specific topology characteristics of the network, such as the connectivity degree, in the selection process of the cluster heads. To evaluate the performance of our proposal, we compare it to classical HEED-based (Hybrid, Energy-Efficient Distributed Clustering) networks. Simulation results show that significant energy conservation can be achieved.