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Distance estimation is of great importance for localization and a variety of applications in wireless sensor networks. In this paper, we develop a simple and efficient method for estimating distances between any pairs of neighboring nodes in static wireless sensor networks based on their local connectivity information, namely the numbers of their common one-hop neighbors and non-common one-hop neighbors. The proposed method involves two steps: estimating an intermediate parameter through a Maximum-Likelihood Estimator (MLE) and then mapping this estimate to the associated distance estimate. In the first instance, we present the method by assuming that signal transmission satisfies the ideal unit disk model but then we expand it to the more realistic log-normal shadowing model. Finally, simulation results show that localization algorithms using the distance estimates produced by this method can deliver superior performances in most cases in comparison with the corresponding connectivity-based localization algorithms.