The connectivity model of a power distribution network can easily become outdated due to system changes. Maintaining and sustaining an accurate connectivity model is a key challenge for most distribution utilities today. This work presents novel analytics techniques that can infer the connectivity model from measurements already available from a distribution network. Our techniques utilize voltage data from customer smart meters and circuit metering points to identify and correct errors in the connectivity model. We report analysis results based on data collected from multiple feeders of a large electric distribution network in North America. Our analysis shows that customer voltage measurements exhibit hierarchical correlations, which can be exploited to cluster customers under the same distribution transformer or same phase with high accuracy. To the best of our knowledge, this is the first large scale measurement study of voltage data collected from smart meters and its use in inferring customer to transformer and phase connectivity information.