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The connectivity of moving vehicles is one of the key metrics in vehicular ad-hoc networks (VANETs), which critically influences the performance of data transmission. Due to lack of in-depth analysis of real-world vehicular mobility traces, we do not understand the connectivity in realistic large-scale urban scenario. Specifically, the mechanism of how the mobility of networked vehicles impacts on the network connectivity remains unknown. In this contribution, we aim to unveil the underlaying relationship between mobility and connectivity of VANETs. To achieve this goal, we employ some key topology metrics, including component speed and component size, to characterize the mobility and connectivity. In our investigation of a largescale real-world urban mobility trace dataset, we discover to our surprise that there exists a dichotomy in the relationship between component speed and size. This dichotomy indicates that mobility destroys the connectivity with a power-law decline when the component speed is larger than a threshold and otherwise it has no apparent impact on connectivity. Based on this observation, we propose a mathematical model to characterize this relationship, which agrees well with empirical results. Our findings thus offer a comprehensive understanding of the relationship between the mobility and connectivity in urban vehicular scenarios, based on which helpful guidelines can be provided in design and analysis of VANETs.Index Terms-Vehicular ad-hoc networks, network topology, mobility modeling, connectivity of network

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