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This paper investigates the probabilistic connectivity of wireless sensor networks in the presence of channel fading. Due to the stochastic nature of wireless channels in sensor networks, the geometric disk shaped model widely used for connectivity analysis of sensor networks can be misleading. In this paper, we develop a mathematical model to evaluate the probabilistic connectivity of sensor networks which incorporates the characteristics of wireless channels, multi-access interference, the network topology and the propagation environment. We present an analytical framework for the computation of node isolation probability and network connectivity under different channel fading models. We also analyze the connectivity of sensor networks in the presence of unreliable sensors. We present numerical and simulation results that compare different regular topologies in terms of several metrics such as node isolation probability, end-to-end connectivity, and network connectivity.