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The influence of node mobility on the convergence time of averaging gossip algorithms in networks is studied. It is shown that a small number of fully mobile nodes can yield a significant decrease in convergence time. A method is developed for deriving lower bounds on the convergence time by merging nodes according to their mobility pattern. This method is used to show that if the agents have 1-D mobility in the same direction, the convergence time is improved by at most a constant. Upper bounds on the convergence time are obtained using techniques from the theory of Markov chains and show that simple models of mobility can dramatically accelerate gossip as long as the mobility paths overlap significantly. Simulations verify that different mobility patterns can have significantly different effects on the convergence of distributed algorithms.