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As the capacity and communication ability of mobile ad hoc and sensor networks are dependent on the set of communication links of the nodes, the design of any protocol for such networks should take into account the link dynamics. In this work, we investigate the behavior of the communication links of a node in a random mobility environment. Analytical expressions characterizing various properties related to the creation, lifetime and expiration of links are presented. The derived link properties can be used to design efficient algorithms for routing and medium access, or to analyze the performance of existing network protocols. A number of applications of the derived properties, such as the selection of a stable set of routes, route cache lifetime optimization, design of efficient proactive updating strategies and analysis of route lifetime are discussed.