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Due to limitations on transmission power of wireless devices, areas with sparse nodes are decisive to some extreme properties of network topology. In this paper, we assume wireless ad hoc and sensor networks are represented by uniform point processes or Poisson point processes. Asymptotic analyses based on minimum scan statistics are given for some crucial network properties, including coverage of wireless sensor networks, connectivity of wireless ad hoc networks, the largest edge length of geometric structures, and local-minimum-free geographic routing protocols. We derive explicit formulas of minimum scan statistics. By taking the transmission radius as a major parameter, our results are applied to various network problems. This work offers a unified approach to solve various problems and reveals the evolution of network topology. In addition, boundary effects are thoroughly handled.