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In the wireless ad hoc networks, for prolonging the communication duration of the nodes, the transmission power is required to be minimized to conserve the limited battery life. In addition, for the wireless ad hoc networks to be applicable, the networks are required to he connected. Unfortunately, the two requirements are against each other. In this paper, by analyzing the probability of isolated node, we obtain the relationships between transmission range, service area and network connectedness. Furthermore, we propose a generalized (N,B) wireless ad hoc network model to investigate the impact of boundary nodes on the network connectivity, equivalent service area and average node degree.