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On the connectivity in finite ad hoc networks

Connectivity and capacity analysis of ad hoc networks has usually focused on asymptotic results in the number of nodes in the network. In this letter we analyze finite ad hoc networks. With the standard assumption of uniform distribution of nodes in [0, z], z > 0, for a one-dimensional network, we obtain the exact formula for the probability that the network is connected. We then extend this result to find bounds for the connectivity in a two-dimensional network in [0, z]/sup 2/.