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Connectivity is one of the fundamental properties in wireless multi-hop networks (e.g., wireless sensor/ad hoc network), and is also a prerequisite for providing many network functions. A question naturally follows is: what is the minimum transmission range that ensures a given network to be connected with a high probability? Or equivalently, what is the minimum value of the average node degree that ensures a given network to be connected with a high probability? Here the average node degree means the average number of neighbors of each node.
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