The topology attributes of both connectivity and coverage in a wireless sensor network depend on the spatial distribution of the nodes and their transmission range. This paper first models the network with random node distribution as a geometric random graph. Then it proposes an analytical expression of the required critical transmission range of a node, for a given node density, to create an almost surely connected network. Equivalently, if the maximum range of the nodes is given, it can estimate effectively how many nodes are needed to cover a certain area with a connected network. With experimental test in various scenarios, the method is proved to achieve guaranteed degrees of coverage and connectivity, valuable for researchers in this area.
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