Abstract
In this chapter, we study the phase transition behavior of k-connectivity (k = 1, 2, …) in large wireless networks where a total of n nodes are randomly and independently distributed following a uniform distribution in a unit cube [0, 1] d (d = 1, 2, 3), and each node has an identical transmission range r(n). It has been shown that the phase transition of k-connectivity becomes sharper as the total number of nodes n increases. In this chapter, we investigate how fast such phase transition happens, and derive a general formula for the phase transition width of k-connectivity for large enough n and for any fixed positive integer k in d-dimensional space by resorting to a Poisson approximation for the node placement. The results in this chapter are important for understanding the phase transition phenomenon in network connectivity.
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