On the minimum node degree and connectivity of a wireless multihop network
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Extremal Properties of Three-Dimensional Sensor Networks with Applications
IEEE Transactions on Mobile Computing
Phase transition width of connectivity of wireless multi-hop networks in shadowing environment
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
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Considering a wireless multi-hop network where a total of n nodes are randomly, independently and uniformly distributed in a unit square in R2 and each node has a uniform transmission power, a fundamental problem is to investigate the connectivity of such networks. In this letter, we prove that the probability of having a connected network and the probability of having no isolated node asymptotically converges to the same value as n goes to infinity for an arbitrary wireless channel model satisfying certain intuitively reasonable conditions.