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Connectivity in one-dimensional geometric random graphs: Poisson approximations, zero-one laws and phase transitions
Consider n points (or nodes) distributed uniformly and independently on the unit interval [0,1]. Two nodes are said to be adjacent if their distance is less than some given threshold value.For the underlying random graph ...
On the random graph induced by a randomized predistribution scheme under full visibility (Extended version)
We consider the random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We show the existence of a zero-one law for the absence of isolated nodes, and ...