On the random graph induced by a randomized predistribution scheme under full visibility (Extended version)

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2008

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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 complement it by a Poisson convergence for the number of isolated nodes. Leveraging earlier resu lts and analogies with Erd\H{o}s-Renyi graphs, we explore similar results for the property of graph connectivity. Implications for secure connectivity are discussed.

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Extended version of a paper submitted to ISIT 2008, Toronto (Canada), July 2008.

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