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Random key graphs are random graphs induced by the random key predistributionscheme of Eschenauer and Gligor under the assumption of full visibility. Forthis class of random graphs we show the existence of a zero-one law for theappearance of triangles, and identify the corresponding critical scaling. Thisis done by applying the method of first and second moments to the number oftriangles in the graph.

A zero-one law for the existence of triangles in random key graphs