On the existence of triangles in random key graphs

Authors:
Osman Yağan;Armand M. Makowski
Affiliations:
Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD;Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD
Venue:
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Year:
2009

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Abstract

Random key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. For this class of random graphs we show the existence of a zero-one law for the appearance of triangles, and identify the corresponding critical scaling. This is done by applying the method of first and second moments to the number of triangles in the graph.