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

TL;DR

This paper establishes a zero-one law for the appearance of triangles in random key graphs, identifying the critical scaling for their existence using probabilistic methods.

Contribution

It introduces a zero-one law for triangles in random key graphs and determines the critical scaling, advancing understanding of their structural properties.

Findings

Zero-one law for triangle existence in random key graphs

Identification of critical scaling for triangles

Application of first and second moment methods

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.