On the Eschenauer-Gligor key predistribution scheme under on-off communication channels: The absence of isolated nodes

Abstract

We consider the Eschenauer-Gligor key predistribution scheme under the condition of partial visibility with i.i.d. on-off links between pairs of nodes. This situation is modeled as the intersection of two random graphs, namely a random key graph and an Erdös-Rényi (ER) graph. For this class of composite random graphs we give various improvements on a recent result by Yağan [17] concerning zero-one laws for the absence of isolated nodes.