Component Evolution in General Random Intersection Graphs
SIAM Journal on Discrete Mathematics
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We study a connectivity property of a secure wireless network that uses random pre-distribution of keys. A network is composed of n sensors. Each sensor is assigned a collection of d different keys drawn uniformly at random from a given set of m keys. Two sensors are joined by a communication link if they share a common key. We show that for large n with high probability the connected component of size Ω(n) emerges in the network when the probability of a link exceeds the threshold 1-n. Similar component evolution is shown for networks where sensors communicate if they share at least s common keys. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009