Component evolution in a secure wireless sensor network

Abstract

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 (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.

Component Evolution in General Random Intersection Graphs

“…Behrisch [2] extended the above-mentioned result of Erdős and Rényi [10] to the random intersection graph G(n, m, P * ) with binomial distribution P * and m = n α , α > 1. For degenerate P * , a similar result was shown in [4]. In the present paper, we extend (1) to random intersection graphs G(n, m, P * ) with general P * in the case where n ln 2 n = o(m).…”

Recent Progress in Complex Network Analysis: Models of Random Intersection Graphs

“…The phase transition in the component size of an active random intersection graph has been studied in Behrisch (2007), Bloznelis (2010b), Bloznelis et al (2009), Godehardt et al (2007), and Rybarczyk (2011a). The effect of the clustering property on the phase transition in the component size and on the epidemic spread has been studied in Lagerås and Lindholm (2008), Bloznelis (2010c), Britton et al (2008) respectively.…”

Poisson Approximation of the Number of Cliques in Random Intersection Graphs

“…for the binomial distribution with the parameter which is itself a random variable. Unfortunately, in the other interesting case of the uniform random intersection graph (in which P (m) is the degenerate distribution), which is used for example to model wireless sensor networks [2], [4], [7], it seems it will not be straightforward to prove the analogous result.…”

“…[15] and [16]), network user profiling (see [14]), secure wireless networks (see, e.g. [4] and [7]), and epidemics (see [3] and [5]). …”