Applications of Random Intersection Graphs to Secure Sensor Networks – Connectivity Results

Random intersection graphs was introduced by SingerCohen [6]. These graphs have recently received considerable attention in the literature and been used in diverse applications [1,2,7–13]. In a general random intersection graph, each node is assigned a set of items in some random manner, and any two nodes establish an undirected edge in between if and only if they have at least a certain number of items in common. In this paper, we consider random s-intersection graphs defined as follows. In a random s-intersection graph with n nodes, each node selects Kn distinct items uniformly at random from the same item pool that has Pn different items, and any two nodes have an edge in between upon sharing at least s items, where 1 ≤ s ≤ Kn ≤ Pn holds, and Kn and Pn are functions of n for generality. We denote a random s-intersection graph by Gs(n,Kn, Pn). Random intersection graphs have numerous application areas including secure wireless sensor networks [8, 10, 11, 13], social networks [1], cryptanalysis [2], and clustering [12]. We detail the use of random intersection graphs to model secure sensor networks.