Results on Vertex Degree and K-Connectivity in Uniform S-Intersection Graphs

Abstract. We present results related to the vertex degree in a uniform s-intersection graph which has received much interest recently. Specifically, we derive the probability distribution for the minimum vertex degree, and show that the number of vertices with an arbitrary degree converges to a Poisson distribution. A uniform s-intersection graph models the topology of a secure wireless sensor network employing the widely used s-composite key predistribution scheme. Our theoretical findings is also confirmed by numerical results.