On Applicability of Random Graphs for Modeling Random Key Predistribution for Wireless Sensor Networks

We study the applicability of random graph theory in modeling secure connectivity of wireless sensor networks. Specifically, our work focuses on the highly influential random key predistribution scheme by Eschenauer and Gligor to examine the appropriateness of the modeling in finding system parameters for desired connectivity. We use extensive simulation and theoretical results to identify ranges of the parameters where i) random graph theory is not applicable, ii) random graph theory may lead to estimates with excessive errors, and iii) random graph theory gives very accurate results. We also investigate the similarities and dissimilarities in the structure of random graphs and key graphs (i.e., graphs describing key sharing information between sensor nodes). Our results provide insights into research relying on random graph modeling to examine behaviors of key graphs.