Zero-One Laws for Connectivity in Random Key Graphs

• Published in: IEEE transactions on information theory Vol. 58; no. 5; pp. 2983 - 2999
• Main Authors: Yagan, Osman, Makowski, A. M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Complement; Context; Detection, estimation, filtering, equalization, prediction; Educational institutions; Exact sciences and technology; Graph connectivity; Graphs; Information theory; Information, signal and communications theory; key predistribution; Law; Laws; Limiting; Materials; Networks; random key graphs; Sensors; Services and terminals of telecommunications; Signal and communications theory; Signal, noise; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Telemetry. Remote supervision. Telewarning. Remote control; Wireless networks; Wireless sensor networks; wireless sensor networks (WSNs); zero-one laws; key predistribution; Graph connectivity; wireless sensor networks (WSNs); Wireless telecommunication; Wireless network; Connectedness; zero―one laws; Sensor array; Signal detection; Remote sensing; random key graphs; Random graph
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2181331

The random key graph is a random graph naturally associated with the random key predistribution scheme introduced by Eschenauer and Gligor in the context of wireless sensor networks (WSNs). For this class of random graphs, we establish a new version of a conjectured zero-one law for graph connectivity as the number of nodes becomes unboundedly large. The results reported here complement and strengthen recent work on this conjecture by Blackburn and Gerke. In particular, the results are given under conditions which are more realistic for applications to WSNs.