Wireless sensor networks (WSNs) are usually missioned to gather critical information in hostile and adversarial environments, which make them susceptible to compromise and revelation. Therefore, establishing secure communication in such networks is of great importance necessitating utilization of efficient key distribution schemes. In order to address such methods, several works using probabilistic, deterministic and hybrid approaches have been introduced in past few years. In this paper, we study the connectivity of key-distribution mechanisms in secured topologies of wireless sensor networks. We explore the effect of the radio range on the connectivity of the network and provide a lower bound on the radio range under which the cover time of the underlying topology decreases significantly. We also deduce that any broadcasting algorithm in such a network is performing only by a factor O(nβ), where β ε (0, 1), worse than broadcasting algorithms in unsecured topologies. Our numerical results and simulation experiments validates the correctness and efficiency of our analysis.