Key management is one of the fundamental building blocks of security services. In a network with resource constrained nodes like sensor networks, traditional key management techniques, such as public key cryptography or key distribution center (e.g., Kerberos), are often not effective. To solve this problem, several key pre-distribution schemes have been proposed for sensor networks based on random graph theory. In these schemes, a set of randomly chosen keys or secret information is pre-distributed to each sensor node and a network is securely formed based on this information. Most of the schemes assumed that the underlying physical network is dense enough, that is, the degree of each node is high. In this paper, we revisit the random graph theory and use giant component theory by Erd¨os and R´enyi to show that even if the node degree is small, most of the nodes in the network can be connected. Further, we use this fact to analyze the Eschenhauer et. al’s, Du et. al’s, and Cha...