Many social network studies have focused on identifying communities through clustering or partitioning a large social network into smaller parts. While community structure is important in social network analysis, relatively little attention has been paid to the problem of “core structure” analysis in many social networks. Intuitively, one may expect that many social networks possess some sort of a “core” which holds various parts of the network (or constituent “communities”) together. We believe that it is just as important to uncover and extract the “core” structure - referred to as the “nucleus” in this paper - of a social network as to identify its community structure. In this paper, we propose a scalable and effective procedure to uncover the “nucleus” of social networks by building upon and generalizing ideas from the existing k-shell decomposition approach. We employ our approach to uncover the nucleus in several example communication, collaboration, interaction, location-based and online social networks. Our methodology is very scalable and can also be applied to massive networks (hundreds million nodes and billion edges).