Structural capital focuses on the advantages derived from the patterns of an actor's connections within a social network. This paper investigates structural social capital in the form of brokerage and closure through the lens of triadic analysis in four popular and public online social networks, namely, Facebook, Twitter, Slashdot, and YouTube. Through a ratio of the census of open and closed triads, the analysis reveals that these four networks are overwhelmingly rich in brokerage capital. Brokerage triads are further classified into three types according to the role of the broker: (i) Tertius Gaudens (broker as a competitor); (ii) Tertius Inguens (broker as a coordinator); and (iii) Conduit (broker as a mediator). Closure triads are further classified according to the number of mutual dyadic connections. Exploring the distributions of brokerage and closure classes and their constituent triads reveals that for each online social network (OSN) these proportions are deeply rooted in the purpose and objectives of socialization. On Facebook, users form relationships for social sharing, and nurture these bonds based on strong offline friendships. Relationships on Twitter serve two purposes, social sharing and gathering news and information. Finally, users on Slashdot and YouTube create links based on their shared interests in news stories and videos respectively, and appear less interested in cultivating friendships.