It has often been taken as a working assumption that directed links in
information networks are frequently formed by "short-cutting" a two-step path
between the source and the destination -- a kind of implicit "link copying"
analogous to the process of triadic closure in social networks. Despite the
role of this assumption in theoretical models such as preferential attachment,
it has received very little direct empirical investigation. Here we develop a
formalization and methodology for studying this type of directed closure
process, and we provide evidence for its important role in the formation of
links on Twitter. We then analyze a sequence of models designed to capture the
structural phenomena related to directed closure that we observe in the Twitter
data