  Focus theory describes how shared memberships, social statuses, beliefs, and
places can facilitate the formation of social ties, while two-mode projections
provide a method for transforming two-mode data on individuals' memberships in
groups into a one-mode network of their possible social ties. In this paper, I
explore the opposite process: how social ties can facilitate the formation of
groups, and how a two-mode network can be generated from a one-mode network.
Drawing on theories of team formation, club joining, and organization
recruitment, I propose three models that describe how such groups might emerge
from the relationships in a social network. I show that these models can be
used to generate two-mode networks that have characteristics commonly observed
in empirical two-mode social networks, and that they encode features of the
one-mode networks from which they were generated. I conclude by discussing
these models' limitations, and future directions for theory and methods
concerning group formation.
