  We introduce an agent-based acquaintance model in which social links are
created by processes in which there is no explicit homophily. In spite of the
homogeneous nature of the social interactions, highly-clustered social networks
can arise. The crucial feature of our model is that of variable transitive
interactions. Namely, when an agent introduces two unconnected friends, the
rate at which a connection actually occurs between them depends on the number
of their mutual acquaintances. As this transitive interaction rate is varied,
the social network undergoes a dramatic clustering transition. Close to the
transition, the network consists of a collection of well-defined communities.
As a function of time, the network can also undergo an \emph{incomplete}
gelation transition, in which the gel, or giant cluster, does not constitute
the entire network, even at infinite time. Some of the clustering properties of
our model also arise, but in a more gradual manner, in Facebook networks.
Finally, we discuss a more realistic variant of our original model in which
there is a soft cutoff in the rate of transitive interactions. With this
variant, one can construct network realizations that quantitatively match
Facebook networks.
