  Consider a population of individuals and a network that encodes social
connections among them. We are interested in making inference on finite
population and super-population estimands that are a function of both
individuals' responses and of the network, from a sample. Neither the sampling
frame nor the network are available. However, the sampling mechanism implicitly
leverages the network to recruit individuals, thus partially revealing social
interactions among the individuals in the sample, as well as their responses.
This is a common setting that arises, for instance, in epidemiology and
healthcare, where samples from hard-to-reach populations are collected using
link-tracing mechanisms, including respondent-driven sampling. In this paper,
we study statistical properties of popular network sampling mechanisms. We
formulate the estimation problem in terms of Rubin's inferential framework to
explicitly account for social network structure. We then identify key modeling
elements that lead to inferences with good frequentist properties when dealing
with data collected through non-ignorable network sampling mechanisms. We
demonstrate these methods on a study of the incidence of HIV in Brazil
