  Knowing the structure of an offline social network facilitates a variety of
analyses, including studying the rate at which infectious diseases may spread
and identifying a subset of actors to immunize in order to reduce, as much as
possible, the rate of spread. Offline social network topologies are typically
estimated by surveying actors and asking them to list their neighbours. While
identifying close friends and family (i.e., strong ties) can typically be done
reliably, listing all of one's acquaintances (i.e., weak ties) is subject to
error due to respondent fatigue. This issue is commonly circumvented through
the use of so-called "fixed choice" surveys where respondents are asked to name
a fixed, small number of their weak ties (e.g., two or ten). Of course, the
resulting crude observed network will omit many ties, and using this crude
network to infer properties of the network, such as its degree distribution or
clustering coefficient, will lead to biased estimates. This paper develops
estimators, based on the method of moments, for a number of network
characteristics including those related to the first and second moments of the
degree distribution as well as the network size, using fixed-choice survey
data. Experiments with simulated data illustrate that the proposed estimators
perform well across a variety of network topologies and measurement scenarios,
and the resulting estimates are significantly more accurate than those obtained
directly using the crude observed network, which are commonly used in the
literature. We also describe a variation of the Jackknife procedure that can be
used to obtain an estimate of the estimator variance.
