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Knowing the structure of an offline social network facilitates a variety ofanalyses, including studying the rate at which infectious diseases may spreadand identifying a subset of actors to immunize in order to reduce, as much aspossible, the rate of spread. Offline social network topologies are typicallyestimated by surveying actors and asking them to list their neighbours. Whileidentifying close friends and family (i.e., strong ties) can typically be donereliably, listing all of one's acquaintances (i.e., weak ties) is subject toerror due to respondent fatigue. This issue is commonly circumvented throughthe use of so-called "fixed choice" surveys where respondents are asked to namea fixed, small number of their weak ties (e.g., two or ten). Of course, theresulting crude observed network will omit many ties, and using this crudenetwork to infer properties of the network, such as its degree distribution orclustering coefficient, will lead to biased estimates. This paper developsestimators, based on the method of moments, for a number of networkcharacteristics including those related to the first and second moments of thedegree distribution as well as the network size, using fixed-choice surveydata. Experiments with simulated data illustrate that the proposed estimatorsperform well across a variety of network topologies and measurement scenarios,and the resulting estimates are significantly more accurate than those obtaineddirectly using the crude observed network, which are commonly used in theliterature. We also describe a variation of the Jackknife procedure that can beused to obtain an estimate of the estimator variance.

Inferring Structural Characteristics of Networks with Strong and Weak Ties from Fixed-Choice Surveys