Mathematical Modeling and Inference for Degree-capped Ego-centric Network Sampling

The structure of social networks is usually inferred from limited sets of observations via suitable network sampling designs. In offline social network sampling, for practical considerations, researchers sometimes build in a cap on the number of social ties any respondent may claim. It is commonly known in the literature that using a cap on the degrees begets methodologically undesirable features because it discards information about the network connections. In this paper, we consider a mathematical model of this sampling procedure and seek analytical solutions to recover some of the lost information about the underlying network. We obtain closed-form expressions for several network statistics, including the first and second moments of the degree distribution, network density, number of triangles, and clustering. We corroborate the accuracy of these estimators via simulated and empirical network data. Our contribution highlights notable room for improvement in the analysis of some existing social network data sets.