Probability Snowball Sampling from Graphs, with an Application to Actor-Actor Network

Abstract One can study any real graphs based on the subgraphs obtained by probability sampling. This is useful when it is either infeasible or too costly to process the whole graph due to various reasons. We consider probability snowball sampling (SBS) from graphs, where the initial node sample is selected with known probabilities, and each following wave of observation is carried out exactly as specified. The literature on design-based inference for probability SBS from graphs has limited scope, and there does not exist any design-unbiased strategy that generally makes use of units (or networks of units) obtained after the initial sample. In this paper, we adopt a unified framework for T-wave SBS from graphs, where the study units are not limited to the nodes in the graph but may be any finite-order subgraphs, say, triangles, cycles, or stars. We propose two practical design-unbiased strategies for estimating the corresponding graph totals, which considerably extend the previous approaches to probability SBS. The practitioners are thereby provided with richer choices to improve sampling efficiency, which we will demonstrate with an application to the actor-actor network from IMDb.