Bipartite incidence graph sampling and weighting

Abstract

Graph sampling is a statistical approach to study real graphs, which represent the structure of many technological, social or biological phenomena of interest. We develop bipartite incident graph sampling (BIGS) as a feasible representation of graph sampling from arbitrary finite graphs. It provides also a unified treatment of the existing unconventional sampling methods which were studied separately in the past, including indirect, network and adaptive cluster sampling. The sufficient and necessary conditions of feasible BIGS representation are established, given which one can apply a family of Hansen-Hurwitz type design-unbiased estimators in addition to the standard Horvitz-Thompson estimator. The approach increases therefore the potentials of efficiency gains in graph sampling. A general result regarding the relative efficiency of the two types of estimators is obtained. Numerical examples are given to illustrate the versatility of the proposed approach.