Keywords: social networks, sampling, hard to reach populations, random walks, MCMC
Much of the network literature up to this point has focused on measurements which can only occur on complete network data; however there exist many networks which can only be accessed via sampling methods either because of the scale of the network (e.g., Facebook) or because the population of interest cannot be enumerated (e.g., the network of homeless). Methods for network sampling have been developed for online and offline cases in parallel, both introducing important concepts and ideas, but fail to fully integrate into a coherent theory. We begin the exercise of integrating these two literatures and compare their findings via simulation analysis. We, further, look to use simulations to develop core methods for variance estimation, power analysis and to develop a set of good heuristics on the use and quality of measuring network properties from different types of sampling procedures. In this work we focus on comparing random walk, reweighted random walk, and Metropolis-Hastings random walk sampling procedures. We also explore effective sample size for power analysis in comparing group level differences and study the collision estimator, an estimate of network size.