Graph sampling: Estimation of degree distributions

Online social networks and the World Wide Web lead to large underlying graphs that might not be completely known because of their size. To compute reliable statistics, we have to resort to sampling the network. In this paper, we investigate four network sampling methods to estimate the network degree distribution and the so-called biased degree distribution of a 3.7 million wireless subscriber network. We measure the quality of our estimates of the degree distributions by using the Kolmogorov-Smirnov statistic. Among all four sampling methods, node sampling yields Pareto optimal sample sizes in terms of the Kolomogorov-Smirnov statistic for the degree distribution, while node-by-edge sampling yields optimal sample sizes for the biased distribution. We also find that random walk sampling performs better than the Metropolis-Hastings random walk.