A matrix completion bootstrap method for estimating scale-free network degree distribution

Abstract

Scale-free networks are very common in real practice. The key to analyze scale-free networks is the statistical inference of degree distribution. However, one observed network only allows us to calculate network statistics such as nodal degree, but does not provide enough information for further inference such as constructing confidence intervals. Borrowing the spirit of bootstrap, by generating network samples as bootstrap samples, we are then able to quantify statistical accuracy of various network statistics. In this paper, we propose a novel network bootstrap method named 1-BNB where bootstrap samples are generated via 1-bit matrix completion. We focus on constructing confidence interval for network degree distribution. Extensive simulation studies are conducted to demonstrate the finite sample performance of our newly propose method. A collaboration network among statisticians, a social network and an electrical grid network are studied for illustration purpose.