Monotone Sampling of Networks

Determining the graph-theoretic properties of large real-world networks like social, computer, and biological networks, is a challenging task. Many of those networks are too large to be processed e ciently and some are not even available in their entirety. In order to reduce the size of available data or collect a sample of an existing network, several sampling algorithms were developed. They aim to produce samples whose properties are close to the original network. It is unclear what sample size is su cient to obtain a sample whose properties can be used to estimate those of the original network. This estimation requires sampling algorithms that produce results that converge smoothly to the original properties since estimations based on unsteady data are unreliable. Consequently, we evaluate the monotonicity of sampled properties while increasing the sample size. We provide a ranking of common sampling algorithms based on their monotonicity of relevant network properties using the results from four nework classes.