Rapid Bayesian Inference of Global Network Statistics Using Random Walks

We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability distribution of any network node-based property, and of the network size, after only a small fraction of network nodes has been explored. The Bayesian nature of our approach provides rigorous estimates of all parameter uncertainties. We demonstrate our framework on several standard examples, including random, scale-free, and small-world networks, and apply it to study epidemic spreading on a scale-free network. We also infer properties of the large-scale network formed by hyperlinks between Wikipedia pages.