Strong Localization in Personalized PageRank Vectors

Abstract. The personalized PageRank diffusion is a fundamental tool in network analysis tasks like community detection and link prediction. This tool models the spread of a quantity from a small, initial set of seed nodes, and has long been observed to stay localized near this seed set. We derive a sublinear upper-bound on the number of nonzeros necessary to approximate a personalized PageRank vector on a power-law graph. Our experimental results on power-law graphs with a wide variety of parameter settings demonstrate that the bound is loose, and instead supports a new conjectured bound.