When Rank Trumps Precision: Using the Power Method to Compute Google?s PageRank

Abstract

The PageRank algorithm, developed by Google founders Larry Page and Sergey Brin, assigns ranking scores to webpages that reflect their relative importance. These scores are based primarily on the link structure of the Web graph and correspond to elements of a dominant left eigenvector, called the PageRank vector, of the stochastic Google matrix. When the starting vector is a probability vector, the iterates of the power method applied to the Google matrix converge to the PageRank vector. Determining when to stop the iterations requires deciding when an iterate vector is good enough. Existing termination criteria rely on various measures of distance between successive iterate vectors. In this dissertation, we investigate how well a power method iterate vector approximates the PageRank vector, we show that the existing termination criteria do not guarantee accurate ranking, and we provide a computationally efficient criterion for determining relative rankings, exact rankings, and ranking intervals of PageRank scores.