Models and Algorithms for Pagerank Sensitivity a Dissertation Submitted to the Institute of Computational and Mathematical Engineering and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

e PageRank model helps evaluate the relative importance of nodes in a large graph, such as the graph of links on the world wide web. An important piece of the PageRankmodel is the teleportation parameter α. We explore the interaction between α and PageRank through the lens of sensitivity analysis. Writing the PageRank vector as a function of α allows us to take a derivative, which is a simple sensitivity measure. As an alternative approach, we apply techniques from the eld of uncertainty quantication. Regarding α as a random variable produces a new PageRankmodel in which each PageRank value is a random variable. We explore the standard deviation of these variables to get another measure of PageRank sensitivity. One interpretation of this new model shows that it corrects a small oversight in the original PageRank formulation. Both of the above techniques require solving multiple PageRank problems, and thus a robust PageRank solver is needed. We discuss an inner-outer iteration for this purpose. e method is low-memory, simple to implement, and has excellent performance for a range of teleportation parameters. We show empirical results with these techniques on graphs with over 2 billion edges.