Efficient pagerank approximation via graph aggregation

We present a framework for approximating random-walk based probability distributions over Web pages using graph aggregation. We (1) partition the Web's graph into classes of quasi-equivalent vertices, (2) project the page-based random walk to be approximated onto those classes, and (3) compute the stationary probability distribution of the resulting class-based random walk. From this distribution we can quickly reconstruct a distribution on pages. Inparticular, our framework can approximate the well-known PageRank distribution by setting the classes according to the set of pages on each Web host. We experimented on a Web-graph containing over 1.4 billion pages, and were able to produce a ranking that has Spearman rank-order correlation of 0.95 with respect to PageRank. A simplistic implementation of our method required less than half the running time of a highly optimized implementation of PageRank, implying that larger speedup factors are probably possible.