Paradoxical Effects in PageRank Incremental Computations

Deciding which kind of visiting strategy accumulates high-quality pages more quickly is one of the most often debated issues in the design of web crawlers. This paper proposes a related, and previously overlooked, measure of effectiveness for crawl strategies: whether the graph obtained after a partial visit is in some sense representative of the underlying web graph as far as the computation of PageRank is concerned. More precisely, we are interested in determining how rapidly the computation of PageRank over the visited subgraph yields node orders that agree with the ones computed in the complete graph; orders are compared using Kendall's ô . We describe a number of large-scale experiments that show the following paradoxical effect: visits that gather PageRank more quickly (e.g., highest-quality first) are also those that tend to miscalculate PageRank. Finally, we perform the same kind of experimental analysis on some synthetic random graphs, generated using well-known web-graph models: the results are almost opposite to those obtained on real web graphs.