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6 1 ⋅ introduction The random surfer model is but one interpretation of the PageRank model. In Higham [2005], it is shown that PageRank is related to playing pinball. Place a ball at a page on the web. Suppose that the ball moves according on these rules: with probability β, it stays put; with probability γ, it moves to a page that links to the current page; and with probability 1 − β − γ, the game ends. Although this model does not use α, the probabilities β and γ are defined from the PageRank parameters. See the paper for the definitions, as they are needlessly tangential. The average length of time that this game lasts is the PageRank of that page. Another view of PageRank is as “Google Juice.”6 Consider pages with 6 We feel obliged to document this high PageRank values. This means that a random surfer is quite likely to be on these pages. Why? There are two possibilities: either many pages link to them, or a few high PageRank pages—where the surfer is already likely to be found—link to them. It is this latter case that gives rise to the notion of “Google Juice.” If a page already has a high PageRank value, it can contribute its influence to another page. Thus, another interpretation of PageRank is a system where importance “flows” along links between pages. We hope that these alternate views of the PageRank model provide further intuition for the PageRank method. Having multiple viewpoints on a problem is an important aspect of any numerical research. What is obvious or trivial from one perspective is often difficult to perceive from another. In some cases, these viewpoints provide the intuition necessary to close important open problems. 1.4 other uses for pagerank So far, we’ve seen that PageRank on the web models where we find a random surfer, that this process generalizes to a centrality measure on an arbitrary graph, and that there are many ways to change and interpret the PageRank model. There are still other uses for PageRank. clustering Theproblemofclusteringistofindwaystodivideagraphinto pieces by separating the nodes into cohesive groups. One approach is to find a set of strongly related nodes, call that a group, remove it from the graph, and repeat until the graph is empty. PageRank helps find a group of strongly related nodes, as Andersen et al. [2006] demonstrate. They show that a modified personalized PageRank, where the surfer only resets to a single page ( called the target), produces a group of pages near the target. Further, they show that they can use a customized PageRank algorithm to compute these groups of nodes extremely quickly. sports ranking PageRankalsohelpstoranksportsteams.Intworecent contributions, both Langville [2009] and Govan et al. [2008] extend term. Please see http://c2.com/cgi/ wiki?GoogleJuice for a corroborating definition.PDF Image | ALGORITHMS FOR PAGERANK SENSITIVITY DISSERTATION
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