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6 1 ⋅ introduction not to follow a link. Rather, the surfer in this new model restarts at one of only a few pages. If the pages relate to one person, then the resulting PageRank vector is called a personalized PageRank vector. If the pages are topically related, then the vector may be called a topic-specific PageRank vector. In either case, what the surfer does when not following links on a page determines the type of pages that are important. 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 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 6 We feel obliged to document this term. Please see http://c2. com/cgi/wiki?GoogleJuice for a corroborating definition.PDF Image | Instagram Cheat Sheet
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