The idea is that there is a random surfer, who starts on web page then browses through in a somewhat random way. [...] This random walk is a Markov chain, a traversal of a matrix that gives the probability of moving to any state from any other state, with the total probabilities for the destinations from any given page adding up to 1. PageRank attempts to find extract a vector of weights from that table, with one weight per page - they aren't related to any particularly query, so are only ever going to be a factor in a page being returned on a results page.

He includes the code to create a page rank rating for a sample set of data with the results showing the differences in ranking based on frequency of times the "page" is linked to and how that relates to the rankings of the other pages.

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