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People think about PageRank in lots of different ways. People have compared PageRank to a “random surfer” model in which PageRank is the probability that a random surfer clicking on links lands on a page. Other people think of the web as an link matrix in which the value at position (i,j) indicates the presence of links from page i to page j. In that case, PageRank corresponds to the principal eigenvector of that normalized link matrix.
Disclaimer: Even when I joined the company in 2000, Google was doing more sophisticated link computation than you would observe from the classic PageRank papers. If you believe that Google stopped innovating in link analysis, that’s a flawed assumption. Although we still refer to it as PageRank, Google’s ability to compute reputation based on links has advanced considerably over the years. I’ll do the rest of my blog post in the framework of “classic PageRank” but bear in mind that it’s not a perfect analogy.
Probably the most popular way to envision