Incidentally: that Markov chain thing? Suppose you make a Markov chain out of all the world's web pages, where each step moves you from a page to a randomly sel

Incidentally: that Markov chain thing? Suppose you make a Markov chain out of all the world's web pages, where each step moves you from a page to a randomly selected page it links to, or (occasionally for a page that has links, and unconditionally for a page with no links) to a completely random page. Then the entries in that unique eigenvector -- equivalently, the long-term probabilities of landing on each page -- are basically the Google pagerank. (I'm sure Google's pagerank computation has lots of tweaks in it, and they certainly consider things other than pagerank to determine their search results. But pagerank was their original key idea.)