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I believe that I’ve said before that PageRank is computed continuously; there are machines that take inputs to the PageRank algorithm at Google and compute the resulting PageRanks. So at any given time, a url in Google’s system has up-to-date PageRank as a result of running the computation with the inputs to the algorithm.
As originally published, the PageRank formula was a computationally intensive procedure. Two things have changed: 1) The formula has been modified but Google has not shared the specifics. 2) A mathematically equivalent form was found (that's common enough in mathematics) and it made continual calculation realistic.
maybe I should try Bing ;)
But it was almost six weeks from getting the first link to actually moving in the SERPS. We've gone up to #3 which is great, but if Pagerank is calculated continuously, then why was there no ranking movement for six weeks?
It could have taken several weeks for G* to re-index the old pages with your new links.
For example, the PR calculation could place more weight on older links than newer ones.
To keep up with this volume of information, our systems have come a long way since the first set of web data Google processed to answer queries. Back then, we did everything in batches: one workstation could compute the PageRank graph on 26 million pages in a couple of hours, and that set of pages would be used as Google's index for a fixed period of time. Today, Google downloads the web continuously, collecting updated page information and re-processing the entire web-link graph several times per day. This graph of one trillion URLs is similar to a map made up of one trillion intersections. So multiple times every day, we do the computational equivalent of fully exploring every intersection of every road in the United States. Except it'd be a map about 50,000 times as big as the U.S., with 50,000 times as many roads and intersections.