The interesting thing about the recent patents and updates to patents is that they explain way to efficiently accomplish these mind boggling calculations.. The reasonable assumption for the past ten or so years has been that it takes about three months for the influence of link to become noticeable in the engine results pages. So it's reasonable to assume that the value of link is folded into Google's ranking algorithm at faster rate than three months.. it's absolutely reasonable to update our estimate of how long it takes for link to take effect. The period for link to take effect is probably on the order of week to fifteen days. In three months there is no way to know whether change in ranking is due to single link, another link that was added to your site, links dropping off of site or even totally unrelated change with Google's core ranking algorithm.. change in Google's algorithm could decide that your site is not good fit for certain keyword phrases. Or it could be that your site offeres user experience and Google's algorithm is handing out prizes for UX that week.. There are too many things going on externally to your site, and too many factors directly related to your site that are changing, in order to put your finger on it and say with any confidence that this single factor is what caused change in rankings.. So the answer to the question about how long to wait until link has taken effect is to not wait.
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