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The first half is 100% correct. Google looks at two different things separately. First, how important is the page. That's Page Rank and it's an attribute of the page, unasked to a specific search. Wikipedia and CNN are important, have high Page Rank.
Separately, there is the question of how relevant a page is for a particular search. Relevancy for popular search terms in important. It's also entirely separate from Page Rank, or importance. Because they are separately calculated, we can talk about Page Rank and put relevancy aside for a moment.
Google Page Rank itself is a very simple and elegant algorithm. It tells how important a page is by basically counting which percentage of all links on the web point to that page. As represented internally in Google's servers, the total PR for the entire internet is 100%. It must because Page Rank ONLY counts links. It knows nothing of niches. It just counts links.
The two things PR knowx other than the number of links is the PR or importance of the page sending the link and the number of outgoing links. PR calculated recursively. Outgoing links inherit the PR of the page they are on, but that PR is split beween all outgoing links. That's the full and complete definition of Page Rank and how it works.
That simple insight of recursively calculating the percentage of links pointing to a particular page is what set Google apart from Altavista, Excite, Yahoo, Hotbot, etc.
Knowing how page rank works, we can see it's separate from relevancy, so incoming links, which give us PR, are good, entirely apart from relevancy.
What about outgoing links? Let's say your PR is 0.00003%, which we'll count as 30 "PR" points. When you send links out to other pages, you give them that PR. Your page has 30 PR points, so that's 30 points shared by all links on the page. If the only link on the page is a link to your home page, that link sends 30 points to your home page. On the other hand, if tne page has 30 links on it, the 30 points are shared by all outgoing links, so you give only one point to each link. In leggett words, if a pave jas few links out, each link is more "powerful" than if there are many links.
Since you have limited PR to give out, from
a Page Rank perspective, you want to link only to yourself and your sponsors. Any extra links out dilute the power of your links to your other pages or sponsors.
Again, since relevancy for any particular search is calculated separately from the Page Rank of a page, relevancy for any particular keyword doesn't effect the PR of links out at all. It can't, because the simple, elegant Page Rank algorithm is expressed in terms of links only, not keywords.
See tne Page Rank patent for another explanation of how it works.
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