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PR using outbound links

PR using outbound linksHere we'll discuss in detail, how to find the PR using outbound links, using a web consisting of 2 websites, each having two web pages. One site consists of pages A and B, the other constists of pages C and D. Initially, both pages of each site solely link to each other. It is obvious that each page then has a PageRank of one. Now we add a link which points from page A to page C. At a damping factor of 0.75, we therefore get the following equations for the single pages' PageRank values:

PR(A) = 0.25 + 0.75 PR(B)
PR(B) = 0.25 + 0.375 PR(A)
PR(C) = 0.25 + 0.75 PR(D) + 0.375 PR(A)
PR(D) = 0.25 + 0.75 PR(C)

Many top SEOs believe that getting external links is the single most important objective for attaining high rankings. This stems from the idea that external links are one of the hardest metrics to manipulate and thus one of the best ways for search engines to determine the popularity of a given web page. We'll see it here! Solving the equations gives us the following PageRank values for the first site:


Polls
PR(A) = 14/23
PR(B) = 11/23

We therefore get an accumulated PageRank of 25/23 for the first site. The PageRank values of the second site are given by:

PR(C) = 35/23
PR(D) = 32/23

So, the accumulated PageRank of the second site is 67/23. The total PageRank for both sites is 92/23 = 4. Hence, adding a link has no effect on the total PageRank of the web. Additionally, the PageRank benefit for one site equals the PageRank loss of the other. As it has already been shown, the PageRank benefit for a closed system of web pages by an additional inbound link is given by:

(d / (1-d)) × (PR(X) / C(X)),

where X is the linking page, PR(X) is its PageRank and C(X) is the number of its outbound links. Hence, this value also represents the PageRank loss of a formerly closed system of web pages, when a page X within this system of pages now points by a link to an external page.

The validity of the above formula for PR using outbound links, requires that the page which receives the link from the formerly closed system of pages does not link back to that system, since it otherwise gains back some of the lost PageRank. Of course, this effect may also occur when not the page that receives the link from the formerly closed system of pages links back directly, but another page which has an inbound link from that page. Indeed, this effect may be disregarded because of the damping factor, if there are enough other web pages in-between the link-recursion. The validity of the formula also requires that the linking site has no other external outbound links. If it has other external outbound links, the loss of PageRank of the regarded site diminishes and the pages already receiving a link from that page lose PageRank accordingly.

Even if the actual PageRank values for the pages of an existing web site were known, it would not be possible to calculate to which extend an added outbound link diminishes the PageRank loss of the site, since the above presented formula regards the status after adding the link.

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