4. The Effect of Inbound Links (continued)

The Actual Effect of
Additional Inbound Links

At a damping factor of 0.5, the accumulated PageRank of all pages of our site is given by

PR(A) + PR(B) + PR(C) + PR(D) = 14

Hence, by a page with a PageRank of 10 linking to one page of our example

site by its only outbound link, the accumulated PageRank of all pages of the site is increased by 10. (Before adding the link, each page has had a PageRank of 1.) At a damping factor of 0.75 the accumulated PageRank of all pages of the site is given by

PR(A) + PR(B) + PR(C) + PR(D) = 34

This time the accumulated PageRank increases by 30. The accumulated PageRank of all pages of a site always increases by

(d / (1-d)) × (PR(X) / C(X))

where X is a page additionally linking to one page of the site, PR(X) is its PageRank and C(X) its number of outbound links. The formula presented above is only valid, if the additional link points to a page within a closed system of pages, as, for instance, a website without outbound links to other sites. As far as the website has links pointing to external pages, the surplus for the site itself diminishes accordingly, because a part of the additional PageRank is propagated to external pages.

The justification of the above formula is given by Raph Levien and it is based on the Random Surfer Model. The walk length of the random surfer is an exponential distribution with a mean of (d/(1-d)). When the random surfer follows a link to a closed system of web pages, he visits on average (d/(1-d)) pages within that closed system. So, this much more PageRank of the linking page - weighted by the number of its outbound links - is distributed to the closed system.

For the actual PageRank calculations at Google, Lawrence Page und Sergey Brin claim to usually set the damping factor d to 0.85. Thereby, the boost for a closed system of web pages by an additional link from page X is given by

(0.85 / 0.15) × (PR(X) / C(X)) = 5.67 × (PR(X) / C(X))

So, inbound links have a far larger effect than one may assume.

4. The Effect of Inbound Links (continued)

This article reproduced with permission of eFactory.
© 2002 eFactory Internet-Agentur KG Online-Marketing - written by Markus Sobek
PageRank and Google are trademarks of Google Inc., Mountain ViewCA, USA.
PageRank is protected by US Patent 6,285,999.