8. The Yahoo Bonus and its Impact on Search Engine Optimization (continued)

Modification of the
PageRank Algorithm

If assigning special starting values at the begin of the PageRank calculations has no effect on the results of the computation, this does not mean that it is not possible to influence the PageRank of websites or web pages by an intervention in the PageRank

algorithm. Lawrence Page, for instance, describes a method for a special evaluation of web pages in his PageRank patent specifications (United States Patent 6,285,999). The starting point for his consideration is that the random surfer of the Random Surfer Model may get bored and stop following links with a constant probabilty, but when he restarts, he won't take a random jump to any page of the web but will rather jump to certain web pages with a higher probability than to others. This behaviour is closer to the behaviour of a real user, who would more likely use, for instance, directories like Yahoo or ODP as a starting point for surfing.

If a special evaluation of certain web pages shall take place, the original PageRank algorithm has to be modified. With another expected value implemented, the algorithm is given as follows:

PR(A) = E(A) (1-d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))

Here, (1-d) is the probability for the random surfer no longer following links. E(A) is the probability for the random surfer going to page A after he has stopped following links, weighted by the number of web pages. So, E is another expected value whose average over all pages is 1. In this way, the average of the PageRank values of all pages of the web will continue to converge to 1. Thus, the PageRank values do not vaccilate because of the special evaluation of web pages and the impact of PageRank on the general ranking of web pages remains stable.

	In our example, we set the probability for the random surfer going to page A after he has stopped following links to 0.1. The probability for him going to page B is set to 0.9. Since our web consists of two pages E(A) equals 0.2 and E(B) equals 1.8. At a damping factor d of 0.5 we get the following equations for the calculation of the single pages' PageRank values:

PR(A) = 0.2 × 0.5 + 0.5 × PR(B)
PR(B) = 1.8 × 0.5 + 0.5 × PR(A)

If we solve these equations we get the following PageRank values:

PR(A) = 11/15
PR(B) = 19/15

The sum of the PageRank values remains 2. The higher probability for the random surfer jumping to page B is reflected by its higher PageRank. Indeed, the uniform interlinking between both pages prevents our example pages' PageRank values from a more significant impact of our intervention.

So, it is possible to implement the special evaluation of certain web pages into the PageRank algorithm without having to change it fundamentally. It is questionable, indeed, what criteria is used for the evaluation. Lawrence Page suggests explicitly the utilization of real usage data in his PageRank patent specifications. Google, meanwhile, collects usage date by means of the Google Toolbar. And Google would not even need as much data, as if the whole ranking was solely based on usage data. A limited sample would be sufficient to determine the 1,000 or 10,000 most important pages on the web. The PageRank algorithm can then fill the holes in usage data and is thereby able to deliver a more accurate picture of the web.

Of course, all statements regarding the influence of real usage data on PageRank are pure speculation. Even if there is a special evaluation of certain web pages at all will in the end, stay a secret of the people at Google.

8. The Yahoo Bonus (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.