9. Additional Factors Influencing PageRank

It has been widely discussed if additional criteria beyond the link structure of the web have been implemented in the PageRank algorithm since the scientific work on PageRank has been published by Lawrence Page and Sergey Brin. Lawrence Page himself outlines the following potential influencing factors in his patent specifications for PageRank:

Visibility of a link
Position of a link within a document
Distance between web pages
Importance of a linking page
Up-to-dateness of a linking page

First of all, the implementation of additional criteria in PageRank would result in a better approximation of human usage regarding the Random Surfer Model. Considering the visibility of a link and its position within a document implies that a user does not click on links completely at haphazard, but rather follows links which are highly and immediately visible regardless of their anchor text. The other criteria would give Google more flexibility in determing in how far an inbound link of a page should be considered important, than the methods which have been described so far.

Whether or not the above mentioned factors are actually implemented in PageRank can not be proved empirically and shall not be discussed here. It shall rather be illustrated in which way additional influencing factors can be implemented in the PageRank algorithm and which options the Google search engine thereby gets in terms of influencing PageRank values.

Modification of the PageRank Algorithm

To implement additional factors in PageRank, the original PageRank algorithm has again to be modified. Since we have to assume that PageRank calculations are still based on numerous iterations and for the purpose of short computation times, we have to consider to keep the number of database queries during the iterations as small as possible. Therefore, the following modification of the PageRank algorithm shall be assumed:

PR(A) = (1-d) + d (PR(T1)×L(T1,A) + ... + PR(Tn)×L(Tn,A))

Here, L(Ti,A) represents the evaluation of a link which points from page Ti to page A. L(Ti,A) withal replaces the PageRank weighting of page Ti by the number of outbound links on page Ti which was given by 1/C(Ti). L(Ti,A) may consist of several factors, each of them having to be determined only once and then being merged to one value before the iterative PageRank calculation begins. So, the number of database queries during the iterations stays the same, although, admittedly, a much larger database has to be queried at each step in comparison to the computation by use of the original algorithm, since now there is an evaluation of each link instead of an evaluation of pages (by the number of their outbound links).

9. Additional Factors Influencing PageRank (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.