3. The Implementation of PageRank in the Google Search Engine (continued)

The PageRank Display
of the Google Toolbar

PageRank became widely known by the PageRank display of the Google Toolbar. The Google Toolbar is a browser plug-in for Microsoft Internet Explorer which can be downloaded from the Google web site. The Google Toolbar provides some features for searching Google more comfortably.

	The Google Toolbar displays PageRank on a scale from 0 to 10. First of all, the PageRank of an actually visited page can be estimated by the width of the green bar within the display. If the user holds his mouse over the display, the Toolbar also shows the PageRank value.

If we take into account that PageRank can theoretically have a maximum value of up to dN+(1-d), where N is the total number of web pages and d is usually set to 0.85, PageRank has to be scaled for the display on the Google Toolbar. It is generally assumed that the scalation is not linearly but logarithmically. At a damping factor of 0.85 and, therefore, a minimum PageRank of 0.15 and at an assumed logaritmical basis of 6 we get a scalation as follows:

Toolbar PageRank	Real PageRank
0/10 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 10/10	0.15 0.9 5.4 32.4 194.4 1,166.4 6,998.4 41,990.4 251,942.4 1,511,654.4 9,069,926.4	- - - - - - - - - - -	0.9 5.4 32.4 194.4 1,166.4 6,998.4 41,990.4 251,942.4 1,511,654.4 9,069,926.4 0.85 × N + 0.15

It is uncertain if in fact a logarithmical scalation in a strictly mathematical sense takes place. There is likely a manual scalation which follows a logarithmical scheme, so that Google has control over the number of pages within the single Toolbar PageRank ranges. The logarithmical basis for this scheme should be between 6 and 7, which can for instance be rudimentary deduced from the number of inbound links of pages with a high Toolbar PageRank from pages with a Toolbar PageRank higher than 4, which are shown by Googe using the link command.

3. The Implementation of 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.