Page Rank Done by: Asem Battah Supervised by: Dr. Samir Tartir Done by: Asem Battah Supervised by: Dr. Samir Tartir

Introduction: PageRank is what search engine uses to determine the importance of a web page. It's one of many factors used to determine which pages appear in search results.

The History of PageRank: PageRank was developed by Google founders Larry Page and Sergey Brin at Stanford. At the time that Page and Brin met, search engines typically linked to pages that had the highest keyword density, which meant people could game the system by repeating the same phrase over and over to attract higher search page results.

How dose it work? PageRank assigns a rank or score to every search result. The higher the page's score, the further up the search results list it will appear. Scores are partially determined by the number of other Web pages that link to the target page. Each link is counted as a vote for the target. The logic behind this is that pages with high quality content will be linked to more often than mediocre pages. Not all votes are equal. Votes from a high-ranking Web page count more than votes from low-ranking sites. You can't really boost one Web page's rank by making a bunch of empty Web sites linking back to the target page.

Cont. The more links a Web page sends out, the more diluted its voting power becomes. In other words, if a high- ranking page links to hundreds of other pages, each individual vote won't count as much as it would if the page only linked to a few sites. Other factors that might affect scoring include the how long the site has been around, the strength of the domain name, how and where the keywords appear on the site and the age of the links going to and from the site. Google tends to place more value on sites that have been around for a while.

Pagerank algorithm: PR(A) = (1-d) + d (PR(T1)/C(T1) PR(Tn)/C(Tn)) Where: PR(A) is the PageRank of page A, PR(Ti) is the PageRank of pages Ti which link to page A, C(Ti) is the number of outbound links on page Ti and d is a damping factor which can be set between 0 and 1.

Example: Let us denote by A the transition matrix of the graph, A =

Resources: 09/RalucaRemus/Lecture3/lecture3.html 09/RalucaRemus/Lecture3/lecture3.html algorithm1.htm algorithm1.htm algorithm.shtml algorithm.shtml mization/a/pagerankexplain.htm mization/a/pagerankexplain.htm