PageRank Algorithm used by Google inc

1. Motivation
1. Link algorithm(SALSA)
2. Page Rank Algorithm

2. SEARCH PHRASE
• Keyword Density
• Accentuation within a
document
• HTML Tags
• Not resistant against
automatically generated web

3. Link popularity
algorithm
• Inbound Links.
• Decieve Search Engines
• Creating masses of inbound links

6. Page rank
algorithm
PageRank is an expected value for the random surfer visiting a
page, when he restarts this procedure as often as the web has
pages
• Comparision of pages
• The higher the better
• Recursive Determination

8. introduction
Sergey Brin Larry Page

9. algorithm
PageRank does not rank web sites as a whole,
but is determined for each page individually
*This means that the more outbound links a page T has, the less will page A
benefit from a link to it on page T.

10. The random surfer
model
• The probability that the random surfer
clicks on one link is solely given by the
number of links on that page
• The surfer does not click on an infinite
number of links, but gets bored sometimes and
jumps to another page at random.
damping factor ‘d’

11. Different
notation

12. characteristic
A
b c
PR(A) = 0.5 + 0.5 PR(C) PR(A) = 14/13 = 1.07692308
PR(B) = 0.5 + 0.5 (PR(A) / 2) PR(B) = 10/13 = 0.76923077
PR(C) = 0.5 + 0.5 (PR(A) / 2 + PR(B)) PR(C) = 15/13 = 1.15384615

13. The iterative
Iteration PR(A) PR(B) PR(C)
0 1 1 1
1 1 0.75 1.125
2 1.0625 0.765625 1.1484375
3 1.07421875 0.76855469 1.15283203
4 1.07641602 0.76910400 1.15365601
5 1.07682800 0.76920700 1.15381050
6 1.07690525 0.76922631 1.15383947
7 1.07691973 0.76922993 1.15384490
8 1.07692245 0.76923061 1.15384592
9 1.07692296 0.76923074 1.15384611
10 1.07692305 0.76923076 1.15384615
11 1.07692307 0.76923077 1.15384615

14. Implementation in
google search engine
• Page specific factors
• Body text
• Content of title tag
• URL of document
• Anchor text of inbound links
• Page rank
Page Inbound IR
factors links Score
* IR score is multiplied with the Page Rank

16. Effect of
inbound links
• d × PR(X) / C(X)
where PR(X) is the PageRank of page X and C(X) is the total number of
its outbound links. But page A usually links to other pages itself. Thus, these pages
get a PageRank benefit also. If these pages link back to page A, page A will have an
even higher PageRank benefit from its additional inbound link
• Influence of Damping Factor

17. • Initially all have Pagerank 1
• We presume a constant Pagerank PR(X) of 10
• Damping factor is equal to 0.5
PR(A)= 0.5 + 0.5 (PR(X) + PR(D)) = 5.5 + 0.5 PR(D)
PR(B)= 0.5 + 0.5 PR(A)
PR(C)= 0.5 + 0.5 PR(B)
PR(D)= 0.5 + 0.5 PR(C)
PR(A) = 19/3 = 6.33
PR(B) = 11/3 = 3.67
PR(C) = 7/3 = 2.33
d × PR(X) / C(X) = 0,5 × 10 / 1 = 5
PR(D) = 5/3 = 1.67
* The higher the damping factor, the larger is the effect of an additional inbound link for
the PageRank of the page that receives the link and the more evenly distributes
PageRank over the other pages of a site.

18. Effect of
outbound links
PR(A) = 0.25 + 0.75 PR(B)
PR(B) = 0.25 + 0.375 PR(A)
PR(C) = 0.25 + 0.75 PR(D) + 0.375 PR(A)
PR(D) = 0.25 + 0.75 PR(C)
PR(A) = 14/23 PR(C) = 35/23
PR(B) = 11/23 PR(D) = 32/23
*Adding a link has no effect on the total PageRank of the web. Additionally, the
PageRank benefit for one site equals the PageRank loss of the other.

19. Dangling links
PR(A) = 0.25 + 0.75 PR(B)
PR(B) = 0.25 + 0.375 PR(A)
PR(C) = 0.25 + 0.375 PR(A)
PR(A) = 14/23
PR(B) = 11/23
PR(C) = 11/23
Dangling links could have major impacts on PageRank.

20. • In order to prevent PageRank from the
negative effects of dangling links, pages
wihout outbound links have to be removed
from the database until the PageRank values
are computed.
• According to Page and Brin, the number
of outbound links on pages with dangling
links is thereby normalised
PR(C) = 0.25 + 0.375 PR(A) = 0.625
*The accumulated PageRank does not equal the number of pages, but at least
all pages which have outbound links are not harmed from the danging links

21. Effect of the number
of pages
PR(A) = 260/14 PR(A) = 266/14 PR(A) = 13.97 PR(A) = 11.97
PR(B) = 101/14 PR(B) = 70/14 PR(B) = 10.73 PR(B) = 9.23
PR(C) = 101/14 PR(C) = 70/14 PR(C) = 8.30 PR(C) = 7.17
PR(D) = 70/14 PR(D) = 5.63
* The PageRank algorithm tends to privilege smaller web sites.

22. The distribution of
pagerank for s.e.o.
PR(A) = 8 PR(A) = 7
PR(B) = 2.5 PR(B) = 3
PR(C) = 2.5 PR(C) = 3
PageRank will distribute for the purpose of search engine optimisation more equally
among the pages of a site, the more the hierarchically lower pages are interlinked.

23. Concentration of
outbound links
PR(A) = 1 PR(A) = 17/13
PR(B) = 2/3 PR(B) = 28/39
PR(C) = 2/3 PR(C) = 28/39
PR(D) = 2/3 PR(D) = 28/39
Concentrate external outbound links on as few pages as possible, as long as it does not lessen a
site's usabilty.

24. Link exchanges
PR(A) = 4/3 PR(D) = 4/3 PR(A) = 3/2 PR(D) = 3/2
PR(B) = 5/6 PR(E) = 5/6 PR(B) = 3/4 PR(E) = 3/4
PR(C) = 5/6 PR(F) = 5/6 PR(C) = 3/4 PR(F) = 3/4
A link exchange is thus advisable, if one page (e.g. the root
page of a site) shall be optimised for one important key

25. Additional factors
• Visibility of a link
• Position of a link within a
document
• Distance between web
pages
• Importance of a linking page

26. Bibliography
• Wikipedia
• Pr.efactory.de
• Youtube
• Google Images

27. questionnaires