PageRank is a link analysis algorithm and it assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is referred to as the PageRank of E and denoted by {\displaystyle PR(E).} PR(E). Other factors like Author Rank can contribute to the importance of an entity. A PageRank results from a mathematical algorithm based on the webgraph, created by all World Wide Web pages as nodes and hyperlinks as edges, taking into consideration authority hubs such as cnn.com or usa.gov. The rank value indicates an importance of a particular page. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). A page that is linked to by many pages with high PageRank receives a high rank itself. Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[5] In practice, the PageRank concept may be vulnerable to manipulation. Research has been conducted into identifying falsely influenced PageRank rankings. The goal is to find an effective means of ignoring links from documents with falsely influenced PageRank. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com),the IBM CLEVER project, the TrustRank algorithm and the hummingbird algorithm.

1. Page Rank Algortihm
Guided by- Rashmita Routray Submitted by:Siddharth Satyajit Kar
Affiliation- Assistant Professor Redg.No:1341012069
Department-CSE Branch :CSE

2. Background
o Two popular algorithms were introduced in 1998 to rank web pages by
popularity and provide better search results. They are:
o HITS (Hypertext Induced Topic Search)
o Page Rank
o HITS was proposed by Jon Kleinberg who was a young scientist at IBM in
Silicon Valley and now a professor at Cornell University.
o Page Rank was proposed by Sergey Brin and Larry Page, students at
Stanford University and the founders of Google.
o This is the technology that is implemented at the heart of Google search
engine.

3. The Web’s hyperlink structure forms a massive directed
graph.
The nodes in the graph represent web pages and the
directed arcs or links represent the hyperlinks.
Hyperlinks into a page are called inlinks and point into nodes and outlinks
point out from nodes. They are discussed in details later.
Page Rank
Proposed by Sergey Brin and Larry Page.
Thesis:
A web page is important if it is pointed to by
other important web pages.

4. Types Of Links
1)Inbound links or Inlinks :
• Inbound links are links into the site from the outside.
• Inlinks are one way to increase a site's total Page Rank.
• Sites are not penalized for inlinks.
2) Outbound links or Outlinks :
• Outbound links are links from a page to other pages in a site or other
sites.
3) Dangling links :
• Dangling links are simply links that point to any page with no
outgoing links.

5. Introduction to Page Rank Algorithm
• Page Rank is a numeric value that represents the importance of a page
present on the web.
• When one page links to another page, it is effectively casting a vote for the
other page.
• More votes implies more importance.
• Importance of the page that is casting the vote determines the importance
of the vote.

6. • A web page is important if it is pointed to by other important web pages.
• Importance of each vote is taken into account when a page's Page Rank is
calculated.
• Page Rank is Google's way of deciding a page's importance.
• It matters because it is one of the factors that determines a page's ranking
in the search results
Page Rank Notation- “PR”.

7. Basic Understanding of Page Rank
algorithm
• Initially 2 sites are there with PR
of 100(Site A) and 9(Site B)
respectively .
• Site A has two outlinks.So value
of each outlink will be 100/2=50.
• Site B has three outlinks.So value
of each outlink will be 9/3=3.
• Site C is pointed by one outlink of
A (50) and one outlink of B (3) .So it has a value of (50+3)=53.
• Site D is pointed by one outlink of A(50) only .So it has a PR value of
50.
• Again C(53) has 2 outlinks so each outlink have value (53/2).While
D(50) has two outlinks each with value of (50/2)=25.
• So the order is A > C > D > B

8. Algorithm
The original Page Rank algorithm which was described by Larry Page and
Sergey Brin is given by PR(A) = (1-d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))
where,
• PR(A) – Page Rank of page A
• PR(Ti) – Page Rank of pages Ti which link to page A
• C(Ti) - number of outbound links on page Ti
• d - damping factor which can be set between 0 and 1
A simple way of representing the formula is, (d=0.85) Page Rank (PR) =
0.15 + 0.85 * (a share of the Page Rank of every page that links to it) .
The amount of Page Rank that a page has to vote will be its own value *
0.85.

9. • This value is shared equally among all the pages that it links to.
• Page with PR 4 and 5 outbound links > Page with PR8 and 100 outbound
links.
• The calculations do not work if they are performed just once. Accurate
values are obtained through many iterations.
• Suppose we have 2 pages, A and B, which link to each other, and neither
have any other links of any kind. Page Rank of A depends on Page Rank
value of B and Page Rank of B depends on Page Rank value of A.
• We can't work out A's Page Rank until we know B's Page Rank, and we can't
work out B's Page Rank until we know A's Page Rank. But performing more
iterations can bring the values to such a stage where the Page Rank values
do not change. Therefore more iterations are necessary while calculating
Page Ranks

10. Mathematics of Page Rank Algorithm
The page rank equation is as follows,

11. Example of Page Rank Algorithm
(1) -> Outlinks =2 ,inlinks=1
(2) -> Outlinks =0
,inlinks=2
(3) -> Outlinks =2
,inlinks=1
(4) -> Outlinks =2
,inlinks=2
(5) -> Outlinks =2
,inlinks=2
(6) -> Outlinks =1
,inlinks=2

12. Calculation of Page Rank

13. Additional Factors to consider
• Visibility of a link .
• Position of a link within a document .
• Importance of a linking page .
• Up-to-dateness of a linking page .

14. Conclusion
Even though formula for calculating PageRank seems to be difficult,
it is easy to understand. But when a simple calculation is applied
hundreds of times, the results can seem complicated. And we can
not predict the result of these iterations. Surely, more practice can
yield more observations.
PageRank is important factor considered in Google ranking, but it is
not the only factor considered. e.g. now a days Google is paying a
lot of attention to the link’s anchor text while deciding relevancy of
target page.
Page Rank is one of the important factor, one should be well aware
of PageRank while designing the website.

15. Reference
• PageRank," in Wikipedia, Wikimedia Foundation, 2016. [Online].
Available: https://en.wikipedia.org/wiki/PageRank. Accessed: Aug.
24, 2016.
• Google PageRank - algorithm,". [Online]. Available:
http://pr.efactory.de/e-pagerank-algorithm.shtml. Accessed: Aug.
24, 2016.
• [Online]. Available:
http://www.cs.sjsu.edu/faculty/pollett/masters/Semesters/Fall11/t
anmayee/Deliverable3.pdf. Accessed: Aug. 24, 2016.
• Amy N.Langville and Carl D.Meyer’s Google’s Page Rank and
Beyond .

16. Thank You.