The document discusses PageRank, an algorithm that assigns a numerical ranking to websites to indicate their relative importance. It defines PageRank as a number given to a page based on the number and quality of links to it, with more incoming links from important pages increasing a page's rank. The document provides the PageRank calculation formula and shows an example of running the algorithm over multiple iterations on a sample network of web pages to calculate their PageRank values. It notes that Page B had the highest PageRank after 30 iterations. Finally, it mentions implementing PageRank in Spark and Scala.

1. PageRank - Spark/Scala
Yubraj Pokharel

2. PageRank Algorithm Implementation in Spark

3. What is PageRank?
PageRank of a web page is a number given to the page which represents the
relative importance of that page in comparison to all other web pages.
A web page contains inbound and outbound links.
A page which has more inbound links is considered more important.

4. How to calculate it?
PR(A) = (1-d) + d * (PR(T1) / C(T1) + ... + PR(Tn) / C(Tn))
PR(A) => pagerank of a web page
d => damping factor
PR(Tn) => page ranks of web pages inbound to the web page whose page rank
we are calculating
C(Tn) => number of outbound links in the web page specified by PR(Tn)

5. How it is calculated?
Links
(A, B)
(B, C)
(B, E)
(C, A)
(C, D)
(C, E)
(D, A)
(D, C)
(E, B)
Initial Page Ranks
PR(A) = 1.0
PR(B) = 1.0
PR(C) = 1.0
PR(D) = 1.0
PR(E) = 1.0

6. 1st iteration
Links
(A, B)
(B, C)
(B, E)
(C, A)
(C, D)
(C, E)
(D, A)
(D, C)
(E, B)
PR(A) = 0.15 + 0.85*(⅓ + ½ ) =
0.8583333333333333
PR(B) = 0.15 + 0.85 * (1/1 + 1/1) = 1.85
PR(C) = 0.15 + 0.85 * (½ + ½) = 1.0
PR(D) = 0.433333333333
PR(E) = 0.858333333333

7. 2nd iteration
Links
(A, B)
(B, C)
(B, E)
(C, A)
(C, D)
(C, E)
(D, A)
(D, C)
(E, B)
PR(A) = 0.15 + 0.85*(1 / 3 +
0.433333333333 / 2) = 0.6175
PR(B) = 1.60916666666666
PR(C) = 1.12041666666666
PR(D) = 0.43333333333333
PR(E) = 1.21958333333333

8. 30th iteration
Links
(A, B)
(B, C)
(B, E)
(C, A)
(C, D)
(C, E)
(D, A)
(D, C)
(E, B)
(B, 1.685860900896)
(E, 1.1661421381814026)
(C, 1.0575926664315842)
(A, 0.6407530390774026)
(D, 0.4496512554136104)
B is the most ranked page

9. Spark/Scala Code

10. References
1. http://www.cs.princeton.edu/~chazelle/courses/BIB/pagerank.htm
2. http://www.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html
3. http://www.ams.org/samplings/feature-column/fcarc-pagerank
4. http://www.umiacs.umd.edu/~jbg/teaching/INFM_718_2011/lecture_3.pdf
5. http://www.cse.cuhk.edu.hk/~cslui/CMSC5702/mapreduce_hadoop2.pdf

11. Questions??

12. Thank you :)
-happy coding