1. Lecture #11 PageRank (II)
CS492 Special Topics in Computer Science:
Distributed Algorithms and Systems
Lecture #11 PageRank (II)

2. Remind : PageRank Algorithm
PR(A) = (1-d) + d( PR(T1)/C(T1) PR(Tn)/C(Tn) )
= (1-d) + d( )
PR(A) : PageRank of page A
PR(Ti) : PageRank of Pages Ti which has link to pageA
C(Ti) : number of outbound links on page Ti
d : damping factor ( between 0 and 1 )

3. Simple Example
PR(A) = (1-d) + d( )
let d = 0.85 A B C

4. How to calculate PageRank
PR(A) = PR(C)
PR(B) = (PR(A) / 2)
PR(C) = (PR(A) / 2 + PR(B))
Method 1 : Solving the equations
Do the math
Method 2 : Iterative Computation of Page Rank
Huge size of Web : hard to solve the equations
Iterative computation of PageRank values

5. Solve the equations Solve these equations Answers
PR(A) = PR(C)
PR(B) = (PR(A) / 2)
PR(C) = (PR(A) / 2 + PR(B))
Answers
PR(A) =
PR(B) =
PR(C) =

6. Iterative Computation of Page Rank
Set initial PageRank values to all pages
Calculate PageRanks for all pages in several iterations
Stop iteration when PageRanks converge

7. What does PageRank mean?
Random surfer
who is given a web page at random and keep clicking on links. (never hit back button)
eventually gets bored and starts on another random page
PageRank
the probability that the random surfer visits a page
the proportion of time that the random surfer spends on each page

8. What is the damping factor?
PR(A) = (1-d) + d( )
Damping factor
(1-d) : the probability at each page the random surfer will get bored and request another random page
The higher d, the more likely will the random surfer keep clicking links

9. Loop which acts as a Rank Sink
Rank Sink Problem
What if we don’t have the damping factor?
No way to escape loop (A-B-C).
Loop which acts as a Rank Sink A B C

10. Dangling Link (Dead End)
Danglink link points to any page with no outgoing links
CA and BA are dangling links
A cannot distribute its weight to the network.
How to fix
Method 1 : Remove dangling links until all the PageRanks are calculated.
Method 2 : Make random jump to any other page

11. References
[PBMW] L. Page, S. Brin, R. Motwani, T. Winograd, “The PageRank citation ranking: bringing order to the web,” WWW 1998 [BP98] Sergey Brin, Lawrence Page, “The anatomy of a large-scale hypertextual Web search engine,” Computer Networks and ISDN Systems, Vol. 30, [BGS05] Monica Bianchini, Marco Gori, Franco Scarselli, “Inside PageRank,” ACM Transactions on Internet Technology, Vol. 5, No. 1, Feb [LM04] Amy N. Langville, Carl Meyer, “Deeper inside PageRank,” Internet Mathematics, Vol. I, No. 3, [K99] Jon Kleinberg, “Authoritative sources in a Hyperlinked Environment,” Journal of the ACM 46:5 (1999).