CS492 Special Topics in Computer Science
Distributed Algorithms and Systems
Lecture 4
“The PageRank Citation Ranking:
Bringing Order to the Web”
L. Page, S. Brin, R. Motwani, T Winograd
1998
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Origin of “Google”
 Googol

10^100
 Motivation behind


Human maintained indices such as Yahoo!
Explosive growth
Hostnames
Active
http://news.netcraft.com
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Design Goals of Google
 Improved search quality


In 1997, 1 out of 4 top search engines found itself
High precision in finding relevant document was necessary
 Academic search engine research



Search engine technology went commercial: an black art
To build systems that a good number of people could use
To build an architecture to support novel research on
large-scale Web data
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Weakness of Existing Approaches
 Calculate similarities


Based on flat, vector-space model of each page
Prone to cheating (Web spamming or search engine
persuasion)
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Basic Idea of PageRank
 Exploit the topological structure of hypertextual
systems
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Simple Example
0.4
A
C
0.2
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0.4
B
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Related Work
 Academic citation analysis

Similarities
 Graph
structure;
paper = node, web page = node
citation = link, URL = link
 “node” authority independent of “node” content

Differences
 Uniform
unit of info (paper) versus
great variability in quality, usage, citations, and length
 Equal link weight vs variable importance
A backlink from Yahoo! vs. from a friend
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Which Page Should Be Ranked Higher?
John Doe
A
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B
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Simple Expression
page rank of
set of pages pointing at
out-degree of
Question: role of c?
Answer: total rank of all web pages constant
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Dangling links
 Pages without outgoing pointers

Example: Pages not yet downloaded
 Do not affect the calculation much

Remove them, calculate ranks, and add them back
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Loop
A
C
B
Question: ranks of A, B, and C?
Answer: infinite! (rank sink)
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Basic Algorithm
page rank of
set of pages pointing at
out-degree of
dumping factor
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Matrix Representation
where
and
Question: Where to start?
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Iterative Algorithm
where
and
Question: Will it converge?
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Example
[LM04]
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Turn the Problem into a Markov Process
[LM04]
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Evenly Split Rank of Dangling Links
[LM04]
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Final Solution
 Eigenvector of P = steady state rank
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Spam Rank
[BGS05]
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Questions
 Where to start?

Find a nondegenerate start vector
 What if there are two pages that point to each other
and no one else and there is a page that points to
one of them?

Role of dumping factor guarantees no rank sink
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References
[BP98] Sergey Brin, Lawrence Page, “The anatomy of a large-scale hypertextual Web search
engine,” Computer Networks and ISDN Systems, Vol. 30, 1998.
[BGS05] Monica Bianchini, Marco Gori, Franco Scarselli, “Inside PageRank,” ACM Transactions on
Internet Technology, Vol. 5, No. 1, Feb. 2005.
[LM04] Amy N. Langville, Carl Meyer, “Deeper inside PageRank,” Internet Mathematics, Vol. I, No.
3, 2004.
[K99] Jon Kleinberg, “Authoritative sources in a Hyperlinked Environment,” Journal of the ACM
46:5 (1999).
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