Google PageRank

Google PageRank
Prof. Beat Signer
<bsigner@vub.ac.be>

Department of Computer Science
Vrije Universiteit Brussel

http://www.beatsigner.com

December 9, 2008

Overview
 History of PageRank
 PageRank algorithm
 Examples
 Implications for website development

December 9, 2008 Beat Signer, signer@inf.ethz.ch 2

History of PageRank
 Developed as part of an academic
project at Stanford University
 research platform to aid under- Larry Page Sergey Brin
standing of large-scale web data
and enable researches to easily
experiment with new search technologies
 Larry Page and Sergey Brin worked on the project
about a new kind of search engine (1995-1998) which
finally led to a functional prototype called Google


Web Search Until 1998
 Find all documents using a query term
 use information retrieval (IR) solutions
 ranking based on "on-page factors"
 problem: poor quality of search results (order)
 Page and Brin proposed to compute the
absolute qualtity of a page (PageRank)
 based on the number and quality of pages
linking to a page (votes)


PageRank P1 P5 P7 P8
R1 R5 R7 R8

P2 P3 P4 P6
R2 R3 R4 R6

 A page has a high PageRank R if
 there are many pages linking to it
 or, if there are some pages with a high PageRank
linking to it
 Total score = IR score x PageRank

PageRank Algorithm
R( Pj )
R( Pi )  
Pj Bi Lj
P1 P2

1.5
1 1.5
1

 where
 Bi is the set of pages
that link to page Pi P3

 Lj is the number of 0.75
1
outgoing links for page Pj


Matrix Representation
 Let us define a hyperlink P1 P2
matrix H
1 L j if Pj  Bi
H ij  
 0 otherwise
0 1 2 1 
and R  RPi 
P3
H  1 0 0
 
 R  HR 0 1 2 0 
 
R is an eigenvector of H
with eigenvalue 1

Matrix Representation ...
 We can use the power method to find R
t 1
R  HR t

0 1 2 1 
For our example H  1 0 0
 
0 1 2 0 
 

this results in R  2 2 1 or 0.4 0.4 0.2


Dangling Pages
 Problem with pages P1 P2
C
that have no outbound
links (P2)

0 0  C

H  and R  0 0
1 0
0 1 2  0 1 2
C  and S  H  C   
 0 1 2 1 1 2

Strongly Connected Pages (Graph)
1-d
 Add new transition P1 P2
probabilities between
all pages
 with probability d we follow
P4 P3
the hyperlink structure S
 with probability 1-d we
choose a random page
P5
1-d 1-d
G  1  d  1  dS
1
R  GR
n

G  1  d  1  dS
1
Examples n

A2

0.37

A1 A3

0.26 0.37


G  1  d  1  dS
1
Examples ... n

A2 B2

0.185 0.185

A1 A3 B1 B3

0.13 0.185 0.13 0.185

P A  0.5 PB   0.5


G  1  d  1  dS
1
Examples ... n

A2 B2

0.14 0.20

A1 A3 B1 B3

0.10 0.14 0.22 0.20

P A  0.38 PB   0.62


G  1  d  1  dS
1
Examples ... n

A2 B2

0.23 0.095

A1 A3 B1 B3

0.3 0.18 0.10 0.095

P A  0.71 PB   0.29


G  1  d  1  dS
1
Examples ... n

A2 B2

0.24 0.07

A1 A3 B1 B3

0.35 0.18 0.09 0.07

P A  0.77 PB   0.23


G  1  d  1  dS
1
Examples ... n

A2 B2

0.17 0.06

A1 A3 B1 B3

0.33 0.175 0.08 0.06

A4 PB   0.20

P A  0.80
0.125


Implications for Website Development
 First make sure that your page gets indexed
 on-page factors
 Think about your site's internal link structure
 create many internal links for important pages
 be "careful" about where to put outgoing links
 Increase the number of pages
 Ensure that webpages are addressed consistently
 http://www.vub.ac.be  http://www.vub.ac.be/index.php
 Make sure that you get links from good websites

Consistent Addressing of Webpages


Search Engine Optimisations (SEO)
 Internet marketing has become a big business
 white hat and black hat optimisations
 Bad ranking or removal from index can cost a
company a lot of money
 e.g. supplemental index ("Google hell")


Black Hat Optimisations (Don'ts)
 Link farms
 Spamdexing in guestbooks, Wikipedia etc.
 "solution": <a rel="nofollow" href="…">…</a>
 Doorway pages (cloaking)
 e.g. BMW Germany and Ricoh Germany banned in
February 2006
 Selling/buying links
 ...

On-Page Factors (Speculative)
 It is assumed that there are over 200 on-page
and off-page factors
 Positive factors
 keyword in title tag
 keyword in URL
 keyword in domain name
 quality of HTML code
 page freshness (occasional changes)
 …

December 9, 2008 Beat Signer, signer@inf.ethz.ch

On-Page Factors (Speculative) …
 Negative factors
 links to "bad neighbourhood"
 over optimisation penalty (keyword stuffing)
 text with same colour as background (hidden content)
 automatic redirects via the refresh meta tag
 any copyright violations
 …


Off-Page Factors (Speculative)
 Positive factors
 high PageRank
 anchor text of inbound links
 links from authority sites (Hilltop algorithm)
 listed in DMOZ (ODP) and Yahoo directories
 site age (stability)
 domain expiration date
 …


Off-Page Factors (Speculative) …
 Negative factors
 link buying (fast increasing number of inbound links)
 link farms
 cloaking (different pages for spider and user)
 limited (temporal) availability of site
 links from bad neighbourhood?
 competitor attack (e.g. duplicate content)?
 …


Tools
 Google toolbar
 PageRank information not frequently updated
 Google webmaster tools
 meta description issues
 title tag issues
 non-indexable content issues
 number and URLs of indexed pages
 number and URLs of inbound/outbound links
 ...


Questions
 Is PageRank fair?
 What about Google's power and influence?


Conclusions
 PageRank algorithm
 absolute quality of a page based on incoming links
 random surfer model
 computed as eigenvector of Google matrix G
 Implications for website development and SEO
 PageRank is just one (important) factor


References
 The PageRank Citation Ranking: Bringing Order
to the Web, L. Page, S. Brin, R. Motwani and
T. Winograd, January 1998
 The Anatomy of a Large-Scale Hypertextual
Web Search Engine, S. Brin and L. Page,
Computer Networks and ISDN Systems, 30(1-7),
April 1998


References …
 PageRank Uncovered, C. Ridings and
M. Shishigin, September 2002
 PageRank Calculator,
http://www.webworkshop.net/pagerank_
calculator.php


Google PageRank

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