Google PageRank
Prof. Beat Signer
<bsigner@vub.ac.be>
Department of Computer Science
Vrije Universiteit Brussel
http://vub.academia.edu/BeatSigner
December 9, 2008

Overview
 History of PageRank
 PageRank algorithm
 Examples
 Implications for website development
December 9, 2008 Beat Signer, bsigner@vub.ac.be 2

History of PageRank
 Developed as part of an academic Larry Page Sergey Brin
project at Stanford University
 research platform to aid understanding 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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 3

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)
December 9, 2008 Beat Signer, bsigner@vub.ac.be 4

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 5

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 6

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 7

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 8

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 9

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 10

G  1  d  1  dS
1
Examples n
A2
0.37
A1 A3
0.26 0.37
December 9, 2008 Beat Signer, bsigner@vub.ac.be 11

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 12

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 13

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 14

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 15

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 16

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 17

Consistent Addressing of Webpages
December 9, 2008 Beat Signer, bsigner@vub.ac.be 18

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")
December 9, 2008 Beat Signer, bsigner@vub.ac.be 19

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
 ...
December 9, 2008 Beat Signer, bsigner@vub.ac.be 20

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, bsigner@vub.ac.be 21

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
 …
December 9, 2008 Beat Signer, bsigner@vub.ac.be 22

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
 …
December 9, 2008 Beat Signer, bsigner@vub.ac.be 23

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)?
 …
December 9, 2008 Beat Signer, bsigner@vub.ac.be 24

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
 ...
December 9, 2008 Beat Signer, bsigner@vub.ac.be 25

Questions
 Is PageRank fair?
 What about Google's power and influence?
December 9, 2008 Beat Signer, bsigner@vub.ac.be 26

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 27

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
December 9, 2008 Beat Signer, bsigner@vub.ac.be 28

References …
 PageRank Uncovered, C. Ridings and
M. Shishigin, September 2002
 PageRank Calculator,
http://www.webworkshop.net/pagerank_
calculator.php
December 9, 2008 Beat Signer, bsigner@vub.ac.be 29