PageRank
Online Advertising
PageRank
Websites with a high PageRank
PageRank is a patented method (an
algorithm) to assign a numerical weighting to each element of a
hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative
importance within the set. The algorithm may be applied to any
collection of entities with reciprocal quotations and references. The
numerical weight that it assigns to any given element E is also
called the PageRank of E and denoted by
PR(E).
PageRank was developed at Stanford University by Larry Page (hence the name
PageRank) and Sergey Brin as part of a research project about a new kind of
search engine. The project started in 1995 and led to a functional prototype,
named Google, in 1998. Shortly after, Page and Brin founded Google Inc., the
company behind the Google search engine, which still has PageRank as a key element.
PageRank uses links as "votes"
Google describes PageRank as:
 PageRank relies on the uniquely democratic nature of the web by using
its vast link structure as an indicator of an individual page's value. In
essence, Google interprets a link from page A to page B as a vote, by page
A, for page B. But, Google looks at more than the sheer volume of votes, or
links a page receives; it also analyzes the page that casts the vote. Votes
cast by pages that are themselves "important" weigh more heavily and help to
make other pages "important."
In other words, a PageRank results from a "ballot" among all the other pages
on the World Wide Web about how important a page is. A hyperlink to a page
counts as a vote of support. The PageRank of a page is defined recursively and
depends on the number and PageRank metric of all pages that link to it
("incoming links"). A page that is linked to by many pages with high PageRank receives
a high rank itself. If there are no links to a web page there is no support for
that page.
Numerous academic papers concerning PageRank have been published since Page
and Brin's original paper. In practice, the PageRank concept has proven to be
vulnerable to manipulation, and extensive research has been devoted to
identifying falsely inflated PageRank and ways to ignore links from documents
with falsely inflated PageRank.
Important, highquality sites receive a higher PageRank, which Google
remembers each time it conducts a search. Of course, important pages mean
nothing to you if they don't match your query. So, Google combines PageRank with
sophisticated textmatching techniques to find pages that are both important and
relevant to your search. Google goes far beyond the number of times a term
appears on a page and examines all aspects of the page's content (and the
content of the pages linking to it) to determine if it's a good match for your
query.
Google's "rel=nofollow" proposal
In early 2005, Google implemented a new value, "nofollow", for the rel
attribute of HTML link and anchor elements, so that website builders and bloggers
can make links that Google will not consider for the purposes of PageRank — they
are links that no longer constitute a "vote" in the PageRank system. The
nofollow relationship was added in an attempt to help combat comment
spam.
Google toolbar PageRank
The Google Toolbar PageRank measures PageRank from 0 to 10. Many people
assume that the Toolbar PageRank is a proxy value determined through a
logarithmic scale. Google has not disclosed the precise method for determining a
Toolbar PageRank value. Google representatives, such as engineer Matt Cutts,
have publicly indicated that the Toolbar PageRank is republished about once
every three months, indicating that the Toolbar PageRank values are generally
unreliable measurements of actual PageRank value for most periods of the year.
Google directory PageRank
The Google Directory PageRank is an 8unit measurement. These values can be
viewed in the Google Directory. Unlike the Google Toolbar which shows the
PageRank value by a mouseover of the greenbar, the Google Directory doesn't show
the PageRank values. You can only see the PageRank scale values by looking at
the source and wading though the HTML code.
These eight positions are displayed next to each Website in the Google
Directory. cleardot.gif is used for a zero value and a combination of two
graphics pos.gif and neg.fig are used for the other 7 values. The pixel widths
of the seven values are 5/35, 11/29, 16/24, 22/18, 27/13, 32/8 and 38/2 (pos.gif/neg.gif).
"PageRank" as a trademark
The name PageRank is a trademark of Google. The PageRank process has
been patented (U.S.
Patent 6,285,999). The patent is not assigned to Google but to Stanford
University.
Alternatives to the Page rank algorithm are the
HITS algorithm proposed by Jon Kleinberg and the CLEVER project at IBM. Many
HITS concepts are now incorporated into Teoma and Ask.com.
Some algorithm details
PageRank is a
probability distribution used to represent the likelihood that a person
randomly clicking on links will arrive at any particular page. PageRank can be
calculated for anysize collection of documents. It is assumed in several
research papers that the distribution is evenly divided between all documents in
the collection at the beginning of the computational process. The PageRank
computations require several passes, called "iterations", through the collection
to adjust approximate PageRank values to more closely reflect the theoretical
true value.
A probability is expressed as a numeric value between 0 and 1. A 0.5
probability is commonly expressed as a "50% chance" of something happening.
Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a
random link will be directed to the document with the 0.5 PageRank.
Simplified PageRank algorithm
Suppose a small universe of four web pages: A, B,C and
D. The initial approximation of PageRank would be evenly divided between
these four documents. Hence, each document would begin with an estimated
PageRank of 0.25.
If pages B, C, and D each only link to A, they
would each confer 0.25 PageRank to A. All PageRank in this simplistic
system would thus gather to A because all links would be pointing to A.

But then suppose page B also has a link to page C, and page
D has links to all three pages. The value of the linkvotes is divided among
all the outbound links on a page. Thus, page B gives a vote worth 0.125
to page A and a vote worth 0.125 to page C. Only one third of D's
PageRank is counted for A's PageRank (approximately 0.081).

In other words, the PageRank conferred by an outbound link is equal to the
document's own PageRank score divided by the normalized number of outbound links
(it is assumed that links to specific URLs only count once per document).

PageRank algorithm including damping factor
The PageRank theory holds that even an imaginary surfer who is randomly
clicking on links will eventually stop clicking. The probability, at any step,
that the person will continue is a damping factor d. Various studies have
tested different damping factors, but it is generally assumed that the damping
factor will be set around 0.85.
The damping factor is subtracted from 1 (and in some variations of the
algorithm, the result is divided by the number of documents in the collection)
and this term is then added to the product of (the damping factor and the sum of
the incoming PageRank scores).
That is,

or (N = the number of documents in collection)

So any page's PageRank is derived in large part from the PageRanks of other
pages. The damping factor adjusts the derived value downward. The second formula
above supports the original statement in Page and Brin's paper that "the sum of
all PageRanks is one". Unfortunately, however, Page and Brin gave the first
formula, which has led to some confusion.
Google recalculates PageRank scores each time it crawls the Web and rebuilds
its index. As Google increases the number of documents in its collection, the
initial approximation of PageRank decreases for all documents.
The formula uses a model of a random surfer who gets bored after
several clicks and switches to a random page. The PageRank value of a page
reflects the chance that the random surfer will land on that page by clicking on
a link. It can be understood as a Markov
chain in which the states are pages, and the transitions are all equally
probable and are the links between pages.
If a page has no links to other pages, it becomes a sink and therefore
terminates the random surfing process. However, the solution is quite simple. If
the random surfer arrives at a sink page, it picks another
URL at random and
continues surfing again.
When calculating PageRank, pages with no outbound links are assumed to link
out to all other pages in the collection. Their PageRank scores are therefore
divided evenly among all other pages. In other words, to be fair with pages that
are not sinks, these random transitions are added to all nodes in the Web, with
a residual probability of usually d = 0.85, estimated from the frequency
that an average surfer uses his or her browser's bookmark feature.
So, the equation is as follows:

where p_{1},p_{2},...,p_{N}
are the pages under consideration, M(p_{i})
is the set of pages that link to p_{i},
L(p_{j}) is the number
of links coming from page p_{j},
and N is the total number of pages.
The PageRank values are the entries of the dominant eigenvector of the
modified adjacency matrix. This makes PageRank a particularly elegant
metric: the eigenvector is

where R is the solution of the equation

where the adjacency function
is 0 if page
p_{j} does not link to
p_{i}, and normalised such
that, for each j

i.e. the elements of each column sum up to 1.
This is a variant of the
eigenvector centrality measure used commonly in network analysis.
The values of the PageRank eigenvector are fast to approximate (only a few
iterations are needed) and in practice it gives good results.
As a result of
Markov theory, it can be shown that the PageRank of a page is the probability of
being at that page after lots of clicks. This happens to equal t − 1 where t is
the expectation of the number of clicks (or random jumps) required to get from
the page back to itself.
The main disadvantage is that it favors older pages, because a new page, even
a very good one, will not have many links unless it is part of an existing site
(a site being a densely connected set of pages).
For that reason, Google uses over 100 factors to determine the order of
search query results. Except in the Google Directory (itself a derivative of the
Open Directory Project), PageRank is not used to determine search results
rankings.
Several strategies have been proposed
to accelerate the computation of PageRank.
Various strategies to manipulate PageRank have been employed in concerted
efforts to improve search results rankings and monetize advertising links. These
strategies have severely impacted the reliability of the PageRank concept, which
seeks to determine which documents are actually highly valued by the Web
community.
Google is known to actively penalize
link farms
and other schemes designed to artificially inflate PageRank. How Google
identifies link farms and other PageRank manipulation tools are among Google's trade
secrets.
False or spoofed PageRank
While the PR shown in the Toolbar is considered to be accurate (at the time
of publication by Google) for most sites, it must be noted that this value is
also easily manipulated. A current flaw is that any low PageRank page that is
redirected, via a 302 server header or a "Refresh" meta tag,
to a high PR page causes the lower PR page to acquire the PR of the destination
page. In theory a new, PR0 page with no incoming links can be redirected to the
Google home page  which is a PR 10  and by the next PageRank update the PR of
the new page will be upgraded to a PR10. This is called spoofing and is a known
failing or bug in the system. Any page's PR can be spoofed to a higher or lower
number of the webmaster's choice and only Google has access to the real PR of
the page.
Google's home page is often considered to be automatically rated a 10/10 by
the
Google Toolbar's PageRank feature, but its PageRank has at times shown a
surprising result of only 8/10 (which is lower than other, very few, web pages
that are not related to Google) and it seems that this rating was achieved
through the PageRank algorithm, and wasn't programmed into the toolbar by Google
as constant.
Buying text links
For
searchengine optimization purposes webmasters often buy links for their
sites. As links from higherPR pages are believed to be more valuable they tend
to be more expensive. It can be an effective and viable marketing strategy to
buy link advertisements on content pages of quality and relevant sites to drive
traffic and increase a webmaster's link popularity. However, Google has publicly
warned webmasters that if they are or were discovered to be selling links for
the purpose of conferring PageRank and reputation, their links will be devalued
(ignored in the calculation of other pages' PageRanks). The practice of buying
and selling links is intensely debated across the Webmastering community.
Other uses of PageRank
A version of PageRank has recently been proposed as a replacement for the
traditional ISI
impact factor. Instead of merely counting citations of a journal, the
"quality" of a citation is determined in a PageRank fashion.
See also
External links
Home  Up  Google bomb  Google juice  Googleating  Googlebait  PageRank
Online Advertising, made by MultiMedia  Free content and software
This guide is licensed under the GNU
Free Documentation License. It uses material from the Wikipedia.
