PageRank ("PR") is a numeric value that represents how
important a page is on the web. Google figures that when one page links to
another page, it is effectively casting a vote for the other page. The more
votes that are cast for a page, the more important the page must be. Also, the
importance of the page that is casting the vote determines how important the
vote itself is. Google calculates a page's importance from the votes cast for
it. How important each vote is is taken into account when a page's PageRank is
calculated.
Google PageRank Explained
PageRank is a
patented method 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 Page-Rank [Vise and Malseed, 2005]) 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:
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.
More about
PR Help:
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, high-quality 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
text-matching 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 spamdexing.
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 8-unit 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.gif 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 PageRank algorithm are the HITS algorithm proposed by Jon
Kleinberg and the IBM CLEVER project. 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 any-size 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 link-votes 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).
The PageRank Algorithm
We can think of it in a simpler way:-
a page's PageRank = 0.15 + 0.85 * (a "share" of the
PageRank of every page that links to it)
"share" = the linking page's PageRank divided by the number of outbound links
on the page.
A page "votes" an amount of PageRank onto each page that it links to. The
amount of PageRank that it has to vote with is a little less than its own
PageRank value (its own value * 0.85). This value is shared equally between all
the pages that it links to.
From this, we could conclude that a link from a page with PR4 and 5
outbound links is worth more than a link from a page with PR8 and 100 outbound
links. The PageRank of a page that links to yours is important but the number of
links on that page is also important. The more links there are on a page, the
less PageRank value your page will receive from it.
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 p1,p2,...,pN are the pages under consideration, M(pi) is the set of pages
that link to pi, L(pj) is the number of links coming from page pj, 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 pj does not link to pi, 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). The Google Directory (itself a
derivative of the Open Directory Project) is an exception in which 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.
Spoofing is generally detected by running a Google search for a URL with
questionable PR, as the results will display the URL of an entirely different
site (the one redirected to) in its results.
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 search-engine optimization purposes, webmasters often buy links for their
sites. As links from higher-PR 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. Google
officially advises that users should place rel="nofollow" on such purchased
links.
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.
A Web crawler may use Pagerank as one of a number of importance metrics it uses
to determine which URL to visit next during a crawl of the web. One of the early
working papers which was used in the creation of Google is Efficient crawling
through URL ordering, which discusses the use of a number of different
importance metrics to determine how deeply, and how much of a site Google will
crawl. Pagerank is presented as one of a number of these importance metrics,
though there are others listed such as the number of inbound and outbound links
for a URL, and the distance from the root directory on a site to the URL.
PageRank and search engine results PageRank is just one factor, amongst more than 100, used to calculate the rank
of a page in results of searches.
References
Sergey Brin and Lawrence Page (1998). "The anatomy of a large-scale hypertextual
Web search engine". Proceedings of the seventh international conference on World
Wide Web 7, 107-117.
Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd (1999). "The
PageRank citation ranking: Bringing order to the Web".
Matthew Richardson and Pedro Domingos (2002). "The intelligent surfer:
Probabilistic combination of link and content information in PageRank".
Proceedings of Advances in Neural Information Processing Systems.
David Vise and Mark Malseed (2005). The Google Story, 37.
Cho, J., Garcia-Molina, H., and Page, L. (1998). "Efficient crawling through URL
ordering". Proceedings of the seventh conference on World Wide Web.
Working Papers Concerning the Creation of Google. Google. Retrieved on June 30,
2006.
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