Abstract- PageRank is a numeric value that represents how
important a page is on the web. They are used for assigning numerical
weightings to hyperlinked documents (or web pages) indexed by a search engine.
A page rank results from a ballot among all the other pages on the World Wide
Web about how important a page is. Here, we examine all the hyperlinks in a web
page which is

counted as a vote of support. The PageRank algorithm page
is defined recursively and depends on the number and PageRank metric of all
pages that link to it called as incoming links. A page that is linked by many
pages with high rank receives a high rank itself. If there are no links to a
web page there is no support of this specific page. It uses some logarithmic
scale. Here, we program in such a way so that it crawls the entire website and
pulls a series of pages into the database, recording the links between the
pages. The spider chooses randomly amongst all the non-visited links across all
the webs.  It matters because it is one
of the factors that

determines a page’s ranking in the search results.


Keywords- PageRank, World Wide Web, Links, Pages.

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With a sudden
change in growth of the world-wide web exceeding 800 million pages. Web pages
are increasing day by day. These web pages create many challenges for
information retrieval. It is very huge and heterogeneous. In Current scenario
there are over 150 million web pages with a doubling life of less than one
year. More importantly, the web pages are extremely diverse.

addition, Page Rank is extensively used for ranking web pages in order of
relevance 1. PageRank works by counting the number of links to a page to
determine a rough estimate of how important the website is. Page Rank (determines
the importance of webpages based on link structure). Solves a complex system of
score equations. The PageRank algorithm outputs a probability distribution used
to represent the likelihood that a person randomly clicking on links will
arrive at any particular page 1. PageRank can be calculated for collections
of documents of any size. The main objective of our project is to determine the
rank of the webpage and thus, determine the importance of a web page. PageRank
works by counting the number of links to a page to determine a rough estimate
of how important the website is.

However, unlike flat document
collections, the World Wide Web is hypertext and provides considerable
auxiliary information on top of the text of the web pages, such as link
structure and link text. In this mini project, we take advantage of the link
structure of the Web to produce a global importance ranking of every web page.
This ranking, called PageRank, helps search engines and users quickly make
sense of the vast heterogeneity of the World Wide Web. There are different
PageRank algorithms like PageRank (PR), WPR (Weighted PageRank), HITS
(Hyperlink- Induced Topic Search) algorithms these algorithms used for
Information Retrieval 2.

ranking Algorithm:

  This algorithm
is used by all the search engines. It is a method to rank web pages giving to
it a numeric value that represents their importance. Based on the link
structure of the web a page X has a
high rank if:

It has many In-links
or few but highly ranked.

Has few Out-links.




    Although there is already
a large literature on academic citation analysis, there are a number of
significant differences between web pages and the academic publications.

Referred from “Jugo Cho, Hector Garcia-Molina, and
Lawrence Page. Efficient crawling through the URL ordering. In to Appear:
Proceedings of the Seventh International Web

Conference (WWW 98), 1998”. Unlike
academic papers which are scrupulously reviewed, web pages proliferate free of
quality control or publishing costs. With a simple program, huge numbers of
pages can be created easily, artificially inflating citation counts. Referred
from “Ron Weiss, Bienvenido Velez, Mark A. Sheldon, Chanathip Manprempre, Peter
Szilagyi, Andrzej Duda, and David K. Gifford. HyPursuit: A hierarchical network
search engine that exploits content-link hypertext clustering. In Proceedings
of the 7th ACM Conference on Hypertext, pages 180-193, New York, 16-20 March
1996. ACM Press.”. Because the Web environment contains competing profit
seeking ventures, attention getting strategies evolve in response to search
engine algorithms. For this reason, any evaluation strategy which counts
replicable features of web pages is prone to manipulation. Ellen Spertus.
Parasite: Mining structural information on the web. In Proceedings of the Sixth
International WWW Conference, Santa Clara USA, April, 1997, 1997.  It is obvious to try to apply standard
citation analysis techniques to the web’s hyper textual citation structure. So,
a major page like http://www.yahoo.com/ will have tens of thousands of
backlinks (or citations) pointing to it. This fact that the Yahoo home page has
so many backlinks generally imply that it is quite important. Indeed, many of
the web search engines have used backlink count as a way to try to bias their
databases in favour of higher quality or more important pages. However, simple
backlink counts have a number of problems on the web. Some of these problems
have to do with characteristics of the web which are not present in normal
academic citation databases. International Journal of Advanced Research in
Computer Engineering & Technology (IJARCET) Volume 4 Issue 6, June 2015. Page
Rank (determines the importance of webpages based on link structure). Solves a
complex system of score equations. The PageRank algorithm outputs a probability
distribution used to represent the likelihood that a person randomly clicking
on links will arrive at any particular page. Further, academic papers are well
defined units of work, roughly similar in quality and number of citations, as
well as in their purpose – to extend the body of knowledge. Web pages vary on a
much wider scale than academic papers in quality, usage, citations, and length.
This is because the simplicity of creating and publishing web pages results in a
large fraction of low quality web pages that users are unlikely to read.





 The proposed
system is based on hyperlinks. Here, we examine all the hyperlinks in a page
which is counted as a vote of support. The Page Rank of a page is defined
recursively and depends on the number and Page Rank metric of all pages that
link to it called as incoming links. A page that is linked by many pages with
high rank receives a high rank itself. If there are no links to a web page
there is no support of this specific page. It uses some logarithmic scale. Page
Rank of a web page is a numerical number representing the importance of that
web page based on the number of inbound links. The basic concept of PageRank is
that the importance of a page is directly proportional to the number of web
pages linking to that page. So, Page Rank algorithm considers a page more
important if large number of other web pages are linking to that page or if
links are coming from some of most important and popular web pages. Page Rank
of whole website is not valid because page rank is associated with every web
page on the web.

1)       We
have implemented PageRank using traditional PageRank algorithm.

2)       Technology
used to develop PageRank is python.

3)       Apart
from ranking web pages we have created a graph where we can visualize the
webpages which are interlinked with other pages.

We can identify all the web pages which has highest and
lowest importance and we can also open them.












Fig. 1.
System Architecture


           We convert
each URL into a unique integer, and store each hyperlink in a database using
the integer IDs to identify pages 3. First, we sort the link structure by
Parent ID. Then dangling links are removed from the link database for reasons
discussed above (a few iterations removes the vast majority of the dangling
links). We need to make an initial assignment of the ranks. This assignment can
be made by one of several strategies. If it is going to iterate until
convergence, in general the initial values will not affect final values, just
the rate of convergence. But we can speed up convergence by choosing a good
initial assignment. We believe that careful choice of the initial assignment
and a small finite number of iterations may result in excellent or improved

 Memory is allocated for the weights for every
page. If insufficient RAM is available to hold all the weights, multiple passes
can be made (our implementation uses half as much memory and two passes). The
weights from the current time step are kept in memory, and the previous weights
are accessed linearly on disk. Also, all the access to the link database, A, is
linear because it is sorted. Therefore, A can be kept on disk as well. Although
these data structures are very large, linear disk access allows each iteration
to be completed in about 6 minutes on a typical workstation. After the weights
have converged, we add the dangling links back in and precompute the rankings.
Note after adding the dangling links back in, we need to iterate as many times
as was required to remove the dangling links. Otherwise, some of the dangling
links will have a zero weight. With less strict convergence criteria, and more
optimization, the calculation could be much faster. Or, more efficient
techniques for estimating eigenvectors could be used to improve performance.
However, it should be noted that the cost required to compute the PageRank is
insignificant compared to the cost required to build a full text index. One of
the interesting ramifications of the fact that the PageRank calculation
converges rapidly is that the web is an expander-like graph.





Fig. 2.
Links structure of the webpage


Every page has some number of
forward links (out edges) and backlinks. We can never know whether we have
found all the backlinks of a particular page but if we have downloaded it, we
know all its forward links at that time. Web pages vary greatly in terms of the
number of backlinks they have. For example, the Netscape home page has 62,804
backlinks in our current database compared to most pages which have just a few
backlinks. Generally, highly linked pages are more important” than pages
with few links. The reason that PageRank is interesting is that there are many
cases where simple citation counting does not correspond to our common-sense
notion of importance. For example, if a webpage has a link other Yahoo home
page, it may be just one link but it is a very important one. This page should
be ranked higher than many pages with more links but from obscure places.
PageRank is an attempt to see how good an approximation to importance”
can be obtained just from the link structure.


A. Propagation of Ranking through Links


1)  Inbound links:

Inbound links (links into the site from the outside) are one way to
increase a site’s total Page Rank. The other is to add more pages. The linking
page’s Page Rank is important, but so is the number of links going from that
page. Once the Page Rank is injected into your site, the calculations are done again
and each page’s Page Rank is changed. Depending on the internal link structure,
some pages’ Page Rank is increased, some are unchanged but no pages lose any
Page Rank. It is beneficial to have the inbound links coming to the pages to
which you are channelling your Page Rank. A Page Rank injection to any other
page will be spread around the site through the internal links. The important
pages will receive an increase, but not as much of an increase as when they are
linked to directly. The page that receives the inbound link makes the biggest


2)  Outbound links:


links are a drain on a site’s total Page Rank. They leak Page Rank. To counter
the drain, try to ensure that the links are reciprocated. Because of the Page
Rank of the pages at each end of an external link, and the number of links out
from those pages, reciprocal links can gain or lose Page Rank. We need to take
care when choosing where to exchange links. When Page Rank leaks from a site
via a link to another site, all the pages in the internal link structure are
affected. The page that you link out from makes a difference to which pages
suffer the most loss. Without a program to perform the calculations on specific
link structures, it is difficult to decide on the right page to link out from,
but the generalization is to link from the one with the lowest Page Rank. Many
websites need to contain some outbound links that are nothing to do with Page
Rank. Unfortunately, all ‘normal’ outbound links leak Page Rank. But there are
‘abnormal’ ways of linking to other sites that don’t result in leaks. Page Rank
is leaked when Google recognizes a link to another site. The answer is to use
links that Google doesn’t recognize or count. These include form actions and
links contained in JavaScript code. 



Fig. 3. Propagation of Links


3)  Dangling Links:


One issue with this model is dangling
links. Dangling links are simply links that point to any page with no outgoing
links. They affect the model because it is not clear where their weight should
be distributed, and there are a large number of them. Because dangling links do
not affect the ranking of any other page directly, we simply remove them from
the system until all the PageRank’s are calculated. After all the page Ranks
are calculated, they can be added back in, without affecting things
significantly. Notice the normalization of the other links on the same page as
a link which was removed will change slightly, but this should not have a large


4)  Damping factor:

The Page Rank 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 0.8. 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 Page Rank scores.                

any page’s Page Rank is derived in large part from the Page Ranks of other
pages. The damping factor adjusts the derived value downward. Google
recalculates Page Rank scores each time it crawls the Web and rebuilds its
index. The Page Rank value of a page reflects the chance that the random surfer
will land on that page by clicking on a link. 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 Page Rank, pages with no
outbound links are assumed to link out to all other pages in the collection.
Their Page Rank 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 outbound
links on page pj, and N is the total number of page. Based on
the discussion above, we give the following intuitive description of PageRank:
a page has high rank if the sum of the ranks of its backlinks is high. This
covers both the case when a page has many backlinks and when a page has a few
highly ranked backlinks.


B. Computing Page Rank


Assume a small universe of four web
pages: A, B, C and D. The initial approximation of Page
Rank would be evenly divided between these four documents. Hence, each document
would begin with an estimated Page Rank of 0. In the original form of Page Rank
initial values were simply 1. This meant that the sum of all pages was the
total number of pages on the web. Later versions of Page Rank would assume a
probability distribution between 0 and 1. Here we’re going to simply use a
probability distribution hence the initial value of 0. If pages B, C,
and D each only link to A, they would each confer 0 Page Rank
to A. All Page Rank i.e. PR () in this simplistic system would
thus gather to A because all links
would be pointing to A


PR (A) = PR (B) +PR(C) +PR (D).





Fig. 4.  Webpages and
its links


The formula of calculating the points is as following



•       PR
(pi) is the page rank of page pi.

•       PR
(pj) is page rank of page pj which link to page pi.

•       L
(pj) is number of outbound links on page pj.

•       N
is the number of webpages.

•       D
is a damping factor usually set to 0.85.


Fig. 5. Calculating rank using formula (Iteration-1)

If you apply formula or our example using the page rank
algorithm the following operations takes place PageRank of

A = 0.15 + 0.85 * (PageRank (B)/outgoing
links (B) + PageRank (…)/outgoing link (…)

•       Calculation
of A with initial ranking 1.0 per page:

•       If
we use the initial rank value 1.0 for A, B and C we would have the following

•       We
have skipped page D in the result, because it is not an existing page.



C: 0.15


Fig. 6.  Calculating rank using
PageRank formula (iteration-2)

•       Calculation
of A with ranking from ITERATION-


•       If
we use these ranks as input and calculate it again:



C: 0.15

We see that the page rank of page A
is reduced. The PageRank is based on previous calculations and will get more
accurate after more runs. You can add new pages, new links in the future and
calculate the new ranks. This is

one of the tools which search engines use to create their
index. We are going to do this with a set of Web pages.



 We implemented PageRank project using python
programming. In this paper, we have taken on the audacious task of condensing
every page on the World Wide Web into a single number, its PageRank. Using
PageRank, we are able to order search results so that more important and
central Web pages are given preference. In experiments, this turns out to
provide higher quality search results to users. The intuition behind PageRank
is that it uses information which is external to the Web pages themselves –
their backlinks, which provide a kind of peer review. Furthermore, backlinks
from “important” pages are more significant than backlinks from average


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