

The Distribution of PageRank Regarding Search Engine
Optimisation 



Up to this point, it has been described
how the number of pages and the number of inbound and outbound
links, respectively, influence PageRank. Here, it will mainly
be discussed in how far PageRank can be affected for the
purpose of search engine optimisation by a website's internal
linking structure.
In most cases, websites are hierachically structured
to a certain extend, as it is illustrated in our example of a
web site consisting of the pages A, B and C. Normally, the
root page is withal optimised for the most important search
phrase. In our example, the optimised page A has an external
inbound link from page X which has no other outbound links and
a PageRank of 10. The pages B and C each receive a link from
page A and link back to it. If we set the damping factor d to
0.5 the equations for the single pages' PageRank values are
given by
PR(A) = 0.5 + 0.5 (10 + PR(B) + PR
(C))
PR(B) = 0.5 + 0.5 (PR(A) / 2)
PR(C) = 0.5 + 0.5
(PR(A) / 2)
Solving the equations gives us the
follwing PageRank values:
PR(A) = 8
PR(B) =
2.5
PR(C) = 2.5
It is generally not advisable to
solely work on the root page of a site for the purpose of
search engine optimisation. Indeed, it is, in most cases, more
reasonable to optimise each page of a site for different
search phrases.
We now assume that the root page of our example
website provides satisfactory results for its search phrase,
but the other pages of the site do not, and therefore we
modify the linking structure of the website. We add links from
page B to page C and vice versa to our formerly hierarchically
structured example site. Again, page A has an external inbound
link from page X which has no other outbound links and a
PageRank of 10. At a damping factor d of 0.5, the equations
for the single pages' PageRank values are given by
PR(A) = 0.5 + 0.5 (10 + PR(B) / 2 + PR(C) /
2)
PR(B) = 0.5 + 0.5 (PR(A) / 2 + PR(C) / 2)
PR(C) = 0.5
+ 0.5 (PR(A) / 2 + PR(B) / 2)
Solving the equations
gives us the follwing PageRank values:
PR(A) =
7
PR(B) = 3
PR(C) = 3
The result of adding
internal links is an increase of the PageRank values of pages
B and C, so that they likely will rise in search engine result
pages for their targeted keywords. On the other hand, of
course, page A will likely rank lower because of its
diminished PageRank.
Generally spoken, PageRank will
distribute for the purpose of search engine optimisation more
equally among the pages of a site, the more the hierarchically
lower pages are interlinked. 


Well Directed PageRank Distribution by Concentration of
Outbound Links




It has already been demonstrated that external outbound
links tend to have negative effects on the PageRank of a
website's web pages. Here, it shall be illustrated how this
effect can be reduced for the purpose of search engine
optimisation by the systematic arrangement of external
outbound links.
We take a look at another hierarchically structured
example site consisting of the pages A, B, C and D. Page A has
links to the pages B, C and D. Besides a link back to page A,
each of the pages B, C and D has one external outbound link.
None of those external pages which receive links from the
pages B, C and D link back to our example site. If we assume a
damping factor d of 0.5, the equations for the calculation of
the single pages' PageRank values are given by
PR(A) =
0.5 + 0.5 (PR(B) / 2 + PR(C) / 2 + PR(D) / 2)
PR(B) = PR(C)
= PR(D) = 0.5 + 0.5 (PR(A) / 3)
Solving the equations
gives us the follwing PageRank values:
PR(A) =
1
PR(B) = 2/3
PR(C) = 2/3
PR(D) = 2/3
Now, we modify our example site
in a way that page D has all three external outbound links
while pages B and C have no more external outbound links.
Besides this, the general conditions of our example stay the
same as above. None of the external pages which receive a link
from pages D link back to our example site. If we, again,
assume a damping factor d of 0.5, the equations for the
calculations of the single pages' PageRank values are given by
PR(A) = 0.5 + 0.5 (PR(B) + PR(C) + PR(D) / 4)
PR(B)
= PR(C) = PR(D) = 0.5 + 0.5 (PR(A) / 3)
Solving these
equations gives us the follwing PageRank values:
PR(A)
= 17/13
PR(B) = 28/39
PR(C) = 28/39
PR(D) = 28/39
As a result of our modifications, we see that the
PageRank values for each single page of our site have
increased. Regarding search engine optimisation, it is
therefore advisable to concentrate external outbound links on
as few pages as possible, as long as it does not lessen a
site's usabilty. 


Link Exchanges for the purpose of Search Engine
Optimisation




For the purpose of search engine optimisation, many
webmasters exchange links with others to increase link
popularity. As it has already been shown, adding links within
closed systems of web pages has no effects on the accumulated
PageRank of those pages. So, it is questionable if link
exchanges have positive consequences in terms of PageRank at
all.
To show the effects of link exchanges, we take a
look at an an example of two hierarchically structured
websites consisting of pages A, B and C and D, E and F,
respectively. Within the first site, page A links to pages B
and C and those link back to page A. The second site is
structured accordingly, so that the PageRank values for its
pages do not have to be computed explicitly. At a damping
factor d of 0.5, the equations for the single pages' PageRank
values are given by
PR(A) = 0.5 + 0.5 (PR(B) +
PR(C))
PR(B) = PR(C) = 0.5 + 0.5 (PR(A) / 2)
Solving the equations gives us the follwing PageRank
values for the first site
PR(A) = 4/3
PR(B) =
5/6
PR(C) = 5/6
and accordingly for the second site
PR(D) = 4/3
PR(E) = 5/6
PR(F) = 5/6
Now, two pages of our example
sites start a link exchange. Page A links to page D and vice
versa. If we leave the general conditions of our example the
same as above and, again, set the damping factor d to 0.5, the
equations for the calculations of the single pages' PageRank
values are given by
PR(A) = 0.5 + 0.5 (PR(B) + PR(C) +
PR(D) / 3)
PR(B) = PR(C) = 0.5 + 0.5 (PR(A) / 3)
PR(D) =
0.5 + 0.5 (PR(E) + PR(F) + PR(A) / 3)
PR(E) = PR(F) = 0.5 +
0.5 (PR(D) / 3)
Solving these equations gives us the
follwing PageRank values:
PR(A) = 3/2
PR(B) =
3/4
PR(C) = 3/4
PR(D) = 3/2
PR(E) = 3/4
PR(F) =
3/4
We see that the link exchange makes pages A and D
benefit in terms of PageRank while all other pages lose
PageRank. Regarding search engine optimisation, this means
that the exactly opposite effect compared to interlinking
hierachically lower pages internally takes place. A link
exchange is thus advisable, if one page (e.g. the root page of
a site) shall be optimised for one important key phrase.
A basic premise for the positive effects of a link
exchange is that both involved pages propagate a similar
amount of PageRank to each other. If one of the involved pages
has a significantly higher PageRank or fewer outbound links,
it is likely that all of its site's pages lose PageRank. Here,
an important influencing factor is the size of a site. The
more pages a web site has, the more PageRank from an inbound
link is distributed to other pages of the site, regardless of
the number of outbound links on the page that is involved in
the link exchange. This way, the page involved in a link
exchange itself benefits lesser from the link exchange and
cannot propagate as much PageRank to the other page involved
in the link exchange. All the influencing factors should be
weighted up against each other bevor one trades links.
Finally, it shall be noted that it is possible that
all pages of a site benefit from a link exchange in terms of
PageRank, whereby also the other site taking part in the link
exchange does not lose PageRank. This may occur, when the page
involved in the link exchange already has a certain number of
external outbound links which don't link back to that site. In
this case, less PageRank is lost by the already existing
outbound links. 














PageRank and Google are trademarks of Google Inc.,
Mountain View CA, USA.
PageRank is protected by US Patent
6,285,999.
The content of this document may be
reproduced on the web provided that a copyright notice is
included and that there is a straight HTML hyperlink to the
corresponding page at pr.efactory.de in direct
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