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.
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