Page Rank Calculation and its implications

Hi Everybody!

PR concept has troubled me a lot in the past. Only last night I got respite from this PR stuff. Everybody has his own theory about PR. So I decided to go into the depth. Here is what I came out with:

Page Rank or PR is based on the number of back links. This is the equation which calculates PR:

PR(a)=(1-d) +d {PR(t1)/C(t1)+PR(t2)/C(t2) ....+ PR(tn)/C(tn)}

Here,

PR(a)=> Page rank of a web page say 'a'

d=> damping factor. It is the probability that an imaginary surfer will continue clicking on the links randomly. It is usually set to 0.85.

t1, t2, t3...tn => web pages which point to web page 'a'


PR(t1) => page rank of t1 page

PR(t2) => page rank of t2 page
.
.
.
PR(tn) => page rank of tn page



C => Number of outbound links on a web page

C(t1) => Number of outbound links on the t1 page

C(t2) => Number of outbound links on the t2 page
.
.
.
C(tn) => Number of outbound links on the tn page


So,

Page rank of web page 'a'= (1-0.85) + 0.85* {(page rank of t1 page which points to web page 'a')/ (Number of outbound links on the t1 page) + (page rank of t2 page which points to web page 'a')/ (Number of outbound links on the t2 page)....+ (page rank of tn page which points to web page 'a')/ (Number of outbound links on the tn page)

EG:

Lets us suppose three web pages points to web page 'a':

Webpage 'b' with page rank of 9 and 180 outbound links

Webpage 'c' with page rank of 7 and 120 outbound links

Webpage 'd' with page rank of 4 and 1 outbound link


Now,

Page rank of website 'a'= (1-0.85) + 0.85* {(page rank of web page b)/ (Number of outbound links on the web page b) + (1-0.85) + (page rank of web page c)/ (Number of outbound links on the web page c) + (page rank of web page d)/ (Number of outbound links on the web page d)


PR(a)=0.15+0.85 *{(9/180)+(7/120)+(4/1)}

=0.15+0.85 *(0.05+0.058+4)

=3.6418

What we learned from the above equation:

1) PR is not an integer between 0 and 10. It is a floating point number. However Google tool bar shows PR as an integer between 0 and 10.


2) When some one says that PR is based on relevance and quality also in addition to number of incoming links, he is actually talking about the back link pages' PR. If a web page has some useful contents, than only webmaster will link to it and consequently the web page will get PR. So PR is indirectly based on relevance and quality of a back link page.


3) Since content is not taken into account when PR is calculated, it means frequent content updation won't improve your PR directly (indirectly it can as people would love to bookmark a page which provides fresh contents)


4) Not all web pages weight the same when it comes to PR. As you saw in the above example, the web page 'b' with PR of 9 gave back only 0.05 value in comparison to the value of 4 given by the the web page 'd' of PR 4. So don't expect high PR just because you got a link from a very high PR web page. Check out the number of outbound links also on the web page. The number of outbound links eventually decides what fraction of PR value your web page will get.



5) As you can see from the above formula, PR is determined
for each page individually. It means internal pages don't necessarily have lower PR than the home page. It also means back links from you own domain contributes to the overall PR of your home page (which is considered as PR of the website by many webmasters). Thats why efficient inter site linking has good impact on PR. One good example of efficient inter site linking is 'Wikipedia'.



6) Any link from any site contributes something to the overall PR except banned sites.


7) Back links from .edu, .gov, .org or DMOZ and yahoo directories are considered as just another back links when it comes to determining PR. Don't expect any PR boost from these websites.


8) Multiple back links from a same page won't help in increasing overall PR.

Note : Page rank is calculated every time a web page is crawled.

I will write more about PR. some other time. If you have any specific query, then send me a message. More comments are welcomed as usual.

Interesting analysis. I dont think there is anything wrong with the conclusions you've made. However the formula is not that simple. For example a page with 0 bytes content can never gain pagerank by my observations, you have to have something - even "index of" or "coming soon" will do it.

That formula is very helpful to us on how the pr was calculated. But I think we should not always rely on that, who knows google will have their new formula on calculating pr.

I think this formula is differ to real google pr calculations

...sorry but I feel that Google came out with this formula since the inception of Page Rank

and IMO a much more better and in-depth explanation of PR is available at http://en.wikipedia.org/wiki/PageRank

I think that google is ranking the page using like this type of formula but this is not the good think to calculate the PR because its upon google not on me or u to make our own decision Thanks