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Is PageRank Additive?

 6:37 am on Nov 21, 2002 (gmt 0)

If a site A is linked to from sites X,Y,Z each with pagerank y, is the pagerank of A a linear combination of this?

e.g. is PR(A) = ayX + byY + czZ, where a,b,c are some weighings?



 9:31 am on Nov 21, 2002 (gmt 0)

Not sure about your calculation.

But if X,Y,Z have the same PageRank, and they all link to A, it doesn't mean that A will get the same amount of PageRank from each page linking to it, even though they have the same PageRank.

The PageRank value for X,Y,Z will be diveded with the number of links pointing out from the specific page.
So if PageRank value for X (which is the same for Y and Z) is 1, and let's say the damping factor, is 0.85 (that's the damping factor they use in the original Backrub/Google paper [www-db.stanford.edu]), then the remaining PageRank is 0.15, if it then have 2 links pointing out from the page, and one of them is to page A, it will get a PageRank of 0.075

So the PageRank for the page is dived by the number of links pointing out.

(sure hope i'm right about this)


 9:55 am on Nov 21, 2002 (gmt 0)

Small addition to lazerzubb's comment.

from that paper: PR(A) = (1-d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))

the (1-d) comes in with raw Pagerank.

The toolbar Pagerank is log scale of the raw Pagerank. The (1-d) makes no significant contribution to the total Pagerank in practice.

So if three Toolbar Pagerank 5 pages all link to A, and each have three links on their pages, the Toolbar Pagerank of A will be 0.85 (d) times the toolbar Pagerank 5.

To answer your initial question.

Yes as far as we know now, the individual Pagerank of the linking pages can be added to each other, provided you dilute them by the amount of links and you discount the dampening factor.


 4:15 pm on Nov 23, 2002 (gmt 0)

I agree with vitaplease about "d"; the damping factor of 0.85 was the PR passed on, not the PR dissipated. So a page with raw PageRank of 1 would pass on (1 x 0.85 /2) = 0.425 (The current figure is close to 0.9 IMO)

Because of the log scale, the three PR5 links (with each page having 3 links) give logn(n5 x d) instead of the (5 x d) from the raw PR calculation. Taking d=9 this would give roughly 4.55 using Toolbar PR versus 4.97 using raw PR.


 4:19 pm on Nov 23, 2002 (gmt 0)

what if a page has 30 links outgoing and pr5..and then the page splits itself into 30 pages each with a single link and each with a pr5 cause they are all linked from the home page...how muc difference does this make to a link from one of these pages now?


 12:12 am on Nov 24, 2002 (gmt 0)

You've misspelt "addictive".


 3:49 am on Nov 24, 2002 (gmt 0)

No but poor speelling and proper use of capitals CerTaInLy ArE.

Seriously now...I think it may well be. You spend all that time getting links and waiting for the update then find out it was a waste of time so you do it again next month and then again and again. Your wife gives you an ultimatum "its either me or the PR" thats when you know you have a problem.


 4:00 am on Nov 24, 2002 (gmt 0)

>You've misspelt "addictive".

Or did he mean additive?

let us know scorpion and we will fix it.



 4:09 am on Nov 24, 2002 (gmt 0)

Yes, I meant additive, as in adding to each other.


 4:15 am on Nov 24, 2002 (gmt 0)

Your wish is my command.



 6:39 am on Nov 24, 2002 (gmt 0)

Judging from this forum, i'd have to say Pagerank is addictive too. LOL


 7:05 am on Nov 24, 2002 (gmt 0)

CIML is right, i have no idea what i was thinking when i wrote that, must have been thinking of something commpletly different.

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