Wednesday, August 1, 2007

How is PageRank(PR) Calculated?

(webworkshop) PR is a one of the way to calculate the rank of the website. PR also represent how important a page on the web. When one page links to another page, it is effectively casting a vote for the other page. The more votes that are cast for a page, the more important the page must be. Also, the importance of the page that is casting the vote determines how important the vote itself is.


How is PR calculated??? To calculate the PageRank for a page, all of its inbound links are taken into account. These are links from within the site and links from outside the site.

PR(A) = (1-d) + d(PR(t1)/C(t1) + ... + PR(tn)/C(tn))

That's the equation that calculates a page's PageRank. It's the original one that was published when PageRank was being developed, and it is probable that Google uses a variation of it but they aren't telling us what it is. It doesn't matter though, as this equation is good enough.

In the equation 't1 - tn' are pages linking to page A, 'C' is the number of outbound links that a page has and 'd' is a damping factor, usually set to 0.85.

We can think of it in a simpler way:-

a page's PageRank = 0.15 + 0.85 * (a "share" of the PageRank of every page that links to it)

"share" = the linking page's PageRank divided by the number of outbound links on the page.

A page "votes" an amount of PageRank onto each page that it links to. The amount of PageRank that it has to vote with is a little less than its own PageRank value (its own value * 0.85). This value is shared equally between all the pages that it links to. One of the example is shown below.

Now begin again with each page being allocated PR1. Link page A to page B and run the calculations for each page. We end up with:-

Page A = 0.15
Page B = 1
Page C = 0.15

Page A has "voted" for page B and, as a result, page B's PageRank has increased. This is looking good for page B, but it's only 1 iteration - we haven't taken account of the Catch 22 situation. Look at what happens to the figures after more iterations:-

After 100 iterations the figures are:-

Page A = 0.15
Page B = 0.2775
Page C = 0.15

It still looks good for page B but nowhere near as good as it did. These figures are more realistic. The total PageRank in the site is now 0.5775 - slightly better but still only a fraction of what it could be.

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