Page Rank Algorithm

Hope everyone knows what is PageRank. Google's Definition is "The basis of Google's search technology is called PageRank™, and assigns an "importance" value to each page on the web and gives it a rank to determine how useful it is. However, that's not why it's called PageRank. It's actually named after Google co-founder Larry Page."

Google figures that 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. Google calculates a page's importance from the votes cast for it. How important each vote is is taken into account when a page's PageRank is calculated.
How is PageRank 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.

From this, we could conclude that a link from a page with PR4 and 5 outbound links is worth more than a link from a page with PR8 and 100 outbound links. The PageRank of a page that links to yours is important but the number of links on that page is also important. The more links there are on a page, the less PageRank value your page will receive from it.

If the PageRank value differences between PR1, PR2,.....PR10 were equal then that conclusion would hold up, but many people believe that the values between PR1 and PR10 (the maximum) are set on a logarithmic scale, and there is very good reason for believing it. Nobody outside Google knows for sure one way or the other, but the chances are high that the scale is logarithmic, or similar. If so, it means that it takes a lot more additional PageRank for a page to move up to the next PageRank level that it did to move up from the previous PageRank level. The result is that it reverses the previous conclusion, so that a link from a PR8 page that has lots of outbound links is worth more than a link from a PR4 page that has only a few outbound links.

Note that when a page votes its PageRank value to other pages, its own PageRank is not reduced by the value that it is voting. The page doing the voting doesn't give away its PageRank and end up with nothing. It isn't a transfer of PageRank. It is simply a vote according to the page's PageRank value. It's like a shareholders meeting where each shareholder votes according to the number of shares held, but the shares themselves aren't given away. Even so, pages do lose some PageRank indirectly, as we'll see later.

Whichever scale Google uses, we can be sure of one thing. A link from another site increases our site's PageRank. Just remember to avoid links from link farms.

Example:

Now try this. Link page A to both B and C. Also link pages B and C to A. Starting with PR1 all round, after 1 iteration the results are:-

Page A = 1.85
Page B = 0.575
Page C = 0.575

and after 100 iterations, the results are:-
Page A = 1.459459
Page B = 0.7702703
Page C = 0.7702703

In both cases the total PageRank in the site is 3 (the maximum) so none is being wasted. Also in both cases you can see that page A has a much larger proportion of the PageRank than the other 2 pages. This is because pages B and C are passing PageRank to A and not to any other pages. We have channeled a large proportion of the site's PageRank to where we wanted it.