Here's the explanation from Google, how they calculate the Page rank:
To calculate the Page Rank 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 Page Rank. It's the original one that was published when Page Rank was being developed.
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 Page Rank = 0.15 + 0.85 * (a "share" of the Page Rank of every page that links to it) "share" = the linking page's Page Rank divided by the number of outbound links on the page. A page "votes" an amount of Page Rank onto each page that it links to. The amount of Page Rank that it has to vote with is a little less than its own Page Rank 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 Page Rank 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 Page Rank value your page will receive from it.
If the Page Rank 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.
Note that when a page votes its Page Rank value to other pages, its own Page Rank is not reduced by the value that it is voting. The page doing the voting doesn't give away its Page Rank and end up with nothing. It isn't a transfer of Page Rank. It is simply a vote according to the page's Page Rank 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. For a page's calculation, its existing Page Rank (if it has any) is abandoned completely and a fresh calculation is done where the page relies solely on the Page Rank "voted" for it by its current inbound links, which may have changed since the last time the page's Page Rank was calculated.
The equation shows clearly how a page's PageRank is arrived at. But what isn't immediately obvious is that it can't work if the calculation is done just once. Suppose we have 2 pages, A and B, which link to each other, and neither have any other links of any kind. This is what happens:
Step 1: Calculate page A's Page Rank from the value of its inbound links
Page A now has a new Page Rank value. The calculation used the value of the inbound link from page B. But page B has an inbound link (from page A) and its new Page Rank value hasn't been worked out yet, so page A's new Page Rank value is based on inaccurate data and can't be accurate.
Step 2: Calculate page B's Page Rank from the value of its inbound links
Page B now has a new Page Rank value, but it can't be accurate because the calculation used the new Page Rank value of the inbound link from page A, which is inaccurate. The problem is overcome by repeating the calculations many times. Each time produces slightly more accurate values. In fact, total accuracy can never be achieved because the calculations are always based on inaccurate values. 40 to 50 iterations are sufficient to reach a point where any further iterations wouldn't produce enough of a change to the values to matter. This is precisely what Google does at each update, and it's the reason why the updates take so long.
12-15-2007, 04:44 PM
Linear Mode
