Quote:
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Originally Posted by seolearner
Quote:
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Originally Posted by kgun
You can ask (PM) me if you have problems with understanding a formula.
It is a very important paper, and should be read by anybody who want to understand how the pagerank and trustrank are computed.
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I could not get through with the algorithm can you please explain it to me. As i want to understand how the pagerank and trustrank are computed. |
PageRank formula
starting with r(p) in section 2.2. PageRank.
You have a set of internet pages, let us say 20 billion.
Every page in this set has a pagerank, a number 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10
In essence the formula says, you find the pagerank of a page, let us call it P, by a weighted sum of the pagerank of all pages in the set. Pages that does not link to the page, our frind P, naturally get a weight of zero.
Then in greater detail, there is a decay factor, an outdegree (the number of outlinks from a page), and the number of pages in the formula. The pagerank of page q is in the numerator and the outdegree in the denominator. That means if two pages that link to page q have the same pagerank, but different number of outlinks, the page with less outlinks will influence the sum most (the number in the denominator is less). That page has a stronger vote for your page. Message, get links from pages with high pagerank and a low number of outlinks. The rest of the formulae is cosmetics. The decay factor makes it a weighted sum.
Before I continue, was this understandable?
If you do not know what a weighted sum is, here is an example:
USD amount | Weight
....100 ........... 0,2
....200 ........... 0,1
....100 ........... 0,5
....400 ........... 0,2
The weighted sum is:
0,2*100 + 0,1*200 + 0,5*100 + 0,2*400
Note that the weights in this case, as is often the case, sum to 1.
You may think, when you sum over all pages on the internet, you should get a number much greater than 10. Look at the wighted sum above, it can not be greater than the largest amount, USD 400, but that has a relatively low weight. The third amount carries half the weight and will drive the sum towards that number (100). So the highest number you can get is pagerank 10 for our page P.
If you have problems with the sum (greek capital sigma) notation, here are some good educational links:
Important figure, below the sentence
Notice that this notation has several elements labeled in the figure below.
http://www.math.montana.edu/frankw/c...igma/learn.htm
Note, j = index variable, 1 = start, j^2 = formulae and n = end.
This notation is not used in the paper, instead set notation is used. It is not different, if you sum over all index variables in the set, S e.g. Set = S = {1,2,3,4,5, ..., n}.
In essence, you get the first term in the sum by substituting the first value for the index variable in the formulae, then the next. You get the last term in the sum by substituting, in the example above n in the formulae. In the example above, you start by 1, then 2, 3, 4, .... n. Sigma notation for sum is in the end a simplified (compact) notation for a large sum. Think of writing out the sum for all URL's on the internet, and you see the point.
http://mathworld.wolfram.com/Sum.html
http://home.alltel.net/okrebs/page136.html