### Secret of Google revealed!

In the world of World Wide Web, there can hardly be anyone who is unaware of the best and the fastest search engine, Google. It’s incredibly fast, showing search results with detailed information in milliseconds.Google is better than any of the search engines as it makes use of the link structure of the Web to calculate a quality ranking for each web page .This ranking is called **PageRank.
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PageRank is also displayed on the toolbar of your browser if you’ve installed the Google toolbar. But the Toolbar PageRank only goes from 0 – 10 and seems to be something like a logarithmic scale.
In short PageRank is a “vote”, by all the other pages on the Web, about how important a page is. A link to a page counts as a vote of support.
**Quoting from the original Google paper, PageRank is defined like this:**
We assume page A has pages T1...Tn which point to it (i.e., are citations). The parameter d is a damping factor which can be set between 0 and 1. We usually set d to 0.85. There are more details about d in the next section. Also C(A) is defined as the number of links going out of page A.
The PageRank of a page A is given as follows:
**PR(A) = (1-d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))**
Note that the PageRanks form a probability distribution over web pages, so the sum of all web pages' PageRanks will be one.
PageRank or PR(A) can be calculated using a simple iterative algorithm, and corresponds to the principal eigenvector of the normalized link matrix of the web.
But that’s not too helpful so let’s break it down into sections.
1. PR(Tn) - Each page has a notion of its own self-importance. That’s “PR(T1)” for the first page in the web all the way up to “PR(Tn)” for the last page
2. C(Tn) - Each page spreads its vote out evenly amongst all of it’s outgoing links. The count, or number, of outgoing links for page 1 is “C(T1)”, “C(Tn)” for page n, and so on for all pages.
3. PR(Tn)/C(Tn) - so if our page (page A) has a backlink from page “n” the share of the vote page A will get is “PR(Tn)/C(Tn)”
4. d(... - All these fractions of votes are added together but, to stop the other pages having too much influence, this total vote is “damped down” by multiplying it by 0.85 (the factor “d”)
5. (1 - d) - The (1 – d) bit at the beginning is a bit of probability math magic so the “sum of all web pages' PageRanks will be one”: it adds in the bit lost by the d(.... It also means that if a page has no links to it (no backlinks) even then it will still get a small PR of 0.15 (i.e. 1 – 0.85). (Aside: the Google paper says “the sum of all pages” but they mean the “the normalised sum” – otherwise known as “the average” to you and me.
**How is PageRank Calculated?**
This is where it gets tricky. The PR of each page depends on the PR of the pages pointing to it. But we won’t know what PR those pages have until the pages pointing to them have their PR calculated and so on… And when you consider that page links can form circles it seems impossible to do this calculation!
But actually it’s not that bad. Remember this bit of the Google paper:
PageRank or PR(A) can be calculated using a simple iterative algorithm, and corresponds to the principal eigenvector of the normalized link matrix of the web.
What that means to us is that we can just go ahead and calculate a page’s PR without knowing the final value of the PR of the other pages. That seems strange but, basically, each time we run the calculation we’re getting a closer estimate of the final value. So all we need to do is remember the each value we calculate and repeat the calculations lots of times until the numbers stop changing much.

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