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The Math behind Google PageRank…

August 25, 2007 – 2:13 pm | by eMpTycuBe

As you all know, use PageRank is it’s weighted of websites on the world wide wide aka WWW. I just learned that to certain extend PageRank is important for SEO apart from the SEO optimization/ configuration that u guys do all the time. So i googled around to see what is it all about. How is it calculated and how to rank up my own PageRank (actually this is my main intention) :-P

I around to various website inside the WWW arena, until i said to myself… how in the world they calculate PageRank.

So i ended up using the infamous l33t search engine and hit the keyboard with this keyword, "PageRank +wiki", which narrow my search to a wikipedia site.

So basically this the algorithm below was taken from wikipedia site, here is the complete link to it "PageRank"

Why am i so interested to post this one.. well it actually reminds me during my 1st year university days. I took Linear Algebra and this is it… MATRICES!! ..i got an A- for this subject. ok cut the crap …

Below is the algorithm of PageRank

PR(A)= 1 - d + d \left( \frac{PR(B)}{L(B)}+ \frac{PR(C)}{L(C)}+ \frac{PR(D)}{L(D)}+\,\cdots \right)

or (N = the number of documents in collection)

PR(A)= {1 - d \over N} + d \left( \frac{PR(B)}{L(B)}+ \frac{PR(C)}{L(C)}+ \frac{PR(D)}{L(D)}+\,\cdots \right) .

and the derivation is as follow,

PR(p_i) = \frac{1-d}{N} + d \sum_{p_j \in M(p_i)} \frac{PR (p_j)}{L(p_j)}

and behind the derivation is linear algebra … its matrices!

\mathbf{R} = \begin{bmatrix} PR(p_1) \\ PR(p_2) \\ \vdots \\ PR(p_N) \end{bmatrix}

where R is the solution of the equation

\mathbf{R} = \begin{bmatrix} {(1-d)/ N} \\ {(1-d) / N} \\ \vdots \\ {(1-d) / N} \end{bmatrix} + d \begin{bmatrix} \ell(p_1,p_1) & \ell(p_1,p_2) & \cdots & \ell(p_1,p_N) \\ \ell(p_2,p_1) & \ddots & & \vdots \\ \vdots & & \ell(p_i,p_j) & \\ \ell(p_N,p_1) & \cdots & & \ell(p_N,p_N) \end{bmatrix} \mathbf{R}

where the adjacency function \ell(p_i,p_j) is 0 if page pj does not link to pi, and normalised such that, for each j

\sum_{i = 1}^N \ell(p_i,p_j) = 1,

i.e. the elements of each column sum up to 1. and bla bla bla…read the full content here"Wikipedia - PageRank"

Bash/Question: dude ur using picture taken from wikipedia, isnt it plagiarism?

Answer: NO, its not plagiarism, since wikipedia is adopted what is known as a "free content license" under the GNU public license, which allow all text and images authored by the users are and will always remain free for anyone to copy, modify, and redistribute.

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