The idea behind the Google Matrix
Well, here you are again. Another night of drinking, and you are stumbling around town trying to find your way home. But all is not lost! Through the math, we know that you should eventually return home given enough time! You only have a finite amount of places and directions you can go. So travel on you tired drunkard!
Google’s Pagerank algorithm, in essence, follows this drunkard as he wanders aimlessly around the Internet. Although not a drunkard, but rather a random web surfer who “surfs” his way around the directed graph that is the Internet. At each website he enters, there are only a finite number of exits (the links to other websites or pages). The surfer’s likelihood of choosing any of those exits are all equal because he only cares about leaving his current location so all exits are equally appealing to him. So the way to interpret all this information is by construction an nxn matrix, where n is the number of websites on the Internet. When filling out this matrix, the value of that goes in (i,j) is the probability that this surfer travels to page “i” from page “i.” This “Google Matrix” is where all the amazing math ideas are employed in order to make your browsing experience happen, as my math Professor would say, “automagically!”
This is a very simplified version of the construction of the Matrix and there is a lot more that goes into it, trust me. But if you would like to learn more, check out this very simple to read, yet very informative paper
http://www.cems.uvm.edu/~tlakoba/AppliedUGMath/other_Google/Wills.pdf
And if you desire to read a much more complicated yet mathematically pleasing paper, check out
http://www4.ncsu.edu/~ipsen/ps/simax43980.pdf
