PageRank problem

I am embarrassed to ask such question; but I haven't use m开发者_StackOverflow社区ath for a long time I can not recall many concepts learned many years ago.

In the url http://www.javadev.org/files/Ranking.pdf, an example is used for illustrate the page rank mechanism. The relation between page A, B, and C is A links to B and C, B links to C, and C links to A. So the PageRank equation is as below

Equation A)

    PR(A) = 0.5 + 0.5 PR(C) 
    PR(B) = 0.5 + 0.5 (PR(A) / 2)
    PR(C) = 0.5 + 0.5 (PR(A) / 2 + PR(B))

and it comes up with the result

Result B)

    PR(A) = 14/13 = 1.07692308 
    PR(B) = 10/13 = 0.76923077 
    PR(C) = 15/13 = 1.15384615

My question is how Result B is derived from Equation A?

I try e.g. replacing PR(C) in equation PR(A)

    PR(A) = 0.5 + 0.5 (0.5 + 0.5 (PR(A) / 2 + PR(B)))

this seems to end up with an infinite loop. So I am confused how it can derive the result e.g. PR(A) value is 1.07692308?

Appologize for such stupid question.

I appreciate any advice.

Not a stupid question, you're just rusty.

Take your equation and multiply by 16 (not really necessary, but it makes things look nicer):

16 PR(A) = 12 + 2 PR(A) + 4 PR(B)

Now subtract 2 PR(A) from both sides:

14 PR(A) = 12 + 4 PR(B)

Now replace PR(B), using the second part of "equation A":

14 PR(A) = 12 + 2 + PR(A)
13 PR(A) = 14
   PR(A) = 14/13

And the others follow the same way. If you find that an equation winds up being the same on both sides (X = X), it probably means that you did the same substitution twice; just back up and try again. With a little practice you'll get the hang of it.