I am embarrassed to ask such question; but I haven't use math 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):
Now subtract
2 PR(A)
from both sides:Now replace
PR(B)
, using the second part of "equation A":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.