Homework 1, Math 152-205, additional problem:

For this problem, you should consult the class blog if you missed class
on the first day.

A network has two webpages, page A and page B.  The links are as follows:

Page A has 0 links to page A and 2 links to page B.
Page B has 6 links to page A and 2 links to page B.


(Part a) Denote the PageRanks of A and B by  xA  and  xB .  Explain
intuitively what the meaning is of each of the following PageRank equations:

xA + xB = 1
xA = (0/2) xA + (6/8) xB
xB = (2/2) xA + (2/8) xB


(Part b) Guess which webpage will have a higher page rank.  (This is a
guess;  there are no right or wrong answers, the only wrong answer is
not to make a guess.)


(Part c) Solve these equations any way you want.  Explain intuitively
why one webpage has a higher page rank than the other (this should not
be a guess).


(Part d) If Page B has 6,000,000,000 links to page A but all other link
numbers remain the same, what do you expect the PageRanks to be,
roughly speaking?  Which page will have the larger PageRank?