## PageRank

Suppose we compute PageRank with a β of 0.7, and we introduce the additional constraint that the sum of the PageRanks of the three pages must be 3, to handle the problem that otherwise any multiple of a solution will also be a solution. Compute the PageRanks a, b, and c of the three pages A, B, and C, respectively.

$A = \sum_{i\rightarrow{j}} \beta r_i/d_i + (1 - \beta ) e / n$

My R code is this.

M = matrix(c(0,1/2,1/2,0,0,1,0,0,1),ncol=3)
e = matrix(c(1,1,1),ncol=1)
v1 = matrix(c(1,1,1),ncol=1)
v1 = v1 / 3
for( i in 1:5){

v1 =  ((0.7 * M ) %*% v1 ) + (((1 - 0.7 ) * e ) /3 )
}
v1 = v1 * 3

      [,1]
[1,] 0.300
[2,] 0.405
[3,] 2.295