In Python: Consider the above graph with pages $\{1,2,3,4,5,6,7,8\}.$ Implement the topic$-$

specific PageRank algorithm to calculate the rank vectors of all eight pages with the

following specifications:

You can manually define the stochastic adjacency matrix as a $2D$ array in your code.

The topic set $5=\{3,4\}.$

The parameter $=0\mathrm{.}8.$

The stopping threshold $=0\mathrm{.}01.$ That is$,$ the rank vector is updated iteratively if:

${}_j|r_j^{\text{n}\text{e}\text{w}}-r_j^{\text{o}\text{l}\text{d}}|>,$ where $r^{\text{o}\text{l}\text{d}}$ and $r^{\text{n}\text{e}\text{w}}$ are the rank vectors before and after

each update $($iteration$).$

You can implement the matrix$-$vector product calculation in your code, or you can call

built$-$in functions for calculating matrix$-$vector products.

M $=$ np$.$array$([$

$[0,1,0,0,0,0,0,0],$

$[0,0,1,0,0,0,0,0],$

$[1/3,0,0,1/3,1/3,0,0,0],$

$[0,1/2,0,0,0,1/2,0,0],$

$[0,0,0,0,0,0,0,0],$ # Dead end

$[0,0,0,0,0,0,1,0],$

$[0,0,0,0,0,0,0,1],$

$[0,0,0,0,0,1,0,0]$

$])$

$($The rank vectors of all eight pages after applying topic specific PageRank algorithm should be$)$

The rank vectors of all eight pages for The topic$-$specific PageRank algorithm is

$0\mathrm{.}01163530\mathrm{.}02374320\mathrm{.}04168210\mathrm{.}03343410\mathrm{.}01163530\mathrm{.}03390970\mathrm{.}02839740\mathrm{.}0238066$