Problem $1.$ Apply the PageRank algorithm to the graph $($b$)$ below, using teleportation probabilities of

$0\mathrm{.}1,0\mathrm{.}2,$ and $0\mathrm{.}4,$ respectively. What is the impact on the dead$-$end component $($probabilities$)$ of

increasing the teleportation probabilities?

$($a$)$ Dead$-$end node

$($b$)$ Dead$-$end component

$(25$ Points$)$