K$.(30$ pts$)$ For each graph below,

$($a$)$ Find the transition matrix $P.$ Pay close attention to the arrows on the edges.

$($b$)$ Next, find the "Google matrix" $($the adjusted matrix $P^{?}$ as in lecture$).$ For $$ use $0\mathrm{.}01.$

$($c$)$ Next, compute the PageRank of the nodes in graph.

$($d$)$ Finally, state the order in which nodes $($pages$)$ would be presented by PageRank.

Use numpy$/$python$,$ and show your work. That is$,$ cut and paste the commands you used, and the outputs, into

your submission, being clear how you addressed each of $($a$),($b$),($c$),$ and $($d$).$

K$..$

K