Consider the directed network $G=(V,E)$ with $N=5$ nodes and $L=8$ links, in which node $1$ points to nodes $2$ and $3,$ node $2$ points to node $4,$ node $3$ points to nodes $2$ and $4,$ node $4$ points to node $2,$ and node $5$ points to nodes $3$ and $4.$

$($a$)$ Draw the network and write down its adjacency matrix $A.$

$($b$)$ How many weakly$-$connected components and how many non$-$trivial $($i$.$e$.$ with