Let's say you want to find the shortest path $($distance$)$ between node $0$ to node $4$ from the following weighted graph. The numbers inside the $($green$)$ circles represent the node$/$vertex and the numbers beside the edges represent the distance between two nodes. Answer the following questions.

$1.$ Is this a sparse graph or a dense graph?

$2.$ What type of graph representation you would choose to represent this graph in your code? Explain why you would choose that representation.

$3.$ What will be the value $($sum of the edges in the shortest path$)$ of the shortest path distance from node $0$ to node $4?$ What nodes will be included in the shortest path?