Q$1(22$ pts$)$ Use Breadth First Search $($BFS$)$ as the underlying algorithm to determine the node betweenness fraction for the vertices and the pairs in the graph shown below.

$($a$)$ Node BWC $($vertex $7$ with respect to the pair $1,3)$

$($b$)$ Node BWC $($vertex $5$ with respect to the pair $1,3)$