$3.($Exercise $10\mathrm{.}2\mathrm{.}1)$ Below is an example of a social$-$network graph. Use the Girvan$-$Newman approach to find the number of shortest paths from each of the following nodes that pass through each of the edges. $($a$)$ A $($b$)$ B$.$

$4.$ Compute the credits for each edge in the above graph considering the root is a$)$ A and b$)$ B $.$

$5.($Bonus pt$)$ Consider the symmetry of the graph, compute the betweenness of every edge, based on the above credits.