Figure $4$ is an example of a social$-$network graph.

$($a$)$ 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 and $B.$

$($b$)$ Using symmetry, the calculations of $($a$)$ are all you need to compute the betweenness of

each edge. Do the calculation

$($c$)$ Using the betweenness values from $($b$),$ determine reasonable candidates for the

communities in Fig. $4$ by removing all edges with a betweenness above some threshold.

rigure $4$