Exercise $5.$ In this exercise we will consider two versions of the same network: in $($a$)$ a directed

version, and in $($b$)$ an undirected version. The two versions of the network are shown in Figure $1.$

$($a$)$ Consider first the directed version of the graph. Calculate the Katz centrality of node $i,$

labeled on the graph.

$($b$)$ Now consider the undirected version of the same graph. Calculate the betweenness centrality

of node $i.$

$($a$)$ Directed

Figure $1$: Two versions of a network, to be used in Exercise $5.$