Consider the directed network $G=(V,E)$ with $N=5$ nodes and $L=8$ links, in which

node $1$ points to nodes $2$ and $3,$ node $2$ points to node $4,$ node $3$ points to nodes $2$ and

$4,$ node $4$ points to node $2,$ and node $5$ points to nodes $3$ and $4.$

$($g$)$ Calculate the $NN$ matrix $d$ whose element $d_{ij}$ is the length of the shortest

paths from node $i$ to node $j.$ Calculate the efficiency centrality $x_i$ of each node of

the network and rank the nodes, from the most to the least central, according to

their efficiency centrality.