Recalling that the distance between two nodes is the length of a shortest path between them $($assuming the network is connected$),$ we define the diameter of a network as the maximal distance between any pair of nodes, and we define the average distance as the average of the distances between each pair of nodes.$($a$)$ Construct the connected network on $6$ nodes with the largest average distance. Ex$-$ plain your reasoning.$($b$)$ Construct a connected network whose diameter is at least $3$ times its average distance.