Graph Algorithms · Superchallenge problem

A network has $9$ nodes numbered $1$–$9$ with connections $12, 23, 34, 45, 16, 67, 75, 28, 89, 94$. Consider every pair of distinct nodes and its shortest-path distance (in hops). Among all $\binom{9}{2}=36$ pairs, how many achieve the LARGEST such distance (the network's diameter)?