# Calculate appr. weight of hamilton cycle

can i approximate the weight of a hamilton line in a complete weighted graph without implementing any algorithm like NN or calculate the MST? I know the average distance of each node and the metric which is used.

could i just do (average distance) * (metric) * (num of nodes)?

If there are $n$ nodes, then Hamiltonian paths have $n-1$ edges and Hamiltonian cycles have $n$ edges. Among the lists of Hamiltonian paths and cycles of a completed graph, each edge appears as often as every other.
So if the average weight of an edge is $w$ then the average weight of a Hamiltonian path is $(n-1)w$ and the average weight of a Hamiltonian cycle is $nw$.