Question:
which methods for visualising complete weighted and symmetric graphs, i.e. $K_n$, are useful in the sense that they can aid in mathematical research?
The Traveling Salesman Problem may explain what I am looking for: in the euclidean case the visualization of the vertices as points in the euclidean plane together with the depicted optimal tour allows one to see general properties of optimal tours like resp. to judge the optimality of a given tour.
If the instance is not euclidean, e.g. with uniformly distributed random edge weights, assigning coordinates to the vertices for displaying optimal tours incurs large distortions that obscur the original structure and do not allow for drawing any conclusions.
