Combinatorics Question

Given a complete graph with nodes N:

Whats the most uniform way to traverse it for any non-triangular number N?

This has driven me insane for a couple of years now, is there even a solution?

This question makes no sense.

If it's a complete graph, then any node connects to every other node. So you just look at all the edges of your current node. And suddenly you have traversed the graph.