Consider the (sub)graph below. I am allowing for the possibility of additional edges and nodes, and just want to look at the features of this subgraph.
What seems apparent is that there is not a trail that will hit every edge (some edge would have to be repeated). However, this was constructed by overlapping a few closed trails or connecting them via some path.
I am wondering what concepts are available to describe something like this, if any? Specifically, by 'this' I mean a subgraph that is constructed by connecting several closed trails, either by allowing them to share some edges (the two cycles on the left), or by drawing a path between them (for example, there is a vertical path between the figure 8 closed trail and the cycle NOPN).
