What you show here in this image is something similar to one I solved in the past. I used Graph Theory, and searched for all Hamiltonian circuits. Wasn’t easy at all as I remember. You can simplify your graph by just identifying each line by its start and end vertex, but not if you can have some cases as the “green line” where another line hits a centered vertex. By the way, you should know it’s an NP algorithm.
In case you get to it (get to have all circuits), you have a second problem: you have to decide which ones of them are the ones you want (in your case, you have big circuits that can be reduced to two or three smaller ones). If you can simplfy your graph, the “good ones” will be surely the smaller ones (less number of nodes) but if you can’t (because you have some cases as the green line), I can’ t imagine how to select them. Perhaps calculating their area. Really an interesting problem!
Good luck!