The following diagrams are traversable:
1, 2, 3, 7, 8, 9 and 11
If all the points (nodes) have an even number of paths (arcs) leading from them, the diagram will be a circuit (you can end up where you started): diagrams 2, 3, 7 and 9.
If two points (nodes) have an odd number of paths (arcs) leading from them, the diagram will be a tour (you need to start at one of the "odd nodes" and you will finish at the other "odd node"): diagrams 1, 8 and 11.
If more than two points (nodes) have an odd number of paths (arcs) leading from them, the diagram will not be traversable: diagrams 4, 5, 6 and 10.
NB. You cannot have a diagram with an odd number of odd nodes.