Detecting rotational symmetries of spatial structures

Question

I have a spatial graph-like structure. The structure consists of vertices in the 3D space and connecting edges. Are there any algorithms available that would identify the rotational symmetries of these structures? In particular, I'm interested in all the rotational axis along which I can rotate the structure to overlap itself, as well as the degree of rotation. For example, an equilateral triangle (3 vertices + 3 edges) would have one rotational axis perpendicular to its plane, with a degree of 3 and 3 others in its plane, with a degree of 2 each. The closest I could find are molecular packages identifying the symmetry groups of molecular structures. I would prefer not to go that far as I'm only interested in rotational symmetries and not entire group theory description of structures.