I am looking for practical computational methods to lay out graphs in such a way that the geometry of the drawing reflects some of the symmetries of the graph.
Here are two example drawings of two graphs where the colours of the vertices and edges show graph symmetries. As you can see some of those graph symmetries are also geometric symmetries of the drawing.
What practical ways are there to generate similar drawings for an arbitrary graph?
I realize that in most cases this is only possible with compromises. For example, a force directed layout for the second graph above gives the following when restricted to two dimensions:
Fewer of the graph symmetries are reflected in this drawing, but it still shows some of them. That is okay—I am looking for practical solutions, not perfect ones.
Clarification: I am looking for explanations of methods that could be used. Software recommendations are welcome, but I am primarily looking to understand how they work (not simply use them).