> BTW, shouldn't the generator of the automorphism group be presented
> as "(0,2)(1,3)"?

Good luck ever convincing the right systems that this should happen:
GAP's permutation groups don't allow you to permute on the letter 0.
See the translation option of automorphism_group on that... This has
been a pain in the butt since day 1. Your "0" is probably the "4".

> >>  sage: foo.edges()
> >>  [(0, 1, 2), (0, 2, 1), (2, 3, 3)]
> >>  sage: bar.edges()
> >>  [(0, 1, 1), (0, 2, 2), (2, 3, 3)]
> >>  sage: bar.is_isomorphic(foo, edge_labels = True)
> >>  True

Which version of Sage are you using? The edge_labels option should
return True if and only if there is a label-preserving isomorphism, as
it does in your example in Sage 3.2.2:

----------------------------------------------------------------------
| Sage Version 3.2.2, Release Date: 2008-12-18                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: foo = Graph()
sage: bar = Graph()
sage: foo.add_edges([(0,1,2),(0,2,1),(2,3,3)])
sage: bar.add_edges([(0,1,1),(0,2,2),(2,3,3)])
sage: foo.edges()
[(0, 1, 2), (0, 2, 1), (2, 3, 3)]
sage: bar.edges()
[(0, 1, 1), (0, 2, 2), (2, 3, 3)]
sage: bar.is_isomorphic(foo, edge_labels=True)
False

>     2       1       3
> 1 ----- 0 ----- 2 ----- 3
>
> OTOH bar looks like this:
>
>     1       2        3
> 1 ----- 0 ----- 2 ----- 3

You probably know, but you can do:

sage: foo.plot(edge_labels=True)


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