Thank you, Jernej, for bringing up this issue. Turns out I've been
lazy, and hadn't carefully thought about degenerate cases. The line
graph is a bad test because the claw and triangle have the same line
graph... the disconnected pair (claw + C_3) has a vertex-transitive
line graph! The following counts 1,2,4,8,12,21,26,38 (subtract
wherever you think the empty graph doesn't belong)
def is_edge_transitive(G):
A,L = G.automorphism_group(translation=True)
G = G.relabel(L,inplace=False)
E = map(Set,G.edges(labels=False))
Ei= dict((e,i) for i,e in enumerate(E))
gens = []
for g in A.gens():
h = [Ei[Set([g(u),g(v)])]+1 for u,v in E]
gens.append(h)
return PermutationGroup(gens).is_transitive()
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