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sage: G = graphs.PathGraph(3)
sage: G
Path Graph: Graph on 3 vertices
sage: H = G.automorphism_group()
sage: H
Permutation Group with generators [(2,3)]
So that sounds like not necessarily connected, especially since GAP (our group engine) notation starts counting at one, but our graphs (like most Python stuff) starts at zero. That said,
sage: G.automorphism_group??
could give you some clues. Sorry. In this case, a group is just a group. Is there a theorem that says there should be a connection? It's not as if we are giving a subgroup of the easy representation of the permutation group on all vertices; I can't find a matrix() method for G or H.
