Doubled shapes can be done by using [peripheries=2]
on the node
Doubled edges can be done by specifying more than one colour for the edge, separated by a colon. In this case use the same colour twice: [color="black:black"]
(or, to separate them slightly more, do [color="black:invis:black"]
)
I got there eventually! Sorry for the "evolutionary" nature of this answer :-)
So for example
graph G {
Foo [peripheries=2]
Foo -- Bar [color="black:white:black"]
}