In the Euclidean plane, a pair edges A,B are connected, provided there is a path that allows us to travel from A to B.
I don't get your question , James.
Yes, two points are connected if there is path between them. The same holds for two edges. and the same also holds in hyperbolic and elliptic geometry.
My model used euclidian distances but with a toroidal wrap so that there were no edges at all :)
See doi: 10.1111/ecog.02191
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