Well, we have a huge number of kinds of graph generators, honestly, so we could probably say "yes" to every variant of your question, heh.
The original map types that I coded were all based around laying down nodes first, then creating linkages after that. In some versions proximity was valued, in others it was not. In some versions it attempted not to overlap, in others it did not. In some versions it had strict limits on how many linkages a single node could have, in others it had a certain number of planets that it would let have far more.
That was the original approach. Then later I did some that used general maze creation methods by laying down pegs and driving a maze through them, for instance. The snake I did by I believe laying down one node and then laying down the next and immediately linking them. The tree was similar, but with little branches periodically.
Then Keith got into things and started doing the really cool maps, which are more shape-based. All the stuff you see in the last two or three expansions. I'm not sure how he did those exactly, but it's an entirely different approach from mine.
