Seeking advice with node-based space map generation

Hi, I’m working on early prototyping for various systems in my game and am hoping to get some pointers regarding map creation. Specifically, the part I’m unsure about right now relates to generating a space map consisting of planets linked by connecting lines. I’ll add a few pictures to show what I mean.

From the game “Endless Space”:

From the game “Wing Commander Armada” (I think):

And, finally, from the game “AI War”:

So far I’ve not found much detail on how to approach making maps like this from a technical or programming angle. As is common with maps of this sort, I anticipate the player selecting from a few general configurations (eg, clusters, spokes, etc) and adjusting various settings (eg. planet density, number of planets, map size, connection density, etc) to generate a map before starting the game. What sort of algorithms should I be using and what properties must be considered to give good results in the form of a playable and enjoyable map? I’m not asking anyone to hold my hand and tell me every step of the process, but if you can give me any tips or point me towards useful articles I’d really appreciate it.
Thanks in advance.

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