Just some screenshots of a system that "appears" to be a binary star system (but isn't), because their star "spheres" on the Galaxy Map are close enough together that they overlap.

3 images:

1: The address (of Kagong-Anwe)
2: On Map Star System Kagong-Anwe
3: On Map Star System Ogourding

[Edit]: If you save off the two "On Map" images, and use an image viewer with which you can "step" back and forth between the two images, you can clearly see the overlap (without having to jump there in the game to see it).

From the programming perspective, each star system is a different 'game level', no matter where they are located on a map. So even if they where basically on the same spot, than they still would never "overlap" or interact with each other as they are always considered independent.
It still seems to be a slight offset there and the images are a 2D representation of the 3D map so depth is missing. but on galaxy map space, such a distance is probably still 0.5 light years which are still about 4.74 trillion (4,700,000,000,000) km. While naturally, binary stars can be away even more than a light year apart, in game terms, you still would have to jump between them anyway, other wise, with enough time, you would also be able to just 'fly' to the next star - like if 0.5 LY takes 30 minutes to fly traditional, 20 LY would be just about 20 real hours of flight.