In terms of Tonnetz analysis, is there any special significance to a chord that does not form a connected graph when using a Tonnetz diagram? For example an augmented 7th chord ( as in *C-E-G#-Bb* ) is connected for C,E and G#, but the 7th, Bb, it is disconnected.

From that we can see that Bb is not a [3rd, flat 3rd, 4th, 5th, 6th, or flat 6th/sharp 5th] of any of the notes C, E or G#. (Or inversely, using Bb as the root.) 

Is there anything more we can learn from this about an augmented 7th, or other chords that don't form a connected graph?

On a side note: Just tested all 495 4-note combinations and 132 of them are not connected. And of the 220 3-note combinations 96 are not.