We wanted to find the ways to complete the circle, and the maximum distance along connections for 2 points. There are only 2 ways to fill the circle. If we notate them by the number of nodes travelled clockwise with each line, they are 3-3-3-3-3-3-3, and 3-3-3-2-4-4-2. The maximum distance for 2 points would be 2 points 3 circle segments apart. Of course, these would not be connected but would have to have 2 points connected within the 3 segments between them. The length of this is sin(360/7)/2 for the line and π/7 for the arc. This makes our answers 2 and ≈0.9078.