The number of nodes and edges is quadratic and the number of Coulomb repulsions is quartic, so I expect that only is possible to draw up to ~100, perhaps ~1000 or ~10000 using some tricks or aproximations.
Anyway, if you look at the graph of #5, it has two clear parts, the left part (with 16 nodes) that is #4 and the right part (with 16 nodes) that is just another copy of #4. So the structure is like 4-4.
But if you look more carefuly, you can find four copies of #3.
3---3
\ \
3 3
If you magicaly pull the second one to the left, you get 3-3-3-3.
This construction work in all level, so even for 1000000, you will have four parts 999999-999999-999999-999999
And you can expand this in smaller parts, but the structure get's more tricky.
So I expect the 1000000 still to have a fractal like structure with four big parts that are quite similar.
One problem is that each branch can go to the right or to the left, and that is probably choosen a random. At the low level ir cause some noise in the final graphic, but at the high level you get different symmetries of the whole figure. From almos to mirror parts in #13 to a propeler in #6.
I'm not sure how spiky is #1000000. If it's a circle, I epect to see a fer radial lines that show the division 999999-999999-999999-999999. If it' not a circle, I expect to see something like in the images.
The tricky part may be to select the correct ratio of the Coulomb and Hooke forces (and the default rest lenght of the edges?). Sometimes to get a nice limit he contants used in the force model should change with N.