Can we step back and ask what this graph is trying to solve ?

I have three itches that might be solvable by graphs but I might be wrong.

1. Seeing how far my posts are mirrored across the network.
   If I did my homework, that's 2nd degree of my followers effectivly?
2. Do I have users in common with this other user?
   I liked the color grouping of v1 for this.
3. Activity/Liveliness of the users over periods of time.
   By color gradients, maybe?