You would probably have more success running some form of Verlet integration on your vertices. I have to admit, I've only ever done ropes doing that, but you should still get very good looking results with it.

As to finding neighbours, the easiest way is to probably iterate over every vertex and figure out which ones are within X distant and storing that in some kind of lookup table so that you can quickly iterate over your nodes afterwards. The easiest (and least efficient, but who cares if you only ever do it once) method is to just iterate over every vertex and then have an inner loop going over every vertex again checking their distance.