Running Time: Bound One

Now, CONNECTED is constant time and we repeat it |E| times.

JOIN is repeated |V|-1 times and can take up to |V|/2 time.

Total running time: $O(\vert E\vert\log\vert E\vert + \vert V\vert^2)$.

Too loose! We're not really getting much bang from the fact that we merge smaller sets into larger sets.