Proving a graph is connected I have to prove that if a graph G=(V,E) has |V|=2n and every vertex has a degree of n, (with n<-N*) then it is connected. 
I have this so far:
If there are 2n verticles and each one has a degree of n, then the number of connections is n^2.
We know there is no vertex with 0 degree, so if G is not connected, then it consists of at least 2 connected graphs, and all of their verticles also have a degree of n. 
How do i continue?

Suppose the graph is not connected, say the vertex set is partitioned into $V_1$, $V_2$ such that between them there is no edge, then $V_1$ must have at least $n+1$ vertices, so does $V_2$, contradiction.
