$G$ is a graph which contains the same number of edges as its complement

Question

$G$ is a graph which contains the same number of edges as its complement. How many edges does $G$ contain?

$$m = \frac{n(n-1)}{2} - m$$

So:

$$m = \frac{n(n-1)}{4}$$

I'm not sure if this is the final answer to this problem. Can I get more information about $m$ and $n$?

Answer 1

Of course, then $$4\mid n(n-1)\implies 4\mid n\;\; \;\;{\rm or}\;\;\;\;4\mid n-1$$

possibilite $2\mid n$ and $2\mid n-1$ is of course impossibile since $n-1$ and $n$ are one odd and other even.