An N vertices graph which is Isomorphic to its compliment graph have $\frac{(n)(n-1)}{4}$ edges.
sufficient but not necessary condition for such a graph to exist (n)(n-1) should be divisible by 4.
Eg: an complete graph of 4 vertices will have 6 edges now take an 3 edge ($\frac{(4)(3)}{4}$) and draw graph its complementary graph will be exactly isomorphic.
