Let G=(V,E) be a graph. The complement of G is the graph G¯:=(V,[V]2 \ E) where [V]2 is the set of pairs {x,y} of distinct elements of V. If K is a subset of V, the restriction of G to K is the graph G↾K:=(K,[K]2∩E). We prove that if G=(V,E) is a graph and k is an integer, 2 ≤ k ≤ v−2, then there is a k -element subset K of V such that e(G¯↾K)≠e(G↾K), moreover the condition k ≤ v−2 is optimal. We also study the case e(G¯↾K) ≢ e(G↾K)(mod p) where p is a prime number. Following a question from M.Pouzet, we show this: Let G=(V,E) be a graph with v vertices. If e(G) ≠ e(G¯) (resp. e(G)=e(G¯)) then there is an increasing family (Hn)2≤n≤v (resp. (Hn)2≤n≤v−2) of n -element subsets Hn of V such that e(G↾Hn)≠ e(G¯↾Hn) for all n. Similarly if e(G) ≢ e(G¯) (mod p) where p is a prime number, p>v−2, then there is an increasing family (Hn)2≤n≤v of n -element subsets Hn of V such that e(G↾Hn) ≢ e(G¯↾Hn)(mod p) for all integer n∈{2,3,…,v}.