If $\displaystyle |V(G)|=n$. How many non-isomorphic graphs are there? In total, there are $\displaystyle \frac{n(n-1)}{2}$ edges but not all compose non-isomorphic graphs. For example, $\displaystyle G=(\{v_1,v_2,v_3\},\{v_1v_2\})$ and $\displaystyle G=(\{v_1,v_2,v_3\},\{v_1v_3\})$ but they are isomorphic.