Lets call the sum of any three aligned numbers $s$. Then the sum of the three vertical columns is $(A + D + E ) + (A + C + F) + (A + B + G) = 3s$, but this is also equal to $3A + (D + C + B) + (E + F + G) = 3A + 2s$, and hence $3A = s$, or $A = \frac{s}{3}$. Hence $A$ must be the average of any three aligned numbers. It is then easy to see that the only thing $A$ can be is $4$, and hence $\boxed{4}$ cannot be placed in the circle $E$.