The integraloty theorem tells us that if all capacities in a flow network are integers, then there is a maximum flow where every value is an integer
But the most remarkable part is the existence, not every maximum flow! Which means this statement doesn't claim every maximum flow is integer-valued
I cannot figure out why if all capacities are integer, but there exists a maximum flow is not integer-valued!!
Or did I just get wrong idea of this theorem that tries to tell me?