I have ----- (capitalized name of degree level) degree in ----- (subject). - use "in" not "of". So it should be : "I have a (Bachelor's/Masters/PhD) degree in Business Administration." or "I graduated with a - degree in - " or "I graduated from Harvard University with a - degree in -- "
"graduated" just means that you passed a grade or level, and can depend on the school. You can graduate from 4th grade when you are a child in some US schools, but of course you don't have a degree.