If it is simply telling someone about yourself, it would sound more natural to say 'I'm a graduate'. If you were talking about the ceremony, or about the event in the past, you could say 'I graduated in 2016' for instance.

I graduated

Hi, I'm graduated - is a description of your current status I graduated (at..) - defines the accomplishment of an action in the past In the real life you will mostly use "I graduated at ..." because you have to show your diploma. "I'm graduated" is simply the reply to "Are you graduated?" Bye

I'm graduate --> WRONG! It should be "I'm graduating" (Continuous tense)... meaning you are in the process of doing it. I graduated --> Correct (past tense). Means that process is done. "Have you graduated?" --> "Yes, I had."

I graduated