9:59 AM PT -- The Saints just addressed Graham's arrest ... saying the tight end experienced a "medical episode" Friday night, which resulted in him becoming disoriented.
After he was taken into custody, the team says Graham was sent to a nearby hospital to get checked out.
The Saints added Graham likely suffered a seizure ... and spent the night in the medical facility to receive further testing. He is now back with the team.
We broke the story -- Graham was arrested for suspicion of being under the influence of a controlled substance and resisting, delaying and obstructing a police officer.