Are great danes dangerous?

I was at one of my friends house for the first time, and she has 2 great danes. One of them would not leave me alone! He is HUGE! When i first walked in and saw him, i immeadiatly got a bad vibe. He followed me everywhere. When I went to the bathroom, and opened the door when i was finished he barked at me, and I had no choice but to run in the shower. My friends says "he'll never bite anyone, hes very sweet". I DO NOT believe her because he barked at me several times when I walked around. She is a VERY close friends, and I dont want this dog to effect our friendship when I go to her house! I just want to know if this dog is safe or not?!