I can see a pattern forming

My ex moved on very quickly after we broke up. My friends say it won’t last because he’s on the rebound. My best friend also mentioned something which made me think of this pattern that’s happening. When I met him he had a girlfriend, we were just friends so obviously nothing happened and it wouldn’t have either because I don’t believe in cheating. But there was definitely a spark between us. Even though he tried and tried (no guilty conscience whatsoever on his part) I turned him down everytime. He ended up breaking up with his girlfriend over a small argument and then we got together, so I was the rebound basically. We stayed together for 7 and a half years so it was a long time but in that time he turned on me and was abusive and made me rock bottom and without realising it, I was totally dependent on him for everything. It was a slow process so I didn’t notice what was changing around me, He would gaslight me by laughing it off and saying the abuse didn’t happen and that I was mental and psycho. I’m still healing. I found out he was also horrible to the girl before me as well but I’m not sure if he hit her like he did me. I’m sure he would have if they we’re together for longer so she had a lucky escape, I wasn’t so smart and stayed way longer than I should have. Anyway, he left me in the same way he left his ex before me and moved on to his new girlfriend straight away who’s he’s still with. I think she was already waiting in place just like I was. I don’t think the abuse has started yet because it’s still new so they’re still in the honeymoon stage. But can you see some kind of pattern emerging? We have a child together so unfortunately I have to be in contact with him for that reason, although I hate him for what he put me through I know he would NEVER hurt our daughter so I wouldn’t stop contact for her sake. But he HAS to be in a relationship at all times. He cannot be on his own, is that a sign of narcissism?

Sorry I should have mentioned more things but he has shown several signs of narcissism, too many to go into in this post. I was just asking if him needing to be in a relationship because he can’t be on his own, is also one of those signs of narcissism. I’m not basing the whole thing on that alone