Couples and their ex - is it ok?

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So I've been dating my girlfriend for about 5 months now. Its came to my attention that her and her ex still keep in touch. Not like texting everyday or something just if they need to get info from each other but when they do, she gives off this weird vibe through her texts. Almost as if they were really good friends. His texts are mutual no flirting or anything. I know this bc i went through her phone just casually and saw these texts. Then I saw his instagram bc curiosity got the best of me and she likes alot of his pics. On the other hand he doesnt. It seems like he doesnt try to talk to her, which is good. We've told we love each other and i trust she means it. I do. On twittter she will tweet random songs lyrics, like for example " i'll miss you like a child misses their blanket, but i have to move on in life". I cant tell if she means her dad or her ex. Her dad passed away 9 yrs ago and she still have trouble with that. So i cant tell if she's referring anybody at all. I know this sounds weird and it may seem like i have some issues but I just want a second opinion from the public. We both care and love each other but it seems that her ex still lingers somewhere through her thoughts even after almost two yrs since they broke up. What do you guys think? How should I comfort her about this? Or should I even? Please some advice would help.