Confusing relationship with the opposite sex?

Dated a friend I’ve known for awhile right before I left for a trip overseas for 5 months. While gone, she started dating another guy, but wasn’t able to fully let me go. I came back to find her still confused, so backed away for a month during which her relationship ended with the other guy. Not much hope of it recovering. Now, she realized that she loved that guy, but still wants to hang out with me all the time. She’s becoming more and more affectionate, but doesn’t want to date me and often will get caught up in memories of this guy. I feel like I’m in a relationship without any of the perks. I do love her, but I’m not sure what my course of action should be.