I just looked at the HQ photo and I don’t think it’s the shoelace. Graham’s shoelace is darker. And it’s WAY too long to use to tie her hair back. That’s why she ties it on her wrist in Storybrooke.
Emma wasn’t in love with Graham IMO. It was a “what if” kind of thing. She lost him, it was tragic. And she doesn’t wear the swan necklace anymore either. Just the circle necklace. She said she loved Walsh too but doesn’t have a memento of him. I’m not saying Graham wasn’t important, but he’s simply NOT on Killian’s level.