Rhyme never knew what a friend was, until Shiki mentioned it to her. Since that point, she wanted one for her own, to experience what it was like to have one. Sadly, she had no one now, for Shibuya has been invaded by Noise, and this Shibuya wasn't even real.
She only knew three people personally – Beat, Shiki, and Neku - but she couldn't consider them as friends, could she? She didn't feel much with the three, and the bond they had wasn't like what Shiki described it as. Maybe Shiki could be a friend; after all, she had introduced Rhyme into the concept of friends. Defiantly not Neku though, since to her, despite being with Shiki, he has come off as a cold-hearted freak. But maybe, Beat? He is her partner after all, and on several occasions, they did have a close bond. But they were partners, and that's all. Besides, this place was dangerous, so how could a friendship bloom here in all places? Maybe when they manage to escape this fake Shibuya. Yeah, maybe when both Rhyme and Beat and everyone else managed to escape this horrible place, then they could become friends.
No, they were friends, despite the odds, they were friends. And nothing, nothing, would stop them.