It probably depends on the accounts, and the algorithm. If the comparison algorithm uses some sort of distance calculation between 2 users to figure out how close they are, then you could have single directional relationships.

If my comments are on an island of weirdness, you may be the closest person to me while still being really far away. If your comments are relatively normal, you might have a lot of people around who are closer than me. That would make you my doppelganger, but not make me yours.

Edit: I just checked my doppelganger (barry-cotter), and I'm not even in his list :p. I've seen that username appear in a couple other comments under this post. I wonder if there are a few super normal users that a lot of people are closest to.

No. There's no reason for it to be symmetric, there can be unlimited number of your closest neighbour's closest neighbours, that are closer to him than you are. I mean, it's literally measuring distance between dots in the n-dimensional space, and if you'll ask your question about the dots on the paper, the answer will be obvious to you.

FWIW, I'm not even on my #1's list.

The person you're a closest match to, could have a closer match to someone else. Same with their closest match, and so on.