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.

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.