There is almost exactly the same question. But I still don't understand, how is this heuristic working and in what sequence vertexes are passed through. Also there is a picture in a book: 
That shows comparison of nearest-neghbor heuristic and what I believe is a closest-pair heuristic. From the picture I may assume that on the top picture, 0 point was selected first, but on the bottom picture there was selected the leftmost or the rightmost one. Because there is nothing said about first point selection (also the closest-pair heuristic doesn't do any actions in that), I may assume that any algorithm results however good it is won't give you the bottom picture if it doesn't consider, what point to start with.
For now I just want to know, what steps closest-pair heuristic makes. A picture similar to the bottom one with numbers associated with each iteration along with explanation would be appreciated.
Here is the link to the book taken from that post.