In the first line: "Dots are close to each other if they have a lot of common stargazers."

That explains why they are "close to each other" but not what determines which nodes are connected by an edge.

I think it's the other way around. The similarity metric determines which repos have edges (possibly weighted?)

And then some clustering algorithm makes sense of this giant graph by laying out sets of nodes that have a lot of edges to each other, close to each other

The closeness is just layout, the edges is the data structure that determines closeness.

This is correct!

Jaccard similarity returns a value between 0 and 1 (in this case the vast majority of the values being close to 0). I suspect there's a hard-coded threshold value to determine an edge, e.g. if Jaccard similarity between A and B is > 0.2, create an edge.

The author answered that question in the original HN post: https://news.ycombinator.com/item?id=35933981

Basically what others are guessing, lines represent the highest similarity scores based on "stargazers", which also forms the entire map. To anyone confused, the lines only appear once you click into a specific country.