Comment by Jtsummers

The first error seems to be a transcription error, it's correct in their graph representation further down.

The second one isn't an error, but a poor explanation. After a balloon is burst, the balloons now have new neighbors. That is, it isn't this:

  3 1 5 -> pop 1 = 15
  3 _ 5 -> pop 3 = 3

It's:

  3 1 5 -> pop 1 = 15
  3 5   -> pop 3 = 15

The distance between the balloons doesn't make them not neighbors.