Hi. I'm one of the authors. Please read our FAQ. It answers that very question. In short, our de-anonymization algorithm applies to far more than public social networks like twitter, including some very sensitive ones.
We have an FAQ about this paper. It answers many of the misconceptions expressed in the comments here.
In particular, our algorithm applies to much more than public social networks like twitter and flickr. A variety of networks including the phone call network are being shared behind your back in anonymous form, and our de-anonymization techniques apply just as much. You'll probably agree that people expect more privacy there.
See my blog for a variety of demonstrations and thought-experiments of de-anonymization.