Here are some of my thoughts after a quick scan:
1. George Box has a very famous quote: "All models are wrong; some models are useful."
2. Even the model applies correctly for Myspace, it does not mean it is correct for Facebook. I would use a very common terminology - "survival bias/selective bias" for it. The only way to ensure the model is letting it through numerous amount of cases. There is not only one social network is active, can the author predict for them and for the old one? Here is the possible list:
https://en.wikipedia.org/wiki/Social_networking_service
3. When they cited a paper, they are not supposed to agree with them. Some of paper even criticize each other. They may accept the concept of Facebook being cool down but not in couple of years (with different parameters). If you want to make sure they are all agree or not, please make a survey on this. Like I said, you (and probably me) are probably into survival bias.
4. There is a least one mistake here: "discussed in Section ?? [3],". So, was it well proof read?