The author alludes to the fact there are better models for representing social graphs, but I think the pdf linked from the article is missing (or rather, only briefly mentioning) a very important model: The Albert-Barabasi model.
This model basically says that when a new node joins the network, it will prefer to attach itself to already popular nodes. For example, when a new user signs up to Twitter, there's a larger chance it will follow celebs with many followers, than the average Joe. Another example: when a new small ISP starts operating, there's a larger chance it will connect to a well-established higher-tier ISP serving many small ISPs, than to a random ISP. This phenomenon is observed in many other contexts: actors appearing together in movies, citations between scientific papers, sexual relations among people...
This model basically says that when a new node joins the network, it will prefer to attach itself to already popular nodes. For example, when a new user signs up to Twitter, there's a larger chance it will follow celebs with many followers, than the average Joe. Another example: when a new small ISP starts operating, there's a larger chance it will connect to a well-established higher-tier ISP serving many small ISPs, than to a random ISP. This phenomenon is observed in many other contexts: actors appearing together in movies, citations between scientific papers, sexual relations among people...
For more information: http://www.eng.tau.ac.il/~shavitt/courses/LargeG/intro-BigDa... (last 2 pages)
Disclaimer: This is material from a course taught by my advisor.