TDSM 10.13

Reference: [1] (slide 37)

(a) Social networks like Facebook or Instagram.

Power law distribution.

When a new user signs up a Facebook or Instagram account, he/she has a high probability of liking famous celebrities such as C. Ronaldo or Messi, and Hollywood stars.

(b)Sites on the World Wide Web (WWW)

Power law distribution.

In the textbook, chapter 10.4 describes the PageRank algorithm. PageRank relies on the idea that if all roads lead to Rome, then Rome must be a pretty important place. In the WWW, important sites that can be considered as "Rome" are very less. The majority of sites are unknown, such as my GitHub homepage [2]. I believe a very small number of sites refer to my GitHub.

(c)Road networks connecting cities

Bell-shaped distribution.

In the textbook page 323: Road networks must be sparse graphs because of road junctions. The most ghastly intersection I’ve ever heard of was the endpoint of only nine different roads.

(d)Product/customer networks like Amazon or Netflix

Power law distribution.

When I am searching a keyword in Amazon app, best sellers usually come up in the top. Thus I have a high probability to buy the best seller. The number of best sellers is small (if many best sellers, then they can not be considered "best", best means the 1st). Netflix is similar to Amazon. The popular movies usually show up in obvious places.