Barabási–Albert Model

You are an analyst for a streaming platform called StreamWorld, which works like a social network: each movie is a node, and connections between movies represent users who watched both.

StreamWorld grows following a pattern similar to the Barabási–Albert model:

  • Each new movie connects to m = 3 existing movies.
  • The probability of a movie receiving a new connection is proportional to the number of connections it already has (preferential attachment).
At the start (t = 0), there are m₀ = 5 fully connected movies.

At time t = 12000, the network has N = 12000 + m₀ movies, and three movies were released:
- Movie A at tA = 100
- Movie B at tB = 1000
- Movie C at tC = 4000

Which of the following is the correct ranking of their expected degrees ki(t) from largest to smallest, what is the approximate ratio between the largest and smallest, and what is the estimated network diameter D(N)?

  1. A - B - C, ratio ≈ 3.32, D(N) ≈ 8.4
  2. A - C - B, ratio ≈ 6.32, D(N) ≈ 8.4
  3. C - A - B, ratio ≈ 3.32, D(N) ≈ 6.3
  4. A - B - C, ratio ≈ 6.32, D(N) ≈ 4.2
  5. None of the above

Original idea by: Aline Azevedo

Comments

  1. Joao MeidanisOctober 4, 2025 at 6:42 PM

    Questão bacaninha, mas creio que já temos estes temas cobertos.

    ReplyDelete

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