Submission 3

Regarding the following network models with \( 100,000 \) nodes:

  1. Barabási-Albert Model
  2. Scale-Free network with \(\gamma = 2.5, \langle k \rangle = 30 \)
  3. Scale-Free network with \(\gamma = 4, \langle k \rangle = 40 \)
  4. Random network with \( \langle k \rangle = 100 \)

where \( \langle k \rangle \) is average degree, and \( \gamma \) is degree expoent.

What is the sorted list in ascending order of these models such that it is ordered by approximate average distance?
  1. 1, 2, 4, 3
  2. 4, 2, 1, 3
  3. 2, 4, 3, 1
  4. 4, 3, 1, 2
  5. None of the above

Consider:

  • \( e^{12} \approx 100,000 \)
  • \( e^{2} \approx 12\)
  • \( e^{3} \approx 30\)
  • \( e^{4} \approx 40\)
  • \( e^{5} \approx 100\)

Original idea by: Giuliano Macedo.

Comments

Joao Meidanis said…
Very nice question, but how can we get the average distance for a BA network if we know just the number of links?
April 20, 2026 at 8:15 AM
Quiz - MO412 - Giuliano Macedo said…
According to the book on chapter 5 box 5.3: BA models have gamma = 3 and the approximate average distance depends only on N, which is the same formula in box 4.5 for gamma = 3
April 20, 2026 at 8:53 AM
Quiz - MO412 - Giuliano Macedo said…
I've made a mistake, I meant the number of nodes, not links! I've updated it, also I added the explicit ascending order.
April 24, 2026 at 9:32 AM
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