Question for MO412 - 03/04/2026
Consider a scale-free networks G(γ,N) where the degree distribution follows a power law, where is the degree exponent, and is the network size. Addicionaly, consider the following networks:
Analyze the following statements:
I) Most of the real-world large-scale free networks have γ < 2.
II) Given a, we can affirm that both average degree ⟨k⟩ and the second moment ⟨𝑘²⟩ diverge.
III) Given Gb, the average distance will increase as ln(ln(Nb)) as an ultra-small world network.
IV) Gc is in a small-world regime and is similar to a random network.
Given the statements, we can affirm that:
A) Only I is correct.
B) Only II and III are correct.
C) Only III and IV are correct.
D) Only II, III, and IV are correct.
E) None of the above.
Original idea by: Gabriel Talasso
Interesting question, but I think you mean "network families" when you talk about G(2.1, N_a) etc.? Well, maybe not, since you have N_a there, but keep in mind that statements about converge of moments only make sense with respect to families with N growing to infinity. I'll pass.
ResponderExcluirHello professor. Thank you for the feedback!!
ExcluirWhat do you think about updating statement 2 to:
II) Given Ga, we can affirm that both average degree ⟨k⟩ and the second moment ⟨𝑘²⟩ diverge with Na growing to infinity