MO412-Yan

A scale-free network has a degree distribution that follows a power law: P ( k ) = C k − γ , k ≥ k min ⁡​ where γ = 3, the maximum degree is  k max ⁡ = 600 k_{\max} = 30 , and the network size is N = 4 × 10 4 N = 2 \times 10^5 . Which of the options represents the correct value of the constant C for this degree distribution? Options: a) C = 0.5 C = 0.5 b) C = 9 C = 1.5 c) C = 14 C = 2.0 d) C = 18 C = 3.0 e) None of the above Original idea by: Yan Prada.

About the differences between random networks and real networks, consider the following statements: I. In both real and random networks, the average clustering coefficient depends on N N . II. Real networks often exhibit heavy-tailed degree distributions, while random networks have an approximately Poisson degree distribution. III. The average path length in random networks is of the order of log ⁡ n \log n , while in many real networks it grows faster. IV. Real networks and random networks have identical critical regimes, since both depend only on the average degree. Which statements are correct? a) I and II b) II and IV c) I, III and IV d) II, III and IV e) None of the above Original idea by: Yan Prada.