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Degree Correlation - cap 7

 In simple scale-free networks generated by the configuration model, a conflict may arise between the scale-free degree distribution and the absence of multi-links or self-loops. This leads to the concept of the structural cutoff , which determines whether high-degree nodes can connect freely without violating the simple-network constraint. Which of the following statements correctly describes the consequences of this structural cutoff on degree correlations? a)  When the largest node degree in the network remains below the structural cutoff, the network can preserve its scale-free property, maintaining the network with a neutral structure. b)  If the largest node degree exceeds the structural cutoff, the network cannot realize the expected number of hub–hub connections, leading to an apparent disassortative pattern known as structural disassortativity . c)  In networks where all nodes have degrees smaller than the structural cutoff, a neutral structure emerges...
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The Barabási-Albert model - cap. 5

Consider a Barabási-Albert network with parameter m = 2. A node  i  was introduced at time t i = 4 . At a later time t , this node has degree k i ( t ) = 100 . What is the expected average clustering coefficient ⟨ C ⟩  of the network at time t ? a) ⟨ C ⟩ ≈ 0.025 b) ⟨ C ⟩ ≈ 0.030 c) ⟨ C ⟩ ≈ 0.010 d) ⟨ C ⟩ ≈ 0.008 e) None of the above Original idea by: Yan Prada.
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Scale-Free Networks - Cap. 4

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.
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Random Networks - Cap. 3

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.
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Graph Theory - Chap 2

Let G be an undirected, unweighted network without self-loops and with N nodes. For a given node i , let N i denote the number of neighbors of i . Which of the following expressions correctly represents the denominator of the clustering coefficient for node i , given that the nominator L i represents the actual number of connections between the N i neighbors? ( N i (N i − 1) ) / 2 N i 2 ( N i (N i + 1) ) / 2 N i (N i − 1) None of the above Original idea by: Yan Prada.
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