Postagens

Question for MO412 - 17/04/2026

Consider the degree evolution in a network generated by the Barabási–Albert preferential attachment model with nodes following the same dynamical law and assume the continuum approximation when necessary . At time t=100, analyze the attachment probabilities. Given parameters of the model: m 0 = 2 m_0 = 2 m = 2 m = 2   Consider the vertices: v a v_a  with degree k a = 10 k_a = 10 v b v_b  with degree k b = 4 k_b = 4 Analyse the following statements: I) The probability that a new vertex connects to v a v_a v a ​ is approximately 0.025 0.025 . II) The probability of connecting to v a v_a  is 2.5  times greater than connecting  to v b v_b ​ . III) If both vertices had their degrees doubled, the probability of connecting to v a v_a ​ would be 1.25 1.25  times greater than to v b v_b ​ . IV) If each vertex's degree were increased by 2 2 , a new vertex would be 2 times more likely to connect to v a v_a ​ than to v b v . V) Afte...
Postar um comentário
Leia mais

Question for MO412 - 03/04/2026

Consider a  s cale-free networks   G ( γ , N )  where the degree distribution follows a power law, where  γ is the degree exponent, and  N is the network size. Addicionaly, consider the following networks: G a = G ( 2.1 ,  N a ) G_a = G(2.1, N_a) G b = G ( 2.9 ,  N b ) G_b = G(2.9, N_b) G c = G ( 4 ,     N c ) G_c = G(4, N_c) Analyze the following statements: I) Most of the real-world large-scale free networks have γ < 2. II) Given  G 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
2 comentários
Leia mais

Question for MO412 - 20/03/2026

Imagem
Consider two random graphs, G_a and G_b, where edges are created independently with probabilities p_a and p_b, respectively. Additionally, consider the following binomial degree distribution:   Consider:  N_a = 200 and  N_b = 100  Evaluate the following statements: I) The average degree <k> is higher in graph G_b.   II) The variance of the degree distribution in G_b  is greater than in G_a .   III) The expected number of edges in G_a is greater than in G_b.   Select the correct alternative: A) Only I is correct.   B) Only I and II are correct.   C) Only II and III are correct.   D) I, II, and III are correct.  E) None of the above. Original idea by: Gabriel Ukstin Talasso
1 comentário
Leia mais

Question for MO412 - 06/03/2026

Imagem
 Based on these two adjacency matrices, A and B, analyze the following statements: I) Graph A is directed and graph B is undirected. II) Graph A is strongly connected and graph B is disconnected. III) The diameter of graph A is 3 and the diameter of graph B is 2. IV) The average degree of B is 2. Select the correct alternative: A) Only I and III are true. B) Only I and II are true. C) Only I and IV are true. D) Only I is true. E) None of the above. Original idea by: Gabriel Talasso
2 comentários
Leia mais