On an uncorrelated network with degree distribution P(k), the epidemic threshold for an SIR-type process depends not on the mean degree ⟨k⟩ alone but on the ratio ⟨k²⟩/⟨k⟩. For a large scale-free network with degree exponent 2 < α ≤ 3, what does this imply about the threshold transmissibility? a. The very large second moment ⟨k²⟩ drives the critical transmissibility toward very small values, so the network has effectively almost no epidemic threshold b. ⟨k²⟩/⟨k⟩ converges to ⟨k⟩, recovering the homogeneous threshold exactly c. The threshold rises with network size because hubs absorb infection d. The threshold equals 1/⟨k⟩ independently of the variance of the degree distribution e. None of the above Original idea by: João Pedro Carolino Morais
Postagens
Given a network with a defined community division, which has positive modularity, choose the correct alternative: a) Removing an edge from the network will reduce the modularity. b) Merging two different communities into one will increase the modularity. c) Removing an edge between nodes in different communities will increase the modularity. d) Adding an intra-community edge to the network will necessarily increase the modularity. e) None of the above. Original idea by: João Pedro Carolino Morais
Choose the correct alternative for a scale-free network with power-law exponent γ: a) If γ is 2.5, the giant component is immune to node removal, even if nodes are removed in decreasing order of degree. b) If γ is 4, the network remains connected until almost all nodes are removed at random. c) If γ is exactly 4, there is a fraction of randomly removed nodes that will break the network apart. d) If γ is 3.5, removing the highest-degree nodes first is no more damaging than removing nodes at random. e) None of the above.
Given two scale-free networks with degree exponents γ₁ and γ₂, where γ₁ > γ₂, and both networks have the same number of nodes (N) and minimum degree (kₘᵢₙ), which statement is correct? A. The network with γ₁ has larger hubs because its distribution decays faster B. The network with γ₂ has larger hubs because its distribution has a heavier tail C. Both networks have the same maximum degree since N is fixed D. None of the above Original idea by: João Pedro Carolino Morais
Regarding the models G(N, p) and G(N, L), choose the correct alternative: a) For equal values of N, choosing p = 2L/N(N-1) will guarantee that the graphs generated by G(N, p) and G(N, L) have the same number of edges. b) If N1 > N2 and L > 0, any graph generated by G(N1, p) will have more edges than any graph generated by G(N2, L). c) For N1 > N2, and p1 > 0, G(N1, p1) can generate graphs with an impossible number of edges for any graph generated by G(N2, p2) to reach, regardless of the value of p2. d) The degree distribution of graphs generated by G(N, p) follow a power-law, as very often real-world graphs do. e) None of the above. Original idea by: João Pedro Carolino Morais
Consider the following graph: Select the correct alternative: a) The red node has a clustering coefficient of 1. b) The orange node has a bigger clustering coefficient than the blue node. c) Removing the edge between the blue node and the orange node would increase the clustering coefficient of the blue node, but decrease the global clustering coefficient of the graph. d) Removing the edge between the blue node and the orange node would increase the average clustering coefficient of the graph. e) None of the above. Original idea by: João Pedro Carolino Morais