Network Science Questions

In real-world networks, nodes can often be removed, such as when research papers are retracted. Based on the node deletion model, which describes the relationship between adding and removing nodes, identify the incorrect statement regarding the behavior of such networks: a) The network maintains a scale-free characteristic if the number of nodes removed is smaller than the number of new nodes added. b) If the rate of node removal exceeds one (r > 1), the network will enter a declining phase. c) The network's degree distribution will shift from scale-free to exponential when the rate of node removal surpasses a critical threshold related to initial attractiveness. d) The network maintains its scale-free nature if the rate of node removal is equal to the rate of node addition. e) None of the above.  Original idea: Matheus C. Lindino

Consider a scale-free network where the maximum degree of the nodes  k max is given by the formula: k max = k min N 1/(y-1) Given that k min = 3t , N = 5t , and y = 3 , determine the rate of change of k max with respect to t . a) 30t b) (9√5)/2 * √t c) 10√3 * t d) (5√15)/2 * t 3/2 e) None of the above    Original idea by: Matheus Lindino

Consider the following statements regarding the BFS (Breadth-First Search) and DFS (Depth-First Search) algorithms in an undirected graph. Identify which of the statements below are false: I. Both BFS and DFS can be utilized to check if a graph is connected. II. DFS can potentially get caught in a cycle, whereas BFS is immune to this issue. III. DFS is guaranteed to find the shortest path between two vertices, if such a path exists. IV. BFS always finds the shortest path (in terms of the number of edges) between any two vertices, if such a path exists. a) I b) II c) II and III d) II and IV e) None of the above Original Idea: Matheus Lindino

      The graph above represents the social network of a group of people in a research lab, illustrating co-authorship among the researchers. Based on this information, which of the following options is the approximate value of the average clustering coefficient:   A) ⟨C⟩ = 0.2 B) ⟨C⟩ = 0.4 C) ⟨C⟩ = 0.6 D) ⟨C⟩ = 0.8 E) None of the above    Original idea by: Matheus Lindino

  Given the curriculum chart for the Computer Engineering course above, which of the options below indicate the topological order for a student to organize which subjects should be taken? Consider alphabetical/numerical order when performing DFS: a) LA -> CEI -> DC1 -> DC2 -> C1 -> C2 -> C3 -> SP -> A1 -> A2 b) LA -> CEI -> DC1 -> DC2 -> A1 -> A2 -> C1 -> C2 -> C3 -> SP c) C1 -> CEI -> C2 -> LA -> A1 -> DC1 -> C3 -> A2 -> DC2 -> SP d) CEI -> C1 -> DC1 -> A1 -> LA -> C2 -> DC2 -> A2 -> C3 -> SP e) None of the above Original idea by: Matheus Lindino