Network Science Quiz Questions by Jhonatan Cléto

In the online realm Streamland, users form alliances by sharing videos. Two users are connected if they frequently co-watch and comment on each other’s uploads.  Over time, the network develops dense friendship clusters separated by a few key influencers who connect multiple groups. The Streamland Council wants to identify real communities within this network. They test two algorithms: Ravasz’s agglomerative method Girvan-Newman’s divisive method If one influential user bridges two dense fan groups, which algorithm is more likely to identify these two fan groups as separate communities? A)  Both algorithms, because they detect bridge users the same way B) Ravasz’s method, because it merges nodes based on global similarity rather than edge centrality C) Girvan-Newman’s method, because removing high-betweenness links isolates the two dense groups D) Ravasz’s method, because topological overlap decreases across sparse bridges E) None of the above Original idea by: Jhonatan Clét...

A drone delivery company must deliver packages to five floating islands in a futuristic archipelago. The islands are named Aqua (A), Bora (B), Coral (C), Drift (D), and Echo (E). Distances (in km) between islands are shown below:  To minimize battery usage, the drone company decides to plan its route using the Christofides algorithm to approximate the optimal Traveling Salesperson path. What is the approximate minimum total distance the drone will travel to visit all islands once and return to the starting point? A) 24 km B) 25 km C) 26 km D) 27 km E) None of the above Original idea by: Jhonatan Cléto

Regarding the network shown above, which alternative is correct? A) The network is neutral, and the probability of a new edge forming between B and I is equal to that of a new edge forming between E and F. B) The network is assortative, and it is more likely for an edge to form between E and F than between B and I. C) The network is assortative, and it is more likely for an edge to form between B and I than between E and F. D) The network is disassortative, and the probability of a new edge forming between C and L is lower than that of a new edge forming between H and L. E) None of the above. Original idea by: Jhonatan Cléto

In the Ford–Fulkerson method, the bottleneck capacity of an augmenting path is usually defined as the minimum of the residual capacities of its edges. Suppose a path has two edges whose residual capacities vary with time \(t\), \(r_1(t) = t^2 + 1\) and \(r_2(t) = e^t\). Instead of taking the minimum, define the augmenting path capacity as the average of the residuals: \(R(t) = \frac{r_1(t) + r_2(t)}{2}\). What is the derivative \(\frac{dR}{dt}\) at \(t = 1\)? A) 1 B) 2.34 C) 2.72 D) 2.86 E) None of the above Original idea by: Jhonatan Cléto

Consider the following directed graph: I. The shortest path from A to J has length 5, and this is the longest among all shortest paths in the graph. II.  The number of cycles in the graph is exactly half the number of its strongly connected components. III.  If each strongly connected component is collapsed into a single node, there will be two possible topological orderings of the graph. IV.  If node D and all its incident edges are removed, and a new edge from B to E is added, the resulting graph will form a single strongly connected component. Which of the statements are  correct ? A) I, II, and III B) II and III C) Only III  D)  III and IV E) None of the above Original idea by: Jhonatan Cléto

Consider the following statements about detecting cycles using BFS: I. In an undirected graph , a cycle can be detected if BFS discovers an already visited node that is not the parent of the current node. II. In a directed graph , a cycle can be detected during BFS by encountering a node that is currently in the queue (i.e., discovered but not fully processed). III. BFS cannot be used for cycle detection in either directed or undirected graphs. IV. When used to test bipartiteness, BFS indirectly detects cycles of odd length if they exist. V. BFS can always detect cycles in a weighted graph, regardless of whether the weights are positive or negative. Which of the statements are correct ? A) I and II B) I, II and IV C) III and V D) Only IV E) None of the above Original idea by: Jhonatan Cléto