Network Science Quiz Questions 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