2025-002

Consider the directed graph below:



Applying the Kosaraju-Sharir algorithm, we wish to identify the strongly connected components (SCCs) of the graph. Regarding the steps and the result obtained, analyse the statements below:

I. In the first execution of DFS, the completion times of each vertex are used to define the order of exploration in the transposed graph.

II. The transposed graph is obtained simply by inverting all the edges of the original graph.

III. Each tree in the search forest in the second execution of DFS corresponds to a strongly connected component.

IV. The algorithm can identify cycles, but cannot isolate nodes that are not part of any cycle.


Which statements are correct?

A) I, II, and III only.

B) I and IV only.

C) II and III only.

D) All are correct.

E) None of the above.


Author: Giancarlo Maldonado Cárdenas

Comentários

Postar um comentário

Postagens mais visitadas deste blog

2025-004

Consider a simple scale-free network generated through a configuration model with degree exponent  γ = 2.4, minimum degree   kₘᵢₙ = 1, and N = 10⁴ nós. Suppose that the maximum degree is limited by the structural cutoff kₛ ~ N¹ᐟ², and that the empirical degree correlation function follows kₙₙ(k) ~ kᵘ. Based on this scenario, select the correct statement : A) The exponent μ < 0 arises solely from dynamic preferential attachment, since the configuration model preserves assortativity by construction. B) Even though the configuration model is uncorrelated in principle, finite-size effects and the structural cutoff impose an effective dissortativity, resulting in μ < 0. C) Increasing N while maintaining the same γ leads to stronger assortativity, because kₛ grows sublinearly with N. D) Networks with γ < 3 cannot exhibit dissortative mixing, since their hubs dominate the connectivity pattern, forcing μ > 0. E) None of the above. Original idea by: Giancarlo M...
Leia mais

2025-006

Question Consider a network with \( L = 200 \) total edges, composed of multiple communities. Two specific communities, A and B, have total degrees \( k_A = 18 \) and \( k_B = 16 \), with only 2 edges connecting them (\( L_{AB} = 2 \)). Knowing that modularity tends to merge communities when \[ \frac{k_A \cdot k_B}{2L} which of the following statements about detecting these communities is CORRECT? A. Communities A and B will be detected separately because \(\Delta M_{AB} B. The modularity algorithm will inevitably merge A and B due to the resolution limit C. The merger depends exclusively on the number of internal edges in each community D. Such small communities will always have negative modularity E. None of the above Original idea by: Giancarlo Maldonado Cárdenas
Leia mais

2025-001

Imagem
A group of friends is organizing a secret message run using an oriented and unweighted graph. Each number represents a person, and each area indicates so that the message can be reviewed directly. The graph is shown below: The message starts at friend 1. Considering the execution of the Breadth-First Search (BFS) algorithm starting at 1, and assuming that the adjacency lists are sorted in ascending order, which of the options below correctly shows the order of visitation of the nodes? A. 1 – 2 – 3 – 4 – 5 – 6 B. 1 – 3 – 2 – 5 – 4 – 6 C. 1 – 2 – 3 – 5 – 4 – 6 D. 1 – 3 – 5 – 2 – 4 – 6 E. None of the above Autor: Giancarlo Maldonado Cárdenas
Leia mais