2025-297

In the context of community detection in complex networks, which of the following statements most accurately describes the "resolution limit" inherent in modularity (M) maximization?

A. The resolution limit refers to the inability of the Girvan-Newman algorithm to effciently recalculate edge betweenness in large-scale networks, thus preventing its practical application.

B. The resolution limit refers exclusively to divisive methods, indicating that iterative edge removal always fragments the network into individual components before a maximum of modularity can be achieved.

C. The resolution limit is an artifact of the modularity formula, favoring the merging of small communities, even if they are strongly internally connected (such as cliques), into larger communities, to maximize the overall M.

D. The resolution limitation states that modularity (M) will always assign a negative value to any partition that is not a perfect clique, making it difficult to identify dense but incomplete community structures.

E. None of the above

Original idea by: Juan Jose Rodriguez Rodriguez

2025-296

Consider the network below, where each edge is labeled with its edge betweenness centrality.

After applying a divisive community detection algorithm based on edge betweenness, the first split of the network yields the two communities shown below:

Using only this two-community partition, what is the modularity of this division? Round your answer to two decimal places.

1. 0.16
2. 0.20
3. 0.24
4. 0.28
5. None of the above

Original idea by: Luiza Barguil

2025-295

Given the following graph and the respective dendrogram, mark the correct alternative.

a) All division lines produce some weak community.

b) Division line 3 produces 2 weak communities and 2 strong communities.

c) Division line 1 produces one strong and one weak community. 

d) Division line 2 produces at least 2 strong communities.

e) None of the above.

 

 Original idea  by: Giorgio Rossa

2025-293

The Galactic Federation maintains an interplanetary communication network connecting \(N = 1000\) colonies through hyperspace routes. Scientists from the Central Observatory have estimated:

\(\langle k \rangle = 4\), \(\langle k^2 \rangle = 100\)

During a cosmic particle storm, 800 colonies lost communication with the network.  Does the Galactic Federation’s network still maintain a giant component or has it collapsed?

1. The network remains connected, since the critical threshold is \(f_c = 0.96\).
2. The network has collapsed, since the critical threshold is \(f_c = 0.96\).
3. Communication has collapsed, since the critical threshold is \(f_c = 0.67\).
4. Communication is still possible, since the critical threshold is \(f_c = 0.67\).
5. None of the above

Original idea by: Aline Azevedo

2025-292

You are the team leader in your firm’s Cybersecurity Department, responsible for maintaining four critical corporate networks: AegisNet, MercuryGrid, HeliosCloud and VanguardLink 

Early one morning, you notice that several nodes across all four networks have been unexpectedly shut down. A quick inspection of the system logs (graphically depicted below) reveals the exact sequence in which each node went offline. Your mission is to determine whether this incident represents a coordinated cyberattack targeting multiple systems simultaneously, or if it is merely the result of random hardware failures in aging equipment.

Time 0 : 

Time 1:  

Time 2: 

Based on the logs, your best assessment is:

A) It was an attack on all networks

B) It was an attack only on VanguardLink

C) It was an attack only on AegisNet and VanguardLink

D) It was an attack only on AegisNet, MercuryGrid, and VanguardLink

E) None of the above.

Original idea by: Carolina Albuquerque

2025-291

The image below shows the probability that a node belongs to the giant component of an Erdos–Rényi network, estimated as the ratio between the size of the largest connected component and the number of the remaining nodes after the removal of a fraction f of nodes, with the red vertical line representing the breakdown threshold for the created network.

Which of the following alternatives best approximates the number of nodes (N) of the network and the probability for edge creation (p), respectively:

A) N = 500 and p = 0.015

B) N = 750 and p = 0.02

C) N = 1000 and p = 0.005

D) N = 1500 and p = 0.002
E) None of the above.

Original idea by: João Medrado Gondim

2025-290

Consider a complex network subject to random failures and targeted attacks. Which of the following statements best characterizes network robustness?

1. Scale-free networks are equally robust against both random failures and targeted attacks due to their heavy-tailed degree distribution.
2. Random networks (Erdős–Rényi type) typically remain connected longer under random attacks than scale-free networks with the same average degree.
3. The robustness of a network is maximized when the degree distribution follows a power law with exponent close to 5.
4. In scale-free networks, robustness to random node removal arises because most nodes have low degree, while vulnerability to targeted attacks results from dependence on high-degree hubs.
5. None of the above.

Original idea by: Yan Prada Moro