Consider the following partitions over the same graph:
Which alternative lists the partitions in ascending order of modularity ?
A) PA, PB, PC, PD
B) PD, PA, PB, PC
C) PB, PA, PD, PC
D) PA, PD, PB, PC
E) None of the above
Original idea by: Fernando de Facio Rossetti
Given a network with a defined community division, which has positive modularity, choose the correct alternative:
a) Applying a degree-preserving exchange where two inter-community edges are removed and two intra-community edges are created will increase the modularity.
b) Merging two different communities into one will increase the modularity.
c) Removing an edge between nodes in different communities will increase the modularity.
d) Adding an intra-community edge to the network will necessarily increase the modularity.
e) None of the above.
Original idea by: João Pedro Carolino Morais
Regarding the relationships among cliques, strong communities, and weak communities, which of the following statements is correct?
Original idea by: Giuliano Macedo.
Analyze the following statements about the Agglomerative (Ravasz) and Divisive (Girvan–Newman) hierarchical clustering algorithms, and determine whether each statement is True (T) or False (F):
1) The Agglomerative algorithm starts by treating each node in the network as an individual community and repeatedly merges the most similar communities until a stopping condition is reached. This stopping condition occurs when the density inside each community becomes maximal.
2) The Divisive algorithm follows a top-down strategy: it initially treats the entire network as a single community and progressively splits the network into smaller communities.
3) The result of the Agglomerative algorithm depends on the linkage criteria adopted (single, complete, or average linkage).
4) In the Girvan–Newman algorithm, communities are identified by iteratively removing links with high centrality, since these links are more likely to connect different communities.
5) In the Agglomerative hierarchical clustering, once two communities are merged, the algorithm may later separate them again if a stronger similarity pattern is detected.
Choose the correct alternative:
A) F-T-T-F-F
B) T-T-T-F-F
C) F-T-T-T-F
D) F-T-T-T-T
E) None of the above
Original idea by: Gabriela Caspa
Consider the following adjacency matrix of an undirected network
$$A=
\begin{bmatrix}
0&1&1&0&0&0&0\\
1&0&1&1&0&0&0\\
1&1&0&1&1&0&0\\
0&1&1&0&0&1&0\\
0&0&1&0&0&1&1\\
0&0&0&1&1&0&1\\
0&0&0&0&1&1&0
\end{bmatrix}$$
Consider the candidate communities
$$C_1=\{1,2,3,4\}
\qquad
C_2=\{5,6,7\}$$
Which statement is correct?
Original idea by: Antonio De Cesare Del Nero
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?
Consider the network below, where each edge is labeled with its edge betweenness centrality.
Using only this two-community partition, what is the modularity of this division? Round your answer to two decimal places.
Original idea by: Luiza Barguil
Given the following graph and the respective dendrogram, mark the correct alternative.
Original idea by: Giorgio Rossa
.png)
Imagine a Cayley Tree, constructed starting from a central node of degree \( k \). Each node at distance \( d \) from the central node has degree \( k \), until the nodes reachable at distance \( P \) that have degree one, as shown in figure above. Consider \( k+1 \) communities, with communities corresponding to the subtrees rooted at the children of the central node, and the central node by itself being a community. What is the modularity of this partition if \( k=3 \) and \( P=4 \)? Round it up to three decimal places.
Original idea by: Germán Darío Buitrago Salazar
Agglomerative hierarchical clustering can be applied to community detection in graphs. By using dendrograms, one can visualize the order in which nodes merged. This visualization enables the extraction of the underlying community organization.
Consider the following network. The fuchsia nodes are all part of a weak community.
Which option presents a modification that makes this community a strong one?
Original idea by: Christian Konishi
Considering the following undirected graph:
I. {1, 2, 3, 4} is a clique.
II. {1, 2, 3, 4} is a strong community.
III. {5, 6, 7} is a weak community.
IV. {5, 6, 7} is a clique.
V. {4, 5, 6, 7} is a weak community.
Which statements from the options above are correct?
Original idea by: Anderson Nogueira Cotrim
Applying a divisive algorithm on the network below, we obtain the following dendrogram:
 |
| Network |
 |
| Dendrogram |
Original idea by: Pedro Henrique Di Francia Rosso
The generalized modularity \( M \) of a network with \( L \) links partitioned into \( n_c \) communities can be calculated as:
$$M = \sum_{c=1}^{n_c}\left[\frac{L_c}{L}-\left(\frac{k_c}{2L}\right)^2\right]$$
where \( L_c \) is the total number of links within the community \( C_c \) and \( k_c \) is the total degree of the nodes in this community. Consider the following statements about \( M \):
What is correct to assert:
Original idea by: Marcelo Silva
Given the graph below, where each color represents a different
partition, calculate the modularity value. Round it up to two decimals
places.
Given the two networks (each with 3 different colored partitions) shown in the image below:
Which of the networks has the smallest modularity? What is this value, rounded to two decimal places?
Original idea by: Victor Antonio Menuzzo
Considering the following network and its partition in green and pink nodes:
The modularity \( M \) of a partition can be computed using:
$$ M = \sum_{c=1}^{n_c} \left[ \frac{L_c}{L} - \left( \frac{k_c}{2L} \right)^2 \right], $$
where \( n_c \) is the number of sets in the partition and, for each set \( S \), we denote by \( L_c \) the number of links connecting two nodes in the set \( S \), and by \( k_c \) the sum of all degrees of nodes in \( S \). What is the value of \( M \) for the partition depicted above (round to 2 decimal places)?
Original idea by: Tiago Almeida
Consider the two partitions below on the same network:
What are the modularities \( M_a \) and \( M_b \) of the partitions in pictures \( a \) and \( b \), respectively? Round the result to two decimal places, if necessary.
Original idea by: Bruno Almêda
The Hierarchical clustering algorithm helps to uncover the community structure of large real networks. Look at the Dendrogram below and choose the correct community organization, based on the red line cut:
Original idea by: Mauricio Schiezaro
Consider the following partitions over the same graph: Which alternative lists the partitions in ascending order of modularity ? A) PA, PB...
