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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 can depend on the linkage criteria adopted, such as 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 hi...
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Degree correlation

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 Observe the following heatmaps which represent the correlation matrices   e ij   of two different networks (1) and (2). The bars represent the probability of connection between nodes with degrees  k 1  and  k 2 . Notice that some areas are highlighted in the figures, i.e. (u), (v), (w), and (x). Analyze the following statements regarding those areas and network characteristics to further mark them as True or False: 1) In network (1), the highlighted area (u) refers to the connection between a hub and a low-degree node, while the area (v) refers to the connection between two hubs. 2) In network (2), the highlighted area (w) refers to the connection between two low-degree nodes, while the area (x) refers to the connection between two hubs. 3) Network (1) represents a disassortative network since the probability of connection is stronger in the secondary diagonal. 4) Network (2) represents an assortative network. Also, if we applied degree-preserving randomiz...
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The Barabási-Albert Model

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 Consider a growing graph, as in the image, modeled using the Linearized Chord Diagram (left graph). A new node, labeled node 4, is added to the network (right graphs) and connects to existing nodes according to the model’s attachment probabilities p . Evaluate the following statements about the probability of connections formed by node 4 to further mark them as true (T) or false (F): I) Node 2 has the highest probability ( p ≈0.4) of being selected by node 4. II) Nodes 2 and 3 have the same probability ( p ≈0.3) of being selected by node 4. III) The probability that node 4 forms a self-loop is equal to the probability that it connects to node 3. IV) Node 1 has the highest probability of being selected by node 4.  Chose the correct alternative: A) F, T, F, T B) T, F, T, F C) F, F, T, T D) T, T, F, T E) None of the above 
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Scale-free Networks Quiz 5

Read the following statements to further mark them as true or false: A network under scale-free regime results into a hub and spoke topology and the average distance between nodes <d> remains mainly constant regardless of how much the network grows. The average distance <d> at the critical point of a scale-free network denominated as “alpha”, with k_{min} = 1 and k_{max} = 225 is 4,65. The “richer get richer” phenomenon eventually stops and stabilizes in a rapidly growing scale-free network where <k^{2}> reaches a mathematical ceiling.  Choose the correct answer: A) F, T, T B) F, T, F C) T, F, T D) F, T, T E) None of the above 
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Random Networks - Quiz 3

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 Consider the following networks and their characteristics:   Evaluate the following sentences to further mark them as true (T) or false (F): The Alpha Graph is considered a random network because its satisfies the small world property. For the Alpha Graph, the local clustering coefficient is independent of the network size N. For the Beta Graph, the size of the largest cluster N_G/N can be considered to be zero (0).    For the Sigma Graph, the local clustering coefficient is dependent of the node degree because it satisfies the small world property.  Choose the correct answer: A) T, F, T, F B) F, T, T, T C)  F, T, T, F D) F, T, F, T E) None of the above     Original idea by: Gabriela Caspa
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Graph Theory - Question 1

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 Considering the following two undirected Graphs and three Degree Distributions:   Based on the previous figure, evaluate the following sentences to further mark them as true (T) or false (F): Graph (1) matches the Degree Distribution X. Graph (2) matches the Degree Distribution Y. The maximum degree of Graph (1) is greater than that of Graph (2). The diameter of Graph (2) is greater than that of Graph (1). Chose the correct alternative: A) F, T, F, T B) T, F, T, F C) F, T, T, F D) T, T, F, T E) None of the above   Original idea by: Gabriela Caspa
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