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Mostrando postagens de março, 2023

Communities

Analyse the graph below and evaluate the following statements: I - The modularity value for this graph is approximately 0.48. II - Removing nodes 15, 6, and 8 is not expected to significantly impact the modularity: it will increase by only about a hundredth compared to the modularity of the original network. III - Introducing a new green node that connects to nodes 3, 5, and 6 increases the modularity to approximately 0.61. IV - Increasing the modularity might cause the green nodes to transition into lilac or orange. Choose an option with only correct statements: a) I, II and III b) II, III and IV c) II and IV d) I, II and IV e) None of above Original idea by: João Marcos
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Random Graphs

Consider an Erdős-Rényi random graph with N = 1200 nodes. If the average degree of the graph is 50, what is the variance of the degree distribution? a) 49.95 b) 7.78 c) 47.95 d) 6.92 e) None of above Original idea by: João Marcos
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Graph Theory II

Analyse the following graph: Choose the truth statement: A) Both node D and node E have the same clustering coefficient. B) Node F currently has a clustering coefficient of zero, however if we establish a connection between node F and node A, it could potentially become the node with the highest clustering coefficient. C) This graph can be classified as a disconnected graph since not all nodes connect with each other. D) The node C has the highest clustering coefficient. E) None of above Original idea by: João Marcos
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Graph Theory

Given the graph in the figure below, evaluate the assertions: I) There are two paths from router 'A' to router 'H' that are identical in maximum speeds and same path lenght. II) The average degree of this graph is 3.25. III) 32.5% of the nodes have a degree of 3. IV) The fastest path between router A and router G has a bandwidth capacity of 100 Mbps. V) By constructing the Adjacency Matrix, it would be noticed that it is not symmetric. Choose the true statements: A) I, IV and V B) II, and IV C) II,III and IV D) III and IV E ) None of above
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