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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

Calculus

What is the volume generated by rotating the region bounded by the curves y=x^2 and y=4 around the x-axis?


a)2π

b) 4π

c) 8π

d) 16π

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

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