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
Considering the topic of Degree Correlations, analyze the assertions below:
I) Networks with vertices whose degrees are higher than the structural cutoff will exhibit structural assortativity, as the degree (k_s) becomes smaller than the maximum degree (k_max).
II) In a random network, the degree correlation is always positive, indicating a tendency for nodes with high degrees to connect to other nodes with high degrees.
III) Adding new nodes that connect hubs to low-degree nodes will never make the graph disassortative.
IV) In a scale-free network, the degree correlation is always negative, suggesting a preference for nodes with high degrees to connect to nodes with low degrees.
Select the correct one:
a) Only IV
b) I, II
c) I, III
d)II, IV
e) None of above
Original idea by: João Marcos
You probably mean 'Adding new links' instead of 'Adding new nodes' in (III), right? It seems to me that none of the statements is true. Nevertheless, I think I prefer to have less questions of this type in the blog.
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