networked (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

Taking into consideration the directed graph below and a Strong Connected Components context where the first DFS follows an order of [f,g,h,i,j,k,a,b,c,d,e] if possible, choose the most appropriate alternative: a) This graph has 5 SCCs, the smallest of which is formed by 'k' alone. b) The largest SCC (with the greatest number of nodes) is precisely the first SCC found. c) More than half of the SCCs found have 3 nodes. d) This graph has an even number of SCCs and not all the numbers of nodes in each component are prime numbers. e) None of the above.  Original idea by: João Marcos

What is the volume generated by rotating the region bounded by the curves y=x^2 and y=4 around the x-axis? a)2 π b) 4 π c) 8 π d) 16 π e) None of above Original idea by: João Marcos

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

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

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