YuriPadua-graph-algorithms-2023-1

You are a data scientist analyzing the habit network of a community. The network includes good habits (such as Physical Activity, Balanced Diet, Family Principles, etc.), bad habits (such as Smoking, Alcohol, Drugs, Pornography, etc.) and other factors that may influence these habits (such as Positive Friends, Friends with Bad Habits, Internet, etc.). After analyzing the network, you find that the average number of connections per node is 4 and the average of the square of the number of connections per node is 20.  1 - Based on these values, is it likely that the network has a large connected component? 2- Also, based on the graph in the image below (and considering that it is just a snapshot of the community's network), which behaviors should be abolished to separate the bad habits from the good habits in the network? Yes, because the average of the square of the number of connections per node is greater than twice the average number

You are investigating a network that follows the Bianconi-Barabási Model. Consider two nodes, node C with a degree of 8 and a fitness of 0.3, and node D with a degree of 10 and a fitness of 0.7. What is the relative likelihood of a new node connecting to node D compared to node C? Approximately 1.75 times more likely Approximately 2.92 times more likely Approximately 3.33 times more likely Approximately 4.12 times more likely None of the above Hint: In the Bianconi-Barabási Model, the likelihood of a new node connecting to an existing one is proportional to the product of the node's degree and its fitness. The relative probability can then be calculated as the ratio of the products of the degree and fitness of node D to that of node C. This will give you the factor by which a new node is more likely to connect to node D compared to node C. Original idea by: Yuri Souza Padua

Consider a growing network following the Barabási-Albert model. You don't know the initial number of links, but you do know that at time step t = 10,000, a node that joined at step t_i = 1,500 has a degree of k ≈ 10. What could be the degree of a node that joined this same network at time step t_j = 3,000? 7 14 30 120 None of the above Original idea by: Yuri Souza Padua

Which of the following statements is false about random networks and scale-free networks? The degree distribution in a random network follows a Poisson distribution, while in a scale-free network it follows a power law distribution. The random network always has a lower clustering coefficient than the scale-free network. In a scale-free network, most nodes have a low degree, while in a random network, most nodes have a high degree. The largest degree in a random network is always smaller than the largest degree in a scale-free network. None of the above. Original idea by: Yuri Souza Padua PS: Dear professor, I am writing to kindly remind you about my last quiz queston that we talked by email. 😅 Just to help: Link to the last question . I think everything is correct, just the "trick question" (none the above) Thank you very much in advance!  😁 😁 😁 😁 (0.1 in the final grade can make a big difference)

  Considering the network above, which of the options below does not describe a sequence of nodes visited by the BFS algorithm? A) EBFHDACGI B) GDHAEIBFC C) CBFAEIDHG D) ABDCEGFHI E) Nenhuma das alternativas Original idea by: Yuri Souza Padua

  What is the main difference between a node/vertex and an edge/links in a network; and how does this difference contribute to the study of complex networks? A) Vertex and edges are interchangeable terms that can be used to describe any component of a network. This flexibility allows us to study the structure and behavior of complex networks in a variety of contexts and domains. B) Nodes are the individual components of a network, while edges represent the connections between them. This distinction is important because it allows us to study the structure and properties of complex networks at different levels of granularity, from the individual nodes to the network as a whole. C) Nodes are the connections between the individual components of a network, while links represent the individual components themselves. This distinction is important because it allows us to study the flow of information or resources within a network and how this affe