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