João Gondim - MO412

The image below shows the probability that a node belongs to the giant component of an Erdos–Rényi network, estimated as the ratio between the size of the largest connected component and the number of the remaining nodes after the removal of a fraction f of nodes, with the red vertical line representing the breakdown threshold for the created network. Which of the following alternatives best approximates the number of nodes (N) of the network and the probability for edge creation (p), respectively: A) N = 750 and p = 0.02 B) N = 1000 and p = 0.005 C) N = 500 and p = 0.015 D) N = 1500 and p = 0.002 E) None of the above. Original idea by: João Medrado Gondim

Given the following image, corresponding to the average neighbors' degree of three different networks that have the same number of nodes and links, which alternative correctly matches the type of degree correlations and the hatch symbols? A) (  , Neutral),           ( ,  Disassortative),  ( , Assortative) B) (  , Disassortative), ( ,  Neutral),            ( , Assortative) C) (  , Assortative),      ( ,  Disassortative), ( , Neutral) D) (  , Assortative),      ( ,  Neutral),            ( , Disassortative) E) None of the above. Original idea by: João Medrado Gondim

A research group is creating a new social media platform and wants to model its growth using the Barabási–Albert model. They start with a small group of well-connected users. According to the principles of this model, which of the following strategies will most likely lead to the formation of a scale-free network, characteristic of real-world social platforms? A) Each new user connects to existing users at random, with equal probability, regardless of how many followers those users already have. B) Each new user connects to existing users with a probability proportional to their current number of followers (popular users are more likely to attract new followers). C) Each new user connects only to the newest users who joined in the previous step, ensuring recent users stay active and visible. D) Restrict new users to connecting only with users in their immediate geographical surroundings to create localized clusters. E) None of the above. Original idea by: João Medrado Gondim

 Observing the images below: Mark the option that correctly matches the shapes of the nodes in Scale-Free graph and the shapes of the data points in Log-log plot from the created graph: A) ( ,  ), ( ,  ), ( ,  ) B) ( ,  ), ( , ), ( , ) C) ( ,  ), ( ,  ), ( ,  ) D) ( , ), ( ,  ), ( ,  ) B) None of the above. Original idea by: João   Medrado Gondim

 Given the following plot for the theoretical binomial distribution of degrees in a random graph created with 250 nodes, what was the probability (rounded up) of edge creation used? A) 0.01 B) 0.05 C) 0.1 D) 0.2 E) None of the above. Original idea by: João   Medrado Gondim

In a bomb defusing training, were each explosive is wired to another in different ways, the instruction given by the trainers is to use Breadth-First-Search to defuse each bomb in such way that the next defused explosive is neighboring the current one and that the main explosive is defused at last. Facing the following wired explosives structure, which node should be the starting one in order to leave the main explosive (painted in red) to be the last one defused? A) Node 0 B) Nodes 3 and 2 C) Node 3 D) Node 5 E) None of the above. Original idea by: João   Medrado Gondim