Algoritmos em Grafos - Alexandre

 In a social platform, you can be friends with people from many different countries. Suppose you pick two random people with entirely different profiles, what can you expect from the number of steps (friend-of-a-friend connections) that would take for these two to connect? Assume the social platform follows a scale-free network. a) There isn't a feasible number of steps connecting two people, since most people in the network are isolated. b) It could take hundreds of steps, since there isn't anyone in the network that knows a lot of people. c) It will take a small number of steps, as eventually someone will know a lot of people. d) It will take an equal number of steps, as everyone knows the same amount of people. e) None of the above. Original idea by: Alexandre Petrachini

A fungal colony, whose hyphae form a network called the mycelium, started growing on a piece of bread left unattended. The colony started small, at an initial number of spores N = 5000 . It is known for this species to create hyphae (links) at a probability that depends on time, described by the function below: Where t is time in days. Assume that the number of spores remains constant over time and that it follows an Erdős-Rényi network . Give n two different intervals: A day has passed Three days have passed Assign the correct alternatives in respect to attributes about the mycelium growth. a) As one day passes, the network is subcritical, and by three days, it’s supercritical. b) As one day passes, the network is subcritical, and by three days, it remains subcritical. c) As one day passes, the network is critical, and by three days, it’s supercritical. d) As one day passes, the network is already supercritical. e) None of the above Original idea by: Alexandre Petrachini