Random Graph question

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.


Given 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

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