Quiz question 3 (31/03/2023) - Random Networks

Considering the Gilbert model $G(N,p)$, what statements from the following options are correct?

I. The most expected number of links from a network generated with this model is $\frac{pN(N-1)}{2}$

II. If $p>\frac{lnN}{N}$ this model always generates a fully connected network with 100% certainty

III. This model produces a degree distribution that follows a Poisson distribution, which can be approximated by binomial distribution when $N$ is very larger than $⟨k⟩$

IV. A complete network can be generated from this model assuming $p>0$, even if it is not likely

1. I and III
2. II, III and IV
3. I, II and IV
4. I and IV
5. none of above

Original idea by: Anderson Nogueira Cotrim