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 \(p > \frac{ln N}{N}\) 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 \(\left\langle k \right\rangle\)

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