Question 6 - Scale-free Property

  With respect to the Scale-Free Property, given the following statements:

1. One of the key differences between scale-free networks and random networks is that hubs are forbidden in the random networks, but are expected in scale-free networks.
2. In the Anomalous Regime, all nodes are close and connect in the same central hub. Thus the degree of the biggest hub increases linearly with the network size (N), so the average path length depends on N.
3. Most real networks are present in the ultra-small world (Scale-free Regime) because their first and second moments are finite.
4. In the Random Regime, the probability \(P_k\) decays sufficiently fast to make the hubs smaller and less numerous, so the scale-free networks in this regime are more closer to the random networks, being hard to distinguish one from another.

  Which alternative contains all the correct statements?

1. I and IV are true.
2. II and III are true.
3. II and IV are true.
4. I and III are true.
5. None of the above.

  Original idea by: Pedro Henrique Di Francia Rosso