2021-060

Scale-free networks are networks whose degree distribution follows a power law, that is, the probability $p_k$ of a node having degree $k$ is proportional to $k^{-\gamma }$ for a certain constant $\gamma$.

About their degree distributions and properties, which of the following statements is not correct:

1. The scale-free property comes from a finite first moment and an infinite second moment, and for $\gamma <3$ this remains unchanged;
2. Unlike random networks, scale-free networks have a 'tail' in their degree distribution, which supports the presence of hubs;
3. Most real scale-free networks are found in the regime $2<\gamma <3$;
4. Networks with $\gamma <2$ are not graphical. In this regime, the largest hub will tend to have degree greater than the number of nodes $N$, when $N$ grows;
5. None of the above.

Original idea by: Matheus Cerqueira