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 \( \gamma \lt 3 \) 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 \( 2 \lt \gamma \lt 3 \);
4. Networks with \( \gamma \lt 2 \) 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