2022-163

Consider a network containing $N$ nodes and with a minimum degree $k_{min}$. If the degree distribution $p_k$ follows a power law $p_k\sim k^{-\gamma }$, where the exponent $\gamma$ is the degree exponent, what is correct to affirm:

A. The average distance $⟨d⟩$ between two nodes is proportional to $\ln N$ for $2<\gamma \le 3$.

B. The first moment $⟨k⟩$ diverges for $2<\gamma \le 3$.

C. The second moment $⟨k^2⟩$ diverges for $\gamma >3$.

D. The expected size of the largest hub is $k_{min}{N}^{\frac{1}{\gamma -1}}$.

E. None of the above.

Original idea by: Marcelo Silva