2021-026

Considering scale-free networks whose degree distribution follows a power law of the form $$p_k\sim k^{-\gamma },$$which of the alternatives below is correct:

Notation:

$k_{max}=$ maximum degree in the network

$N=$  number of nodes in the network

1. For $\gamma =2$: The second moment of the distribution is finite, thus in many ways the network behaves as a random network.
2. For $\gamma =3$: $k_{max}$ increases faster than $N$
3. For $\gamma <2$: The size of the biggest hub is $O(N)$
4. For $2<\gamma <3$: The average path length increases slower than logarithmically
5. None of the above.

Original idea by: Diego Moreira.