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.