2022-175

The sequence of images below shows some steps for generating the network based on the Barabási-Albert model. Consider that starting with \( m_0 \) nodes, the empty circles mark the newly added node to the network in each timestep \( t \), and the new node's number of links is \( m = 2 \).

Analyze the following statements about the network:

1. Choosing which node will be connected uses the preferential attachment criteria.

2. After \( t \) timesteps, this model generates a network with \( t + m_0 \) nodes.

3. The degree distribution of this network follows the Poisson distribution.

4. This network has the scale-free property.

5. The diameter of this network with N nodes can be estimated by the equation \( D \sim \frac{\ln N}{\ln \ln N} \)

Select the correct alternative:

1. All statements are correct. 
2. Only statements 1, 2, and 3 are correct.  
3. Only statements 3, 4, and 5 are correct.
4. Only statements 1, 2, 4, and 5 are correct. 
5. None of the above.

Original idea by: Rubens de Castro Pereira