2022-130

Consider the following statements about degree correlation in networks:

1. In neutral networks, nodes link to each other randomly, which in turn results in a lack of degree correlation for the linking pattern.
2. A perfectly assortative network is always a complete graph.
3. The correlation exponent can help determine the type of the network. When the correlation exponent is positive, we may say the network is assortative.
4. In assortative networks, nodes tend to link to nodes of similar degree. In other words, hubs tend to connect with hubs, and small-degree nodes tend to connect with small-degree nodes.
5. Degree correlations for directed networks are defined by two coefficients: \( r_{in,out} \) and \( r_{out,in} \).

Select the alternative that lists the correct statements:

1. I, II, and V are correct.
2. Only V is correct.
3. II, III, and IV are correct.
4. I, II, III, and IV are correct.
5. None of the above.

Original idea by: Heitor Mattosinho