2022-134

Not all networks display the expected behavior of hubs linking to other hubs. They do so on some networks, but not on others. These patterns manifest a common feature, degree correlations, which allow us to detect the presence or lack of correlations in a real network. Analyze the degree correlation function knn(k) which expresses the average degree of the neighbors of all degree-k-nodes, and, then, classify the sentences below as true or false.

                                                     

 Inspired by http://networksciencebook.com/chapter/7measuring-degree; purple: knn(k), horizontal line: prediction, green: fit to knn(k)=akμ

1) In a disassortative network hubs prefer to link to high-degree nodes and the best representation for this network is Image A.

2) In a neutral network, there is a lack of degree correlations. Plotting knn(k) in function of k results in a horizontal line as shown in Image C, which demonstrates that the average degree of a node's neighbors is independent of the node's degree k.

3) Image A is a good representation of an assortative network where hubs tend to connect to other hubs. Thus, the higher the degree k of a node, the higher the average degree of its nearest neighbors.

4) In a disassortative network, as shown in Image B, the degree correlation function decreases with k, indicating hubs prefer to link to low-degree nodes.

Now select the option that contains exactly the true statements:

    A. Only 1 and 3

    B. Only 1, 2 and 3

    C. Only 2, 3 and 4

    D. All the statements

    E. None of the above

Original idea by: Márcia Jacobina