Degree Correlations Question

Epidemiologists are studying the spreading of a disease through an interaction network. After collecting data, they find that the network's degree distribution follows a power law \(p_k \sim k^{-\gamma}\) with exponent \(\gamma = 2.5\), suggesting that a small number of highly connected individuals ("superspreaders") play a dominant role in transmission. The network has a minimum degree of \(k_{\text{min}} = 2\), meaning every user follows at least two others, and an average degree of \(\langle k \rangle = 8\). Structural analysis reveals a cutoff \(k_s = 64\), beyond which the simple-graph constraint begins to limit how hubs can connect to one another. Based on this information, which of the following alternatives is correct?

A) \(k_{\text{max}} = 120\), and the network presents structural assortativity because \(k_{s} < k_{\text{max}}\).

B) \(k_{\text{max}} = 64\), and the network does not present structural disassortativity because \(\gamma > 2\).

C) \(k_{\text{max}} = 128\), and the network presents structural disassortativity because \(k_{s} < k_{\text{max}}\).

D) \(k_{\text{max}} = 64\), and the network does not present structural disassortativity because \(k_{s}  \ge k_{\text{max}}\).

E) None of the above

Original idea by: Carlos Trindade