MathJax


Sunday, May 10, 2026

2026-350

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 \( k_{min} = 2\), meaning every user follows at least two others, and an average degree \( \langle k \rangle = 8\). 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?

  1. \(k_{max} = 128\), and the network presents structural assortativity because \(k_s < k_{max}\).
  2. \(k_{max} = 64\), and the network does not present structural disassortativity because \(\gamma > 2\).
  3. \(k_{max} = 128\), and the network presents structural disassortativity because \(k_s < k_{max}\).
  4. \(k_{max} = 64\), and the network does not present structural disassortativity because \(k_s \geq k_{max}\).
  5. None of the above

Original idea by: Carlos Trindade

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