Submission 2

Given a graph and its probability of a node degree \(k\):

For graph \(G \), \( P_k = 2k^{-2}\)

For graph \(G' \), \( P'_k = min(2k^{-2}, 1000)\)

and the following statements:

  1. \(G\) is a scale-free network with \(\gamma = 2\) and \( k_{min} = 2 \)
  2. \(G\) is a scale-free network with \(\gamma = 2\) and \( k_{min} = 1 \)
  3. For larger number of nodes, \(G'\) will not have a scale-free topology because its hubs will be limited by at maximum 1000 links.

Which statements are correct?
  1. Only II
  2. Both II and III
  3. Only I
  4. Both I and III
  5. None of the above

Original idea by: Giuliano Macedo.

Comments

Joao Meidanis said…
Interesting question, but it has a few issues. For instance, it does not specify the range of k in the P_k formulas. Apart from that, the sum of the probablitites does not seem to be 1, as it should be. With these issues, it is hard to assess the statements.
April 12, 2026 at 4:56 PM
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