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

  1. Joao MeidanisApril 12, 2026 at 12:56 PM

    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.

    ReplyDelete

Post a Comment

Popular posts from this blog

Submission 1

Image
A company is looking for people that have really close acquaintances with its three interviewers. Therefore, candidates whose network of acquaintaces average length from each interviewer to the job applicant is closer to 1 will have the most chances to get the job. Given the network of acquaintances of each of the following three applicants, indicate which of the following statements are true (T) or False (F). Robert: John: Casey: Casey has the most chances of getting the job. For Robert’s network of aquaintances: If the clustering coeficient of Taylor were higher while maintaining the same degree, then Robert would have more chances of being hired. The chances of Casey getting the job does not depends on knowing Micah, Mary or Harry. John has the least chances of getting the job. F F T T T T T F T F T F T F F F None of the above
Read more