Random Networks - Quiz 3
Consider the following networks and their characteristics:
Evaluate the following sentences to further mark them as true (T) or false (F):
- The Alpha Graph is considered a random network because its satisfies the small world property.
- For the Alpha Graph, the local clustering coefficient is independent of the network size N.
- For the Beta Graph, the size of the largest cluster N_G/N can be considered to be zero (0).
- For the Sigma Graph, the local clustering coefficient is dependent of the node degree because it satisfies the small world property.
Choose the correct answer:
A) T, F, T, F
B) F, T, T, T
C) F, T, T, F
D) F, T, F, T
E) None of the above
Original idea by: Gabriela Caspa
Nice question, but it raises a number of issues in my head. First of all, what is p? Since we talked about random networks this week, I assume you are using p to denote the parameter in the G(N, p)model. However, no explicit association between Alpha, Beta, or Sigma with this model is mentioned. Other than that, my tendency is to say that Statement 1 is wrong, because not all small world networks are random. However, what is a small world network? That is only defined for families of networks. Same remark applies to Statement 4. Statement 2 also poses a challenge, since dependency on N only applies to network families. Finally, Statement 3 seems false, but obviously so; did you mean to say that the relative size (not the size itself) of the large cluster is zero?
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