Quiz question 06

Considering a scale-free network, where $$P(k) \sim k^{-\gamma}$$, and the critical threshold is given by:


$f_{c} = 1 - \frac{1}{\frac{\langle k^{2} \rangle}{\langle k \rangle} - 1}$


For a network where $2 < \gamma < 3$ and another where $\gamma > 3$, select the correct alternative.

a.) For $2 < \gamma < 3$, the second moment tends to zero and the value of $f_{c}$ tends to zero, indicating extreme fragility to random failures.

b.) For $\gamma > 3$, the second moment diverges, making the network completely robust. 

c.) For $2 < \gamma < 3$, the second moment diverges and $f_{c}$ tends to 1, indicating that the network can sustain the random removal of almost all nodes without losing the giant component.

d.) The value of $f_{c}$ is independent of the exponent $\gamma$, depending only on the network size $N$.

e) None of the above


Original idea by: Julia de Pietro Bigi

Comentários

  1. Joao Meidanis16 de maio de 2026 às 04:19

    Good question. It explores a very important aspect, so I thought that we surely would have questions like it. However, on browsing the blog, I didn't find any. Therefore, I'll take this one. Although a bit on the easy side, it is more difficult that one other question I found on the blog about the same theme (question 221).

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