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
