Consider an Erdos-Rényi network with $N=1000$ nodes and an average degree $\langle k \rangle = 8$. The network undergoes a targeted attack (removal of the highest-degree nodes). Approximately what fraction $f_A$ of nodes needs to be removed to fragment the network? Now, consider a scale-free network with same $N=1000$, $\langle k \rangle = 8$, and $\gamma=2.5$. If the fraction calculated for the Erdos-Rényi network is removed from the scale-free network in a targeted attack, what is expected to happen?
a) $f_A \approx 87.5\%$. The scale free network will also require $f_A \approx 87.5\%$ removal, as the $\langle k \rangle$ is the same.
b) $f_A \approx 12.5\%$. The scale free network will be completely fragmented long before the removal of $f_A$.
c) $f_A \approx 87.5\%$. The scale free network will be completely fragmented long before the removal of $f_A$.
d) $f_A \approx 12.5\%$. The scale free network will also require $f_A \approx 12.5\%$ removal, because the attack is targeted.
e) None of the above
Original idea by: Gabriel Sato
Boa questão, mas não creio que tenhamos estudado fórmulas para a fração crítica de redes aleatórias sob ataque. Sabemos só sob falhas aleatórias.
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