The paper by Reuven Cohen, Keren Erez, Daniel ben-Avraham, and Shlomo Havlin investigates the resilience of large networks, particularly the Internet, to random breakdowns. The connectivity of these networks follows a scale-free power-law distribution, \( P(k) = ck^{-\alpha} \). The authors use percolation theory to determine the critical fraction of nodes, \( p_c \), that need to be removed before the network disintegrates. They find that for \( \alpha \leq 3 \), the transition never occurs unless the network is finite. For the physical structure of the Internet (\( \alpha \approx 2.5 \)), they show that the network is remarkably robust, with \( p_c > 0.99 \). This means that even with a high fraction of nodes removed, a connected cluster spanning the entire Internet remains intact. The study provides a general criterion for the percolation critical threshold and demonstrates that the Internet's connectivity distribution allows for a high critical fraction, highlighting its resilience to random breakdowns.The paper by Reuven Cohen, Keren Erez, Daniel ben-Avraham, and Shlomo Havlin investigates the resilience of large networks, particularly the Internet, to random breakdowns. The connectivity of these networks follows a scale-free power-law distribution, \( P(k) = ck^{-\alpha} \). The authors use percolation theory to determine the critical fraction of nodes, \( p_c \), that need to be removed before the network disintegrates. They find that for \( \alpha \leq 3 \), the transition never occurs unless the network is finite. For the physical structure of the Internet (\( \alpha \approx 2.5 \)), they show that the network is remarkably robust, with \( p_c > 0.99 \). This means that even with a high fraction of nodes removed, a connected cluster spanning the entire Internet remains intact. The study provides a general criterion for the percolation critical threshold and demonstrates that the Internet's connectivity distribution allows for a high critical fraction, highlighting its resilience to random breakdowns.