I aim to demonstrate that scale-free networks exhibit greater resilience to random failures compared to random networks. Are there any analytical approaches available for proving this assertion? Intuitively, one could argue this using probability theory. Scale-free networks, owing to the existence of a few highly connected hub nodes, demonstrate a lower probability of random node failure. However, is there a rigorous analytical proof supporting this observation? In the context of a scale-free network, the probability of randomly selecting a node with a degree of k is calculated as follows:
$p(k)$ ~ $k^{-γ}$
Here, 2<γ<3