2025-290

Consider a complex network subject to random failures and targeted attacks. Which of the following statements best characterizes network robustness?

1. Scale-free networks are equally robust against both random failures and targeted attacks due to their heavy-tailed degree distribution.
2. Random networks (Erdős–Rényi type) typically remain connected longer under random attacks than scale-free networks with the same average degree.
3. The robustness of a network is maximized when the degree distribution follows a power law with exponent close to 5.
4. In scale-free networks, robustness to random node removal arises because most nodes have low degree, while vulnerability to targeted attacks results from dependence on high-degree hubs.
5. None of the above.

Original idea by: Yan Prada Moro