Onion-like networks are both robust and resilient

Tolerant connectivity and flow transmission within capacity are crucial functions as network. However, the threats to malicious attacks based on intelligent node selections and rapid breakdown by cascading overload failures increase more and more with large blackout or congestion in our contemporary networking systems and societies. It has been recently suggested that interwoven loops protect the network functions from such damages, but it is a computationally intractable combinatorial problem to maximize a set of necessary nodes for loops in order to improve the robustness. We propose a new method by enhancing loops in the incremental growth for constructing onion-like networks with positive degree-degree correlations, whose topological structure has the optimal tolerance of connectivity against attacks in the state-of-the-art. Moreover, we find out that onion-like networks acquire adaptive capacity in resilience by a change of routing policy for flow control to absorb cascading overload failures triggered by a single attack and simultaneous multi-attacks. The inhibitory effect is stronger than that in scale-free networks found in many real systems.