The overall function of networked systems is known to be closely related to their structural properties. This structure, i.e., the nodes and the links, might undergo random failures or suffer targeted attacks. Depending on how and where these events occur, the global properties of the network can be severely affected or remain almost unaltered. This roughly defines the concept of network robustness or resilience. In this work we focus our analysis on cascade-based attacks, i.e., those attacks that, by removing a single node, cause disproportionate damage to a large part of the system. Moreover, they evolve nonlocally, which means that the next removed node need not to be in contact with an already removed one. This contrasts, for example, with the typical propagation observed in disease spreading models such as the SIS or SIR. Classical models of cascade propagation assume that each node is assigned a load and a capacity: the former is the total number of shortest path crossing the nodes, used as a proxy for energy or information exchange, and the latter is the maximum load that each node can handle. Inspired by these models, we study for first time the the cascade propagation on multilayer networks. In particular, we address the question of the network robustness in function of several multilayer properties. By means of extensive numerical simulations, we find that this dynamics induces a discontinuous transition in the size of the largest connected component (LCC) (Fig. (a)) and we characterize it. We also compare the cascade propagation on multilayers and on their aggregated counterpart, reporting the similarities and differences among them. We observe that the aggregation process leads to a more robust network. Counter-intuitively to this result, however, we find that the number of layers composing the network plays an important role on the resilience of the global network: by adding more and more layers, the system turns out to be more robust (Fig. (b)). We are able to find an explanation to this phenomenon in terms of the topological quantities, such as the average path length of the resulting networks. Finally, we validate our findings in a real multilayer networks, the European Air Transport Network. The results of this work can be found in [1].
