Network dismantling by physical damage

It is well-understood that the network structure of complex systems affects their robustness; the role played by the shape of spatially embedded networks, however, is less explored. Here, we study the robustness of networks where links are physical objects or physically transfer some quantity, hence the links can be disrupted at any point along their trajectory. To model physical damage, we tile each network with boxes and we sequentially damage these boxes, removing any link from the network that intersects a damaged tile. Using model and empirical networks, we systematically explore how the layout and the structure of networks jointly affect the resulting percolation transition. For example, we analytically and numerically show that randomly damaging a vanishing fraction of tiles is enough to destroy large-scale connectivity in randomly embedded networks. This demonstrates that the presence of long-range links makes networks extremely vulnerable to physical damage. Our work contributes to the emergent theory of physical networks.