Significance: Catastrophic events affecting technological or critical infrastructures are often originated by a cascading failure triggered by marginal perturbations, which are on their turn localized in one of the many interdependent graphs describing the systems. Understanding the robustness of these graphs is therefore of utmost importance for preventing crashes and/or for engineering more efficient and stalwart networked systems. Here we give a fresh framework by means of which cascading failures can be described in a very rich variety of dynamical models and/or topological network structures and which provides a series of quantitative answers able to predict the extent of the system’s failure.

The structural nestedness has important effects on the ecosystem’s robustness, stability, and species diversity, but quantitative analysis tools are still lacking at present. According to the competitive and mutually beneficial interactions among ecosystems species, we designed a quantitative analysis tool of nestedness on ecosystems metrics by mapping the ecosystems into symbolic networks and calculating the network’s competitive nestedness and mutualistic nestedness with an overlap metric, respectively. The results of the real system and network models show that in the competitive and mutualistic coupling network, the competitive nestedness reduces the biodiversity and robustness of the network, but the mutualistic nestedness has the opposite effect. Moreover, the larger the competitive nestedness in the pure structural case, the more unstable the ecological network tends to be. However, once the dynamical governing mechanism is considered, the competitive nestedness would make the system more stable. Our work enables us to understand more specifically the effects of the network structure on ecosystems and helps reveal the mechanism that how nestedness can be changed to increase network stability, species diversity, and robustness.