Generalized Network Dismantling

I a hyper-connected world, systemic instability, based on cascading effects, can seriously undermine the functionality of networks (1). The quick global spread of rumors and fake news may be seen as a recent example (2), while the spread of epidemics is a problem that has been around much longer (3–6). It is well-known that the network structure, for example the exponent characterizing scale-free networks, is of particular importance for the controllability of cascading effects (7). Note that, for certain scaling exponents of scale-free network, the variance or mean value of relevant quantities may not be welldefined, which means that unpredictable or uncontrollable behavior may result. For example, it might be impossible to contain epidemic spreading processes. Similar circumstances may also make it impossible to contain the spread of computer viruses or misinformation—a problem that is not only relevant for the quick increase of cyberthreats, but may also undermine the functionality of markets, societal or political institutions.