  Tipping points occur in diverse systems in various disciplines such as
ecology, climate science, economy or engineering. Tipping points are critical
thresholds in system parameters or state variables at which a tiny perturbation
can lead to a qualitative change of the system. Many systems with tipping
points can be modeled as networks of coupled multistable subsystems, e.g.
coupled patches of vegetation, connected lakes, interacting climate tipping
elements or multiscale infrastructure systems. In such networks, tipping events
in one subsystem are able to induce tipping cascades via domino effects. Here,
we investigate the effects of network topology on the occurrence of such
cascades. Numerical cascade simulations with a conceptual dynamical model for
tipping points are conducted on Erd\H{o}s-R\'enyi, Watts-Strogatz and
Barab\'asi-Albert networks. Additionally, we generate more realistic networks
using data from moisture-recycling simulations of the Amazon rainforest and
compare the results to those obtained for the model networks. We furthermore
use a directed configuration model and a stochastic block model which preserve
certain topological properties of the Amazon network to understand which of
these properties are responsible for its increased vulnerability. We find that
clustering and spatial organization increase the vulnerability of networks and
can lead to tipping of the whole network. These results could be useful to
evaluate which systems are vulnerable or robust due to their network topology
and might help to design or manage systems accordingly.
