  Cascading failures constitute an important vulnerability of interconnected
systems. Here we focus on the study of such failures on networks in which the
connectivity of nodes is constrained by geographical distance. Specifically, we
use random geometric graphs as representative examples of such spatial
networks, and study the properties of cascading failures on them in the
presence of distributed flow. The key finding of this study is that the process
of cascading failures is non-self-averaging on spatial networks, and thus,
aggregate inferences made from analyzing an ensemble of such networks lead to
incorrect conclusions when applied to a single network, no matter how large the
network is. We demonstrate that this lack of self-averaging disappears with the
introduction of a small fraction of long-range links into the network. We
simulate the well studied preemptive node removal strategy for cascade
mitigation and show that it is largely ineffective in the case of spatial
networks. We introduce an altruistic strategy designed to limit the loss of
network nodes in the event of a cascade triggering failure and show that it
performs better than the preemptive strategy. Finally, we consider a real-world
spatial network viz. a European power transmission network and validate that
our findings from the study of random geometric graphs are also borne out by
simulations of cascading failures on the empirical network.
