While recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems, existing models do not capture the combined constraint that space and time impose on the relationships and interactions present in a spatio-temporal complex network. This has important consequences, often resulting in an over-simplification of the resilience of a system and obscuring the network’s true structure. In this paper, we study the response of spatio-temporal complex networks to random error and systematic attack. Firstly, we propose a model of spatio-temporal paths in time-varying spatially embedded networks. This model captures the property that, in many real-world systems, interaction between nodes is non-instantaneous and governed by the space in which they are embedded. Secondly, using numerical experiments on four empirical examples of such systems, we study the effect of node failure on a network’s topological, temporal, and spatial structure. We find that networks exhibit divergent behaviour with respect to random error and systematic attack. Finally, to identify weaknesses specific to the behaviour of a spatio-temporal system, we introduce centrality measures that evaluate the importance of a node as a structural bridge and its role in supporting temporally efficient flow through the network. We explore the disruption to each system caused by attack strategies based on each of these centrality measures. This exposes the complex nature of fragility in a spatio-temporal system, showing that there is a variety of failure modes when a network is subject to systematic attack.
Paper: http://arxiv.org/abs/1506.00627