Evaluating the robustness of temporal networks considering spatiality of connections

Network robustness has been a hot research area of studies on complex networks. Finding out the explanations behind the phenomena that networked systems can still function efficiently after some structural damages or the malfunction of certain nodes is meaningful to both the design of solid systems and the defend against failures. It is still indistinct what kind of resilience networked systems which change their topological structures incessantly over time might have. Nevertheless, earlier studies have frequently overlooked to consider the temporal characteristics which in many real scenarios are of great concern, or have considered only the temporality without spatiality which is not reasonable in the real world case. In this paper, we first take the spatiality of connections and communications between nodes, except for the temporal ordering of connection events which has solely been noticed by previous studies, into consideration for measuring and assessing the robustness of the temporal network. We propose a novel temporal efficiency metric, and correspondingly, develop a new temporal robustness evaluation method for temporal network models. The proposed metric and method show their validity through numerical simulations of three temporal network models and we give our evaluations and discussions.