Data from: Spatio-temporal networks: reachability, centrality, and robustness

Recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems such as urban transport networks. In this paper, we study the response of real-world spatio-temporal networks to random error and systematic attack, taking a unified view of their spatial and temporal performance. We propose a model of spatio-temporal paths in time-varying spatially embedded networks which captures the property that, as in many real-world systems, interaction between nodes is non-instantaneous and governed by the space in which they are embedded. Through numerical experiments on three real-world urban transport systems, we study the effect of node failure on a network's topological, temporal, and spatial structure. We also demonstrate the broader applicability of this framework to three other classes of network. 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 spatio-temporally efficient flows through the network. 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 attacks.

时空网络（spatio-temporal networks）领域的近期进展，使得研究者能够更为精准地刻画诸多现实世界系统，例如城市交通网络。本文以统一视角聚焦真实世界时空网络的时空性能，研究其在随机故障与系统性攻击下的响应特性。我们提出一种面向时变空间嵌入网络的时空路径模型，该模型可捕捉诸多现实系统的共性特征：节点间的交互并非瞬时发生，而是受其所处空间的约束所支配。通过在三个真实城市交通系统上开展数值实验，我们探究了节点失效对网络拓扑结构、时序特性与空间特性的影响。此外，我们还验证了该研究框架在其他三类网络场景中的广泛适用性。为识别时空系统行为所特有的脆弱性来源，我们提出了中心性指标，用于评估节点作为结构桥梁的重要性，以及其在支撑网络时空高效流传输中所扮演的角色。这一研究揭示了时空系统脆弱性的复杂本质，表明当网络遭受系统性攻击时，存在多种不同的失效模式。