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.

近年来，时空网络（spatial and temporal networks）领域的研究进展使得研究者能够更为精准地刻画包括城市交通网络在内的诸多现实世界系统。本文以统一视角审视其时空性能，研究现实世界时空网络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建模方法，该框架可捕捉诸多现实系统的共性属性：节点间的交互并非瞬时发生，且受其所处物理空间的约束。通过对三个真实城市交通系统开展数值实验，我们探究了节点失效对网络拓扑、时间与空间结构的影响。此外，我们还验证了该框架在另外三类网络场景中的广泛适用性。为识别时空系统行为特有的脆弱性来源，我们引入了两类中心性度量：其一用于评估节点作为结构桥梁的重要性，其二用于衡量节点在支撑网络内时空高效流运行时所扮演的关键角色。本研究揭示了时空系统脆弱性的复杂本质，表明当网络遭遇系统性攻击时，存在多种不同的失效模式。