title: Spatio-temporal networks: reachability, centrality and robustness.
abstract: 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.
authors.affiliation: School of Computer Science, University of Birmingham, Edgbaston B15 2TT, UK; Department of Geography, University College London, London WC1E 6BT, UK.
authors.forename: Matthew J
authors.identifier: 0000-0003-0892-0998
authors.initials: MJ
authors.lastname: Williams
authors.affiliation: Department of Geography, University College London, London WC1E 6BT, UK; School of Computer Science, University of Birmingham, Edgbaston B15 2TT, UK.
authors.forename: Mirco
authors.initials: M
authors.lastname: Musolesi
keywords: complex systems; data science; network robustness; transport systems; urban analytics; urban data science