Spatio-temporal networks: reachability, centrality and robustness

TL;DR

This paper investigates the resilience of real-world spatio-temporal networks, such as urban transport, to errors and attacks, by modeling paths that consider space and time, and introduces new centrality measures to identify vulnerabilities.

Contribution

It presents a unified model for spatio-temporal paths, applies it to urban transport networks, and develops centrality measures to assess node importance and network fragility.

Findings

Node failures significantly disrupt network structure and flow.

The framework applies to various network types beyond transport.

Different attack strategies reveal diverse failure modes.

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.