Trip Centrality: walking on a temporal multiplex with non-instantaneous link travel time

Silvia Zaoli,Piero Mazzarisi,Fabrizio Lillo

doi:10.1038/s41598-019-47115-6

Abstract

In complex networks, centrality metrics quantify the connectivity of nodes and identify the most important ones in the transmission of signals. In many real world networks, especially in transportation systems, links are dynamic, i.e. their presence depends on time, and travelling between two nodes requires a non-vanishing time. Additionally, many networks are structured on several layers, representing, e.g., different transportation modes or service providers. Temporal generalisations of centrality metrics based on walk-counting, like Katz centrality, exist, however they do not account for non-zero link travel times and for the multiplex structure. We propose a generalisation of Katz centrality, termed Trip Centrality, counting only the walks that can be travelled according to the network temporal structure, i.e. “trips”, while also differentiating the contributions of inter- and intra-layer walks to centrality. We show an application to the US air transport system, specifically computing airports’ centrality losses due to delays in the flight network.

Highlights

Centrality metrics are a useful tool in network analysis to identify and rank the most important nodes or edges of a network
Walks and paths on a temporal network must respect the temporal ordering of links, and this should be accounted for by temporal centrality metrics
While metrics for static networks can be applied to temporal networks after aggregating over time, i.e. considering all links to be present at the same time, clearly this procedure overestimates the number of walks and paths that can be travelled on the network and neglects the effect of the temporal dynamics on the network’s connectivity[8,9]

Summary

Introduction

Centrality metrics are a useful tool in network analysis to identify and rank the most important nodes or edges of a network. Different generalisations of betweenness and closeness centrality have been proposed[10,11], as well as other temporal metrics based on shortest paths and distances[9,12,13]. Www.nature.com/scientificreports definition of time-respecting walks used therein does not apply to cases where it takes a non-zero time to travel through a link This is true for all transportation networks, for example, where the walk i → j → k can be travelled only if the arrival in j (disappearance of the i → j link) precedes the departure from j to k (appearance of the j → k link), and link duration should be accounted for. To our knowledge, none permit to weight differently inter- and intra-layer temporal walks

Methods

Results

Conclusion