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

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.

New centrality and causality metrics assessing air traffic network interactions

“…It was also shown that when these indicators increase the rankings in the scheduled and realised network tend to be more different. This remains true also when the cancelled flights are excluded from the analysis (see supplementary figure S3 of [8]), proving that the effect of missed connection is recognised. Differently from Katz centrality, in Trip centrality the parameter α weighting the use of one link can be chosen without constraints, because all counted walks are made of a finite number of jumps (at most one per time-frame).…”

“…Differently from Katz centrality, in Trip centrality the parameter α weighting the use of one link can be chosen without constraints, because all counted walks are made of a finite number of jumps (at most one per time-frame). For values of α large enough, say α > 0.05, the ranking according to Trip centrality differs significantly from the ones obtained by Katz or degree centrality (see [8]), as such values of the parameter give importance to walks longer than one, on whose counting Trip Centrality differs.…”

“…This means that centrality losses tend to be larger when delays are larger. In [8] it was shown that the average centrality loss is also increasing with two other delay-related indicators: the average fraction of delayed flights in an airport and the average delay of all flights on that day. It was also shown that when these indicators increase the rankings in the scheduled and realised network tend to be more different.…”

Betweenness centrality for temporal multiplexes

“…We argue that both the temporal and multiplex structure must be accounted for when computing centrality metrics, as they both have a comparable influence on the flow of information 13 . The temporal structure implies that information (e.g.…”

“…minimum connecting time between two flights). These characteristics have rarely been considered in previous works on temporal networks (though see 13 – 15 ).…”