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

## TL;DR

This paper introduces Trip Centrality, a novel temporal multiplex centrality measure that accounts for non-zero travel times and multilayer network structures, demonstrated on the US air transport system.

## Contribution

It presents a new centrality metric that incorporates travel times and multiplex structures, extending previous walk-based centrality measures.

## Key findings

- Trip Centrality effectively captures delays' impact on airport importance.
- Application to US air transport shows significant centrality loss due to delays.
- Method can be generalized to other temporal multiplex networks.

## 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 paths 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.