A Centrality Measure of European Air Traffic

Abstract

A centrality measure is a real valued function that aims to identify the importance of nodes in a graph. The Markov chain and spacey random walk are both discrete stochastic processes that can be used to defi?ne a centrality measure. The stationary distributions of the Markov chain and the spacey random walk come in handy when considering centrality measures. The stationary distributions of these stochastic processes can both be found by considering eigenvector problems. For the ?first-order Markov chain, this translates into a regular eigenvector problem. For the higher-order Markov chain and the spacey random walk, this translates into a Z-eigenvector problem. These stationary distributions exist and are unique in some cases. We eventually apply these centrality measures on real-world data: we investigate centralities in European air traffic by means of a ?first-order Markov chain and a spacey random walk derived from a ?first-order Markov chain.