The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles

^*Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208; ^†European Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble, Cedex, France; and ^‡Avanade Deutschland Gmbh, Campus Kronberg 7, D-61476, Kronberg, Germany

Edited by Kenneth W. Wachter, University of California, Berkeley, CA, and approved April 5, 2005 (received for review October 27, 2004)

Abstract

We analyze the global structure of the worldwide air transportation network, a critical infrastructure with an enormous impact on local, national, and international economies. We find that the worldwide air transportation network is a scale-free small-world network. In contrast to the prediction of scale-free network models, however, we find that the most connected cities are not necessarily the most central, resulting in anomalous values of the centrality. We demonstrate that these anomalies arise because of the multicommunity structure of the network. We identify the communities in the air transportation network and show that the community structure cannot be explained solely based on geographical constraints and that geopolitical considerations have to be taken into account. We identify each city's global role based on its pattern of intercommunity and intracommunity connections, which enables us to obtain scale-specific representations of the network.

Footnotes

↵ § To whom correspondence should be addressed. E-mail: amaral{at}northwestern.edu.
Author contributions: R.G. and L.A.N.A. designed research; R.G., S.M., and L.A.N.A. performed research; R.G., S.M., A.T., and L.A.N.A. analyzed data; and R.G. and L.A.N.A. wrote the paper.
This paper was submitted directly (Track II) to the PNAS office.
↵ ¶ The cumulative degree distribution P(> k) gives the probability that a city has k or more connections to other cities and is defined as $\text{[math]}$ , where p(k) is the probability density function.
↵ ∥ We do not know the geographical coordinates of ≈10% of the 3,663 cities in the giant component of the worldwide air transportation network. Those cities are not plotted in the map. Also, some small cities may be misplaced because of duplications in the three-letter code of the corresponding airport.
↵ ** Alaska and Papua New Guinea are small communities compared with most of the others, which confirms the idea that these are very well defined communities; otherwise, they would be incorporated in a larger community. This fact is particularly important taking into consideration that the community identification algorithm does not take into account the betweenness of the nodes at all.