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

Guimerà, R, Mossa, S, Turtschi, A & Amaral, LAN
Proc. Natl. Acad. Sci. U. S. A. 102, 7794-7799 (2005).

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 multi-community 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 geo-political considerations have to be taken into account. We identify each city's global role based on its pattern of inter- and intra-community connections, which enables us to obtain scale-specific representations of the network.


Non-technical description of the results

The worldwide air transportation network is responsible for the mobility of millions of people every day. Almost 700 million passengers fly each year, maintaining the air transportation system ever so close to the brink of failure. For example, US and foreign airlines schedule about 2,700 daily flights in and out of O'Hare alone, more than 10% of the total commercial flights in the continental US, and more than the airport could handle even during a perfect "blue-sky" day. Low clouds, for example, can lower landing rates at O'Hare from 100 an hour to just 72 an hour, resulting in delays and flight cancellations across the country. The failures and inefficiencies of the air transportation system have large economic costs; flight delays cost European countries 150 to 200 billion Euro in 1999 alone.


Boeing 747 Globe Figure 1. Left, Boeing 747 landing. Right, Cities in the worldwide air transportation system. Different colors indicate membership in different communities.

These staggering numbers prompt several questions: What has led the system this close to the brink of failure? Why haven't planners designed a better system? In order to answer these questions, it is crucial to characterize the structure of the world-wide air transportation network and the mechanisms responsible for its evolution. This problem is, however, far from simple. The structure of the air transportation network is mostly determined by the concurrent actions of airline companies---both private and national---that try, in principle, to maximize their immediate profit. However, the structure of the network is also the outcome of numerous historical "accidents" arising from geographical, political, and economic factors.

Many interconnected systems can be mathematically described as scale-free networks, of which the Internet is an example. In these systems, connectivity is unbalanced: a few nodes are highly connected with others, while most are only sparsely connected. In this study, we analized direct connections between cities from the OAG MAX database, which catalogues the schedule flights of more than 800 of the world's airlines. Specifically, we considered over 500,000 flights between 27,000 pairs of cities scheduled during the first week of November 2000. We demonstrate that the worldwide air transportation network is a scale-free network, like the Internet.

Yet, unlike what is expected for scale-free networks, the air transportation network's busiest hubs are not necessarily the most important. For example, although Paris and Frankfurt have similar traffic levels, Paris is more important for maintaining worldwide connectivity.  We have determined this is because the global network is actually comprised of smaller communities defined by political as well as geographic considerations.

Post scriptum: Airports and national airline companies are often times associated with the image a country or region wants to project. For this reason, many measures---including total number of passengers, total number of flights, or total amount of cargo---quantifying the importance of the world airports are compiled and publicized. For those interested, we append ranked lists with connectedness and centrality of the cities in the database.


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