  We analyze the global structure of the world-wide air transportation network,
a critical infrastructure with an enormous impact on local, national, and
international economies. We find that the world-wide 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.
