Air transportation plays an essential role in the global economy. Therefore, there is a great deal of work to understand better the complex network formed by the links between the origins and destinations of flights. Some investigations show that the world air transportation network exhibits a community and a core-periphery structure. Although precious, these representations do not distinguish the inter-regional (global) web of connections from the regional (local) one. Therefore, we propose a new mesoscopic model called the component structure that decomposes the network into local and global components. Local components are the dense areas of the network, and global components are the nodes and links bridging the local components. As a case study, we consider the unweighted and undirected world air transportation network. Experiments show that it contains seven large local components and multiple small ones spatially well-defined. Moreover, it has a main global component covering the world. We perform an extensive comparative analysis of the structure of the components. Results demonstrate the non-homogeneous nature of the world air transportation network. The local components structure highlights regional differences, and the global component organization captures the efficiency of inter-regional travel. Centrality analysis of the components allows distinguishing airports centered on regional destinations from those focused on inter-regional exchanges. Core analysis is more accurate in the components than in the whole network where Europe dominates, blurring the rest of the world. Besides the world air transportation network, this paper demonstrates the potential of the component decomposition for modeling and analyzing the mesoscale structure of networks.

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