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Complex network theory is a framework increasingly used in the study of air transport networks, thanks to its ability to describe the structures created by networks of flights, and their influence in dynamical processes such as delay propagation. While many works consider only a fraction of the network, created by major airports or airlines, for example, it is not clear if and how such sampling process bias the observed structures and processes. In this contribution, we tackle this problem by studying how some observed topological metrics depend on the way the network is reconstructed, i.e. on the rules used to sample nodes and connections. Both structural and simple dynamical properties are considered, for eight major air networks and different source datasets. Results indicate that using a subset of airports strongly distorts our perception of the network, even when just small ones are discarded; at the same time, considering a subset of airlines yields a better and more stable representation. This allows us to provide some general guidelines on the way airports and connections should be sampled.
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