Network bipartivity and the transportation efficiency of European passenger airlines

•A new way for calculating the bipartivity of networks is introduced.•The bipartivity of the European Low Cost Carriers and Traditional airlines shows significant differences.•Alliances and airline mergers decrease the bipartivity of the corresponding networks.•Bipartivity is strongly correlated with the transportation efficiency of the European airlines.

The analysis of the structural organization of the interaction network of a complex system is central to understand its functioning. Here, we focus on the analysis of the bipartivity of graphs. We first introduce a mathematical approach to quantify bipartivity and show its implementation in general and random graphs. Then, we tackle the analysis of the transportation networks of European airlines from the point of view of their bipartivity and observe significant differences between traditional and low cost carriers. Bipartivity shows also that alliances and major mergers of traditional airlines provide a way to reduce bipartivity which, in its turn, is closely related to an increase of the transportation efficiency.