Network topology and correlation features affiliated with European airline companies

The physics information of four specific airline flight networks in European Continent, namely the Austrian airline, the British airline, the France–Holland airline and the Lufthhansa airline, was quantitatively analyzed by the concepts of a complex network. It displays some features of small-world networks, namely a large clustering coefficient and small average shortest-path length for these specific airline networks. The degree distributions for the small degree branch reveal power law behavior with an exponent value of 2–3 for the Austrian and the British flight networks, and that of 1–2 for the France–Holland and the Lufthhansa airline flight networks. So the studied four airlines are sorted into two classes according to the topology structure. Similarly, the flight weight distributions show two kinds of different decay behavior with the flight weight: one for the Austrian and the British airlines and another for the France–Holland airline and the Lufthhansa airlines. In addition, the degree–degree correlation analysis shows that the network has disassortative behavior for all the value of degree k, and this phenomenon is different from the international airline network and US airline network. Analysis of the clustering coefficient (C(k)) versus k, indicates that the flight networks of the Austrian Airline and the British Airline reveal a hierarchical organization for all airports, however, the France–Holland Airline and the Lufthhansa Airline show a hierarchical organization mostly for larger airports. The correlation of node strength (S(k)) and degree is also analyzed, and a power-law fit S(k)∼k1.1 can roughly fit all data of these four airline companies. Furthermore, we mention seasonal changes and holidays may cause the flight network to form a different topology. An example of the Austrian Airline during Christmas was studied and analyzed.