Network analysis has already a long history in operations research and quantitative social science research. In the past, much attention has been paid to shortest-route algorithms (for example, the travelling salesman problem), where the spatial configuration of networks was put in the centre of empirical investigation. Integer programming, linear and nonlinear programming turned out to offer a proper analytical toolbox. In recent years, we have seen several new trends, in particular, the rise of hub-and-spoke systems in liberalized networks, the emergence of dynamic adjustments to new competitive conditions and the increase in complexity in international networks. Furthermore, it appears that in the past decades many social, spatial and economic systems show an organized pattern characterized by network features, such as transportation, telecommunication, information or energy systems. As a consequence, much attention has recently been paid to the study of network properties emerging in many social, spatial and economic fields, as witnessed by the vast amount of literature published in the past years. Air transport is a prominent example of modern network constellations and will be addressed in this paper from a connectivity perspective. Air transport shows indeed clear network features, which impact on the way single airline carriers operate. The abundant scientific literature on airline networks has addressed this topic in terms of theoretical modelling and empirical measurements on different typologies of airline network configurations. This strand of recent research aimed to measure the network structure in relation to the effects of: (a) the market deregulation in United States in 1978 and in the European Union in the 1990s, (b) new trends in recent airline business strategies denoted as ‘low cost’ principles. Low cost carriers developed rather fast after the deregulation policy, by acquiring a competitive network advantage on traditional airlines, which consequently seemed to reorganise rapidly their airline network to respond to the new market dynamics. In this context, interesting research has emerged that mainly addressed the issue of describing and classifying networks by means of geographical concentration indices of traffic or flight frequency. These measures, such as the Gini concentration index or the Theil index, provide a proper measure of frequency or traffic concentration of the main airports in a simple, well-organized network. However, if a real-world network structure is complex, including multi-hub or mixed point-to-point and hub-spokes connections, the concentration indices may record high values for all types of structure, but fail to clearly discriminate between different network shapes. There is a need for a more appropriate measurement of connectivity structures in complex networks. Starting from the above considerations and research challenges, the present paper aims to investigate the scientific potential and applicability of a series of network connectivity/concentration indices, in order to properly typify and map out complex airline network configurations. Specifically, these various network indicators will be adopted and tested to describe the main properties – in terms of the network connectivity and configuration – of Lufthansa’s airline system.
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