Accessibility plays a fundamental role in the transport network. In fact, accessibility may be used for investigating the (un)even distribution of economic activities, or the (dis)equilibrium in the development of different regional performances. In particular, accessibility analysis can be considered as a first exploratory step in the understanding of people's needs and behaviour, especially in the framework of transport network structures. From the methodological viewpoint, accessibility has a long tradition, starting in the 1950's with the pioneering work by Hansen, who defined accessibility as the potential of opportunity for interaction. Such a definition can also be considered as an integrated framework of all subsequent definitions. The aim of this paper is to explore accessibility in the German commuting network, by focusing attention on the relevance of the impedance form associated with it. The conventional (potential) accessibility function - in the light of the related economic activities - is used as a suitable instrument to identify the major German hub/attraction nodes. In this formulation, different types of decay functions are used as impedance forms. In our applications we consider home-to-work commuters travelling between 439 German districts, for both 2003 and 2007. We carry out a comparative analysis of the accessibility values in these years, by outlining the different emerging hierarchies, resulting from the use of different impedance forms. In addition, we explore which type of accessibility indicator best matches the connectivity network. The final aim is to identify - by means of different accessibility functions - homogeneous vs. heterogeneous characteristics of the German commuting network.

A great deal of attention has recently been paid to the analysis of the structure and evolution of (complex) networks, starting from pioneering contributions in the physical and social sciences-and more recently in the regional and transportation sciences-mainly concerning the relevance of highly connected nodes (hubs). The presence of hubs identifies a network as Scale-Free (SF), because of its intrinsic characteristic of exhibiting power-law distributions in its connectivity structure, and thus highly heterogeneous patterns. The focus of this paper is to explore the homogeneous vs. heterogeneous characteristics of the German commuting network, by focusing on the role of accessibility. The concept of accessibility has a long tradition in the transport economics literature, starting with the fundamental works by Hansen in the 1950's and later on by Weibull in the 1980's. These authors defined accessibility as the potential of opportunities for spatial interaction. Accessibility conceived in this manner should also capture spatial structure effects and thus the network configuration properties, such as connectivity. This conventional accessibility function-in the light of the related economic activities-is be used as a suitable instrument to identify the major German hub/attraction nodes. As the functional form in this potential accessibility, the powerdecay function will be considered-in addition to the negative exponential function-in order to explore the spatial configuration patterns, i.e. whether people perceive commuting cost in log-like way. The connectivity network analysis will then be developed as a benchmark to testing the results emerging from the spatial-economic

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