We use complex network concepts to analyze statistical properties of urban public transport networks (PTN). To this end, we present a comprehensive survey of the statistical properties of PTNs based on the data of fourteen cities of so far unexplored network size. Especially helpful in our analysis are different network representations. Within a comprehensive approach we calculate PTN characteristics in all of these representations and perform a comparative analysis. The standard network characteristics obtained in this way often correspond to features that are of practical importance to a passenger using public traffic in a given city. Specific features are addressed that are unique to PTNs and networks with similar transport functions (such as networks of neurons, cables, pipes, vessels embedded in 2D or 3D space). Based on the empirical survey, we propose a model that albeit being simple enough is capable of reproducing many of the identified PTN properties. A central ingredient of this model is a growth dynamics in terms of routes represented by self-avoiding walks.

The behavior of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable to targeted attacks. In recent studies of public transport networks of fourteen major cities of the world it was shown that these systems when represented by appropriate graphs may exhibit scale-free behavior [C. von Ferber et al., Physica A 380, 585 (2007), Eur. Phys. J. B 68, 261 (2009)]. Our present analysis, focuses on the effects that defunct or removed nodes have on the properties of public transport networks. Simulating different directed attack strategies, we derive vulnerability criteria that result in minimal strategies with high impact on these systems.PACS. 02.50.-r Probability theory, stochastic processes, and statistics -07.05.Rm Data presentation and visualization: algorithms and implementation -89.75.Hc Networks and genealogical trees

We analyze the public transport networks (PTNs) of a number of major cities of the world. While the primary network topology is defined by a set of routes each servicing an ordered series of given stations, a number of different neighborhood relations may be defined both for the routes and the stations. The networks defined in this way display distinguishing properties, the most striking being that often several routes proceed in parallel for a sequence of stations. Other networks with realworld links like cables or neurons embedded in two or three dimensions often show the same feature -we use the car engineering term harness for such networks. Geographical data for the routes reveal surprising self-avoiding walk (SAW) properties. We propose and simulate an evolutionary model of PTNs based on effectively interacting SAWs that reproduces the key features.

We present results of a survey of public transport networks (PTNs) of selected 14 major cities of the world with PTN sizes ranging between 2000 and 46000 stations and develop an evolutionary model of these networks. The structure of these PTNs is revealed in terms of a set of neighbourhood relations both for the routes and the stations. The networks defined in this way display distinguishing properties due to the constraints of the embedding 2D geographical space and the structure of the cities. In addition to the standard characteristics of complex networks like the number of nearest neighbours, mean path length, and clustering we observe features specific to PTNs. While other networks with real-world links like cables or neurons embedded in two or three dimensions often show similar behavior, these can be studied in detail in our present case. Geographical data for the routes reveal surprising self-avoiding walk properties that we relate to the optimization of surface coverage. We propose and simulate an evolutionary growth model based on effectively interacting self-avoiding walks that reproduces the key features of PTN.