A method of examining the structure and topological properties of public-transport networks

• Thorough review of fundamental works in graph theory and network science.
• Combining programming, network and statistical data analysis in transport studies.
• Developing a method to examine and analyze complex public-transport networks.
• Applying the method to explore and analyze real-world public-transport network.
• Analyzing the results and outlining directions for method’s extension and research.

This work presents a new method of examining the structure of public-transport networks (PTNs) and analyzes their topological properties through a combination of computer programming, statistical data and large-network analyses. In order to automate the extraction, processing and exporting of data, a software program was developed allowing to extract the needed data from General Transit Feed Specification, thus overcoming difficulties occurring in accessing and collecting data. The proposed method was applied to a real-life PTN in Auckland, New Zealand, with the purpose of examining whether it showed characteristics of scale-free networks and exhibited features of “small-world” networks. As a result, new regression equations were derived analytically describing observed, strong, non-linear relationships among the probabilities of randomly chosen stops in the PTN to be serviced by a given number of routes. The established dependence is best fitted by an exponential rather than a power-law function, showing that the PTN examined is neither random nor scale-free, but a mixture of the two. This finding explains the presence of hubs that are not typical of exponential networks and simultaneously not highly connected to the other nodes as is the case with scale-free networks. On the other hand, the observed values of the topological properties of the network show that although it is highly clustered, owing to its representation as a directed graph, it differs slightly from “small-world” networks, which are characterized by strong clustering and a short average path length.