Public transportation networks (PTNs) are represented as complex networks in order to analyze their robustness regarding node and link failures, to classify them into different theoretical network models, and to identify the characteristics of the underlying network. Usually, PTNs have a large amount of 1- and 2- degree nodes that blur the analysis and their characterization as complex networks. Subway and train-based transport networks present long single lines that connect central stations to far destinations differently from airport networks that usually have few large airports (hubs) connecting a significant number of small airports. By focusing on relevant network nodes and links and allowing comparisons between PTNs of different transportation modes, this paper proposes the Reduced Model as a simple method of network reduction that preserves the network skeleton (backbone structure) by properly removing 2-degree nodes of weighted and unweighted network representations. Different from other proposed methods, its simple formulation leads to mathematical expressions that show how the reduced model affects fundamental network metrics (degree, path length, and clustering coefficient distributions). The Reduced model is applied to four large real-world PTNs: (i) two Brazilian cities with bus-based transport; (ii) the Seoul metro network; (iii) a worldwide airport network. The results reveal a hub-based hierarchical structure when a large number of intermediary stops are present and small-world properties that emphasizes hub–hub connections after applying the Reduced model. Therefore, the reduced model emphasizes characteristics of the networks that could be difficult to identify without reduction.

A reduced model for complex network analysis of public transportation systems

This paper analyses the robustness of specific public transport networks. Common attributes and which of them have more influence on the networks’ vulnerability are established. Initially, the structural properties of the networks in two graphical representations (L-Space and P-Space) are checked. Afterwards, the spread of problems (traffic jams, etc.) are simulated, employing a model based on a propagation and recovery mechanism, similar to those used in the epidemiological processes. Next, the size of the largest connected subset of stops of the network (giant component) is measured. What is shown is that the faults randomly happened at stops or links, also displaying that those that occurred in the highest weighted links spread slower than others. These others appear at stops with the largest level of betweenness, degree, or eigenvector centralities and PageRank. The modification of the giant component, when several stops and links are removed, proves that the removal of stops with the highest interactive betweenness, PageRank, and degree centralities has the most significant influence on the network’s integrity. Some equivalences in the degree, betweenness, PageRank, and eigenvector centrality parameters have been found. All networks show high modularity with values of index Q close to 1. The networks with the highest assortativity and lowest average number of stops are the ones which a passenger can use to travel directly to their destination, without any change. The Molloy–Reed parameter is higher than 2 in all networks, demonstrating that high integrity exists in them. All stops were characterized by low k-cores ≤3.

/pdf/analysing-the-vulnerability-of-public-transport-networks-45njfods71.pdf

Analysing the Vulnerability of Public Transport Networks

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In this study, the statistical properties and predictability of inter-urban highway traffic flows are investigated in a practical case in Heilongjiang Province, China. We build a topology graph of ...

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Statistical analysis and predictability of inter-urban highway traffic flows: a case study in Heilongjiang Province, China

Common network characteristics of four bus transport networks in Northeast China based on a perfect space P