A Reduced Model For Complex Network Analysis Of Public Transportation Systems

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. (C) 2020 Elsevier B.V. All rights reserved.