Discrete Dynamics in Nature and Society

Volume 2016 (2016), Article ID 1290138, 8 pages

http://dx.doi.org/10.1155/2016/1290138

## Weighted Complex Network Analysis of Shanghai Rail Transit System

^{1}School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, China^{2}School of Transportation Engineering, Tongji University, 4800 Cao’an Road, Shanghai, China^{3}Shanghai Maritime University, College of Transport and Communication, Shanghai, China

Received 30 March 2016; Revised 13 June 2016; Accepted 10 July 2016

Academic Editor: Juan R. Torregrosa

Copyright © 2016 Yingying Xing et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

With increasing passenger flows and construction scale, Shanghai rail transit system (RTS) has entered a new era of networking operation. In addition, the structure and properties of the RTS network have great implications for urban traffic planning, design, and management. Thus, it is necessary to acquire their network properties and impacts. In this paper, the Shanghai RTS, as well as passenger flows, will be investigated by using complex network theory. Both the topological and dynamic properties of the RTS network are analyzed and the largest connected cluster is introduced to assess the reliability and robustness of the RTS network. Simulation results show that the distribution of nodes strength exhibits a power-law behavior and Shanghai RTS network shows a strong weighted rich-club effect. This study also indicates that the intentional attacks are more detrimental to the RTS network than to the random weighted network, but the random attacks can cause slightly more damage to the random weighted network than to the RTS network. Our results provide a richer view of complex weighted networks in real world and possibilities of risk analysis and policy decisions for the RTS operation department.

#### 1. Introduction

There is a rapidly growing literature on the complex networks present in transport systems and complex network analysis is a useful method to analyze the structure of transport systems. For example, studies of worldwide airport networks have shown small-world property and exhibited heavy tailed power-law distributions [1]. For the public transportation systems in Poland, various network properties, such as the distribution of degree and clustering coefficient, have been analyzed [2]. Further, the national highway network of Pakistan has been investigated with weighted complex network analysis of travel routes on the network [3]. Rail transit systems are in essence physical networks that are composed of stations or stops all linked by rails. Latora and Marchiori [4] found that Boston public transportation system exhibits the small-world behavior. Angeloudis and Fisk [5] studied the world’s largest subway systems and found that systems with substantial shared track are less robust than dedicated line systems of similar size. Lee et al. [6] analyzed statistical properties and topological consequences of the Seoul subway system and found that the flow weight distribution exhibited a power-law behavior. Soh et al. [7] contributed a complex weighted network analysis of travel routes on the Singapore rail and bus transportation systems. Zhang et al. [8] summarized the universal characteristics of the urban rail transit networks. Besides topological characteristics of networks, the reliability and robustness of metro networks were also widely studied. By looking at 33 metro systems in the world, Derrible and Kennedy [9] analyzed the complexity and robustness of metro systems and provided insights/recommendations for increasing the robustness of metro networks. Based on complex network theory, Zhang et al. [10] studied the connectivity, robustness, and reliability of the Shanghai subway network. De-Los-Santos et al. [11] provided passenger robustness measures for a rail transit network.

Nevertheless, these literatures, from a complex network perspective, focus more on topological features than dynamic traffic flow. The quantity of traffic in large transport infrastructures is fundamental for a full description of these networks [1]. Therefore, this paper aims at providing a richer and novel view of statistical properties of weighted complex networks. Both the topological and dynamic characteristics can be investigated according to complex network theory in this paper. In addition, the largest connected cluster is introduced to assess the reliability and robustness of weighted complex networks. By proper methods, it is also possible to explore the correlation between passenger flows and the topological structure of rail transit network, thereby providing scientific theoretical guidance for urban rail transit planning, design, and management.

#### 2. Weighted Networks Data

Shanghai RTS network consists of 286 nodes denoting stations and 317 edges accounting for a link connecting two nearest stations. The average degree of the network is , while the maximal degree is 8. As already observed in previous literatures [8, 10], the topology of the network exhibits both scale-free and small-world properties. Datasets that are provided by the Shanghai Shentong Metro Company list the hourly in and out passenger flows for each RTS station and passenger flows between adjacent stations. In this study, passenger flows during morning peak hours from 7:00 to 9:00 in a typical weekday are analyzed, during which the highest volume on a weekday could be observed.

Due to the method of data capture, it is important to note that the paper is not only investigating the topological and functional properties of the RTS network, but also the passenger flows between the different stations. In this work, it is assumed that typical travel was bidirectional, and hence the weight of one edge between a pair of nodes (stations) and is defined to be the sum of passenger flows in both directions and .

#### 3. Weighted Network Analysis of Shanghai Rail Transit Network

In this section, we present a topological and dynamical analysis of the Shanghai RTS network. Table 1 shows comparison analysis of basic network properties of unweighted network (topological) and weighted network (dynamical). As mentioned above, the Shanghai RTS network is comprised of 286 nodes and 317 edges and the average degree of the network is 2.22. The clustering coefficients of the RTS network (including the unweighted network and the weighted network) are 0.0012 and 0.0024, respectively, which both indicate that the local connectivity of the RTS network is very poor. The characteristic path length of the unweighted network between two nodes and is defined in terms of the network distance, which represents the minimum number of links necessary to go from node to node . The network diameter refers to the maximum shortest path and the diameter = 41 for the unweighted network. The network efficiency describes the global connectivity of the network and is given byBut it is more appropriate to use the physical distance rather than the network distance in measuring the real network efficiency . In terms of the physical distance, the characteristic path length, diameter, and network efficiency for the weighted network are given by = 24.49 km, = 116.20 km, and = 0.0352, respectively.