Statistical analysis of the Metropolitan Seoul Subway System: Network structure and passenger flows

Abstract

The Metropolitan Seoul Subway system, consisting of 380 stations, provides the major transportation mode in the metropolitan Seoul area. Focusing on the network structure, we analyze statistical properties and topological consequences of the subway system. We further study the passenger flows on the system, and find that the flow weight distribution exhibits a power-law behavior. In addition, the degree distribution of the spanning tree of the flows also follows a power law.Key words: passenger flow, transportation, subway, power law PACS: 89.75. Hc, 89.40.Bb, 89.65.Lm Complex networks have been an active research topic in the physics community since models for complex networks were announced [1,2]. Subsequently, numerous real networks observed in biological and social systems as well as physical ones have been studied [3,4,5,6,7,8,9,10,11,12,13,14,15]. Those studied also include transportation systems such as airline networks, subway networks, * Permanent address: Department of Physics and Astronomy, Seoul National University, Republic of Korea and highway systems. For example, studies of world-wide airport networks as well as Indian and Chinese airport networks have disclosed small-world behaviors and truncated power-law distributions [6,7,8,9,10]. For the subway systems in Boston and Vienna, various network properties, such as the clustering coefficient and network size, have been reported [11,12]. Further, statistical properties of the Polish public transport network have been examined [13] and the Korean highway system has been analyzed with respect to the gravity model [14].In this manuscript, we consider the Metropolitan Seoul Subway (MSS) system, which consists of N = 380 stations, and serves as the major public transportation mode in the greater Seoul area, Republic of Korea. The system in an earlier phase was analyzed with regard to the accessibility measurement [16].In the present phase, the maximum distance between a pair of stations in the system is 126 km while the minimum value is 238 m. When we construct the subway network with N nodes, each corresponding to a station, the number of links connecting two nearest nodes turns out to be 424. The characteristic path length L is defined in terms of the network distance n ij , which represents the shortest path length between nodes i and j. Usually, the clustering coefficient C also provides an important measure for a complex network. However, since a few nodes of the subway system have only one nearest neighbor, the clustering coefficient C is not well defined. Accordingly, we define the clustering coefficient C * of the subway system, excluding the nodes which have one neighbor. The eccentricity of node i corresponds to the greatest distance between i and other node. The radius R and the diameter D of a network are then defined to be the minimum eccentricity and the maximum eccentricity, respectively, among all nodes. We further define the efficiency according toIn the ideal case for the efficiency ǫ, all nodes are connected to each other, ...

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