The Metropolitan Seoul Subway system is examined through the use of the gravity model. Exponents describing the power-law dependence on the time distance between stations are obtained, which reveals a universality for subway lines of the same topology. In the short (time) distance regime the number of passengers between stations does not grow with the decrease in the distance, thus deviating from the power-law behavior. It is found that such reduction in passengers is well described by the Hill function. Further, temporal fluctuations in the passenger flow data, fitted to the gravity model modified by the Hill function, are analyzed to reveal the Yule-type nature inherent in the structure of Seoul.

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, ...

This study aims to reveal the relationship between industrial agglomeration and transport accessibility in the Seoul metropolitan area. Our study suggests that in spite of the rapid expansion of the Seoul metropolitan area, central business districts still function as centers of the industry and transportation system; the agglomeration of most industrial subsectors are occurring in central areas and only primary and manufacturing sectors' clusters are located out of these areas; both of subway and road networks show higher level of accessibility in central Seoul and big cities. This implies a strong relationship between the industrial agglomeration and the transport accessibility, and such hypothetical relationship is tested for every industrial subsector using logit analysis. Our findings indicate that although there are industrial variations in the magnitude of impacts and the significance level, transport networks are, in general, positively associated with industrial agglomeration and this is especially true for service sectors.

Abstract. The master equation approach is proposed to describe the evolution of passengers in a subway system. With the transition rate constructed from simple geographical consideration, the evolution equation for the distribution of subway passengers is found to bear skew distributions including log-normal, Weibull, and power-law distributions. This approach is then applied to the Metropolitan Seoul Subway system: Analysis of the trip data of all passengers in a day reveals that the data in most cases fit well to the log-normal distributions. Implications of the results are also discussed.