With the development of the public transportation, bus network becomes complicated and hard to evaluate. Transfer time is a vital indicator to evaluate bus network. This paper proposed a method to calculate transfer times using Space P. Four bus networks in China have been studied in this paper. Some static properties based on graph theory and complex theory are used to evaluate bus topological structure. Moreover, a bus network evolution model to reduce transfer time is proposed by adding lines. The adding method includes four types among nodes with random choice, large transfer time, degree, and small degree. The results show that adding lines with nodes of small degree is most effective comparing with the other three types.
Bus network plays more and more significant role in alleviating the increasingly heavy traffic congestion in metropolis due to urban sprawl and population explosion. During the last two decades, there are many researches on transportation systems using complex networks theory such as subway networks [
Complex network theory is a useful tool to analyze network topological structures. It has been successfully applied in many fields including power grid networks [
As a complex network, bus network has its unique traits. Lines play an important role in constituting a bus network; it is necessary to understand the effect of each line. To evaluate the topological structures of bus networks, this paper uses several indicators based on graph theory and complex theory and proposes two indicators concerning transfers. An effective method to calculate the average transfer time considering traffic demand has been proposed using Space P. Moreover, the role of each line playing in transfer times of the whole network has been studied. In the end, four types to reduce total transfer time have been given by adding lines.
This paper focuses on the transfer issues of bus network and aims to find an efficient way to reduce transfer times. The rest of paper is organized as follows. Section
In this paper, we use three forms of matrices to represent the bus network: linestation matrix, weighted adjacent matrix, and adjacent matrix under Space P. Linestation matrix is a basic form to express bus network, where each row stands for a line and each column stands for a station. Take Figure
Simple bus network described by Space P.
Baoding, Jinan, Shijiazhuang, and Suzhou are four medium cities in China. As the economy developed rapidly in these years, the demand of public transportation is high. We collected the four cities bus data from website in 2014. The data contain line name, station name, the distance between two adjacent stations, and the number of overlapped edges between two adjacent stations. Totally, there are 52 lines and 634 stations in Baoding, 100 lines and 883 stations in Jinan, 139 lines and 1299 stations in Shijiazhuang, and 109 lines and 1402 stations in Suzhou. Figure
Statistical properties values of gamma index, average line length, line overlapping degree, average degree, efficiency, degree correlation, and modularity for Baoding, Jinan, Shijiazhuang, and Suzhou.
Indicators 








Baoding  0.4655  15.5  0.437  2.784  0.1011  0.1166  0.838 
Jinan  0.4431  13.4  0.476  2.652  0.0724  0.2661  0.860 
Shijiazhuang  0.4868  15.9  0.435  2.916  0.0901  0.1950  0.854 
Suzhou  0.4860  22.2  0.447  2.912  0.0742  0.1685  0.869 
The topological structures of transit networks of Baoding, Jinan, Shijiazhuang, and Suzhou. The colors represent communities of transit network; the size of nodes represents the degree.
From Table
Besides the aforementioned indicators, this paper focuses on the transferrelated indicators such as the average transfer time of the whole transit network and transfer disutility.
The average transfer time is a significant predictor to evaluate transit network. Intuitively, the higher the average transfer time is the worse the transit performance is. It is hard to calculate the transfer time among the network using the traditional linestation matrix. Here, the adjacent matrix under Space P is used to calculate the average transfer times considering traffic demand. It is calculated with the formula
Transfer disutility is correlated with transfer time and degree. It can be expressed as
Based on the two formulas, the average transfer times of Baoding, Jinan, Shijiazhuang, and Suzhou are 1.0712, 1.3138, 1.4640, and 1.2416 which indicates that the structure of Baoding outperforms the other three. The specific transfer time proportions are given in Table
The proportion of transfer times of the four cities.
Transfer time  0  1  2  3 and more 

Baoding  0.0946  0.7396  0.1658  0 
Jinan  0.0698  0.5588  0.3567  0.0147 
Shijiazhuang  0.0407  0.4698  0.4724  0.0171 
Suzhou  0.0626  0.6337  0.3016  0.0030 
In order to further study the particularity of transfer of bus network, this paper puts emphasis on the transfer between different lines and evolution on transfer by adding lines. Bus network is comprised of lines as basic components, not edges. Therefore, transfer times between lines are so important when evaluating bus network. The transfer times between lines can be calculated as
The total transfer times between any two lines.
In a bus network, some lines are indispensable to reduce the total transfer times. In order to better assess the importance of a line of bus network, each line was deleted separately from the network. Intuitively, the total transfer time of bus network will increase or remain the same after deleting a line. Here, we calculate the ratio between the original total transfer times and modified total transfer times using the formula
As we can see from Figure
The total transfer proportion after deleting a line.
To reduce the transfer times and increase the competitiveness, it is necessary to understand the evolution of bus network. In this part, we seek to reduce transfer times of bus network by adding edges. The aim is to find an effective way to reduce the transfer times. The specific processes are as follows: 20 lines will be added gradually to the network with fourtype principles. Each line contains 20 nodes. The principles to choose nodes are based on
As can be seen from Figure
The transfer ratio with four adding edges modes: random choice, large transfer time, large degree, and small degree.
This paper studied the evaluation of bus networks from topology and transfer perspectives. The average transfer time has an important impact on transit performance. In this paper, the method to calculate transfer time between any two nodes with different traffic demand using Space P has been proposed. Statistical properties show that bus networks are assortative network with multiple communities.
Lines play a significant role in comprising bus network. This paper studied the role of each line of networks by deleting lines. The results show there are several lines in the network which has important influence on transfer times. In order to reduce transfer times, four types of adding lines are applied in the four networks. Four types mean four different nodes choosing methods: random choice, large transfer time, large degree, and small degree. The results show that adding lines among nodes with small degree has the best effect comparing to the other three. The future work should consider the practical traffic demand between any two nodes and other influential factors.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper is supported by National Natural Science Foundation of China (51278030 and 51478036).