The transport network structure plays a crucial role in transport dynamics. To better understand the property of the bus network in big city and reasonably configure the bus lines and transfers, this paper seeks to take the bus network of Beijing as an example and mainly use space L and space P to analyze the network topology properties. The approach is applied to all the bus lines in Beijing which includes 722 lines and 5421 bus station. In the first phase of the approach, space L is used. The results show that the bus network of Beijing is a scalefree network and the degree of more than 99 percent of nodes is lower than 10. The results also show that the network is an assortative network with 46 communities. In a second phase, space P is used to analyze the property of transfer. The results show that the average transfer time of Beijing bus network which is 1.88 and 99.8 percent of arbitrary two pair nodes is reachable within 4 transfers.
Complex networks have been successfully used in many real complex systems since the researches of smallworld networks and scalefree networks [
As an important part of urban transport systems and a trip mode to alleviate the traffic congestion, bus network has been studied by an increasingly large number of researchers. Sienkiewicz and Holyst studied the public transport in 22 Polish cities and found that the degree distribution of these network topologies followed a power law or an exponential function [
In this paper, we investigate the Beijing bus network (BBN) with 722 lines and 5421 nodes. The data can be achieved from the Internet (
This paper is organized as follows. In Section
For easy calculation, there are some assumptions followed.
The station name is the unique identification in the network. Do not account for the condition that some stations have identical names but different parking place.
The stations have slight difference between upstream line and downstream line. In this paper, the construction of the undirected network is based on the stations of the upstream lines.
This paper does not consider the number of links between two stations and the frequency of bus; that is, it does not consider the weight of the network.
The bus network is usually represented by space L, space P [
Illustration of space L (a) and space P (b).
Here we represent network as a graph
The graph of Beijing bus network topology.
The degree
The stations of Beijing bus network with larger degree and the value of degree.
Serial number  Bus station  degree 

1  Sanyuanqiao  21 
2  Liu Li Qiao Dong  20 
3  Beijing Xi station  19 
4  Liu Li Qiao Bei Li  18 
5  Beijing Zhangdong  16 
6  Madian Qiao Xi  16 
7  Xi Dao Kou  16 
8  Chong Wen Men Xi  15 
9  Guang An Men Nei  14 
10  Zuo Jia Zhuang  14 
11  Qianmen  14 
12  Dabei Yao Nan  14 
13  Tianqiao  13 
14  Ma Dian Qiao Nan  13 
15  Bei Tai Ping Qiao Xi  13 
16  Si Hui station  13 
17  Deshengmen  13 
18  Xi Bei Wang  13 
19  Xiyuan  13 
20  Xin Fa Di Qiao Bei  13 
Here, we studied the proportion of the stations with the degree from 1 to 21. Figure
The degree distribution of Beijing bus network.
The average shortest path is the property to reflect the efficiency of information circulating on the network. It is defined as
Cluster coefficient is an important property of characterizing the local cohesiveness of the current node or the extent to which the nodes in the network are clustered together. In the BBN, clustering coefficient reflects the ease of the bus transport among the neighboring bus stations of the current one. It is defined as
The efficiency is the property to characterize the capacity of traffic, and it can be calculated with the formula
Degree correlation reflects the relationship between the degrees of nodes. Nodes with high degree tending to be connected with nodes with high degree are called assortativity. In contrast, nodes with high degree which have the tendency to be connected with low degree are called disassortativity. It can be calculated with the formula [
It is usually found that there are many communities in one complex network; within the community, there are many links, but between the communities, there are fewer links [
Table
The value of the main properties of Beijing bus network.
Network parameters  Value 

Number of nodes ( 
5421 
Number of links ( 
16986 
Number of lines ( 
722 
Average degree (Ak)  3.13 
Average shortest path ( 
20.03 
Cluster coefficient ( 
0.142 
Efficiency ( 
0.066 
Correlation coefficient ( 
0.185 
Number of communities ( 
46 
Modularity ( 
0.905 
The transfer capacity is an important index to evaluate the performance of a bus network, and travelers always expect that they can reach the destination through the least number of transfers. In this paper, the average minimum transfer time is used to evaluate the performance of the transfer capacity. Usually, travelers cannot reach the destination without transfer for a long distance trip, and the minimum transfer time between any two nodes is specific. The average minimum transfer time is the average among all pair nodes.
Table
The specific network of Figure












 


1  1  1  1  1  1  0  0  0  0  0  0  0 

0  0  1  0  0  0  1  1  1  1  0  0  0 

0  0  0  0  1  0  0  0  0  0  1  1  1 
Using the aforementioned method, we can get the minimum transfer time between any two nodes and calculate the average minimum transfer time. But it becomes very hard when the scale of network is becoming huge. In this paper, we use the space P to solve the problem. Firstly, we need to construct the network under space P, where the weight of the network is 1. Secondly, the Floyd algorithm is used to achieve the shortest path between any two nodes. The shortest path value is the minimum line number that needs to use and the transfer time is the needed line number minus 1. Figure
The illustration of transfer network under space P.
Here, we study the BBN. Table
The stations that have most line and the line numbers.
Serial number  Station  Line numbers 

1  Sanyuanqiao  47 
2  Liu Li Qiao Bei Li  40 
3  Beijing Xi Zhan  39 
4  Zuo Jia Zhuang  38 
5  Liu Li Qiao Dong  34 
6  Liu Li Qiao Nan  33 
7  Dongzhimen Wai  31 
8  Gong Zhu Fen Nan  31 
9  Bei Da Di  30 
10  Bei Tai Ping Qiao Xi  29 
11  Jing An Zhuang  29 
12  Xiajia Hutong  29 
13  Qing He  29 
14  Xiyuan  29 
15  Beijing Zhangdong  28 
16  Xi Bei He  28 
17  Xiju  28 
18  Si Hui Zhan  28 
19  Liangmaqiao  28 
20  Mu xi yuan qiao dong  27 
21  Yan Huang yishu Guan  26 
22  Yuquanying Qiao Xi  26 
23  Dongwu Yuan  25 
24  Guang An Men Nei  25 
25  Qianmen  25 
26  Wanshou si  25 
27  Mu Xi Yuan Qiao Xi  25 
28  Kandan Qiao  25 
Figure
The distribution of a station’s amount of lines.
In this paper, the transfer time of BBN is studied by using space P. From Table
The proportion of the transfer time of Beijing bus network.
atr  0  1  2  3  4  4 more  unreachable 

Proportion  0.0168  0.283  0.553  0.141  0.0047  0.00013  0.00137 
In this paper, space L and space P are used to analyze the static properties of Beijing bus network. Space L is used to research the main topology properties of the Beijing bus network. The results show the Beijing bus network has small cluster coefficient, scalefree feature, and assortative correlation and the community structure is obvious. Moreover, we research the transfer property using space P. The result shows that the accessibility of the Beijing bus network is good and the average minimum transfer time is 1.88, which is a little large. A convenient bus network needs less transfers and high performance, and how to reduce transfer time and enhance the bus network dynamical performance is a valuable research.
This paper is supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (20120009110016).