# Exploring the Characteristics of an Intra-Urban Bus Service Network: A Case Study of Shenzhen, China

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{8}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Dataset

#### 2.1. Study Area

^{2}and has a population of more than 15 million, making it the most densely populated among Chinese cities [15,38]. The unique socioeconomic and demographic status of Shenzhen makes it an interesting area for the study of urban bus networks.

#### 2.2. Dataset Collection

## 3. Complex Network Analysis

#### 3.1. Network Construction

_{i}is a bus stop i, and a weight is assigned to each link of a bus line. First, the weight w

_{ij}of edge e

_{ij}between v

_{i}and v

_{j}in the network is initialized as w

_{ij}= 0. For every bus line, the specific rule to obtain the weight matrix W is as follows:

_{i}and v

_{j}can be accessed without any transfer, it is considered that the two nodes are connected to each other, and the corresponding weight w

_{ij}between v

_{i}and v

_{j}is set to plus 1.

_{ij}}.

_{TAZ}= (V, E, W). In this network, node V

_{i}represents TAZ $i$, edge E

_{ij}represents the connection between TAZ i and TAZ j, and weight w

_{ij}represents the number of bus lines that pass through the two TAZs. Ultimately, a TAZ-based network with more than 965 nodes and 71,000 links was constructed for use in the subsequent analysis.

#### 3.2. Topological Analysis of the Bus Service Network Structure

_{i}of a TAZ represents the number of TAZs connected directly to the TAZ by at least one bus line. The degree distribution can be calculated as follows:

_{k}represents the number of TAZs whose degree is equal to k.

_{ij}is the number of edges of the shortest path between nodes i and j. A small average path length indicates good network accessibility.

_{i}between nodes within its neighborhood divided by the maximal possible edges between them:

#### 3.3. Nodes’ Centrality Measurement of the Weighted Bus Network Structure

_{ij}is the shortest path length between TAZ i and TAZ j. The larger the closeness centrality, the more conveniently TAZ i can be accessed from other TAZs by taking a bus. Thus, closeness centrality can represent the accessibility of TAZs.

_{jk}represents the number of all shortest paths between TAZ j and TAZ k, and n

_{jk}(i) is the number of shortest paths that pass through TAZ i. The larger the betweenness centrality, the more critical the TAZ in connecting TAZ pairs by taking the shortest path. Thus, betweenness centrality reflects the importance of a TAZ as a critical bridge in the bus service network.

_{i}is the set of edges that connects with node i; k

_{i}represents the degree of node i; and PR

_{i}represents the PageRank score of node i, and its calculation is an iterative process. The larger the score, the more important the TAZ in the bus service network.

## 4. Result and Discussion

#### 4.1. Statistical Characteristic of the Bus Service Network

#### 4.1.1. Degree Distribution

#### 4.1.2. Small-World Property

#### 4.2. Spatial Characteristic of the Bus Service Network

#### 4.2.1. Charactering Edge Weight of Bus Service Network

#### 4.2.2. Charactering Centrality of Traffic Analysis Zones in Bus Service Network

#### 4.2.3. Correlation of Centrality between Bus Network and Road Network

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Pittschieler, K. Performance improvement of urban bus system: Issues and solution. Int. J. Eng. Sci. Technol.
**2010**, 2, 21–23. [Google Scholar] - Wang, M.; Hu, B.-Q.; Wu, X.; Niu, Y.-Q. The topological and statistical analysis of public transport network based on fuzzy clustering. In Fuzzy Information and Engineering; Cao, B., Li, T.-F., Zhang, C.-Y., Eds.; Springer: Berlin/Heidelberg, Germany, 2009; Volume 2, pp. 1183–1191. [Google Scholar]
- Wu, X.; Dong, H.; Chi, K.T.; Ho, I.W.H.; Lau, F.C.M. Analysis of metro network performance from a complex network perspective. Phys. A Stat. Mech. Appl.
**2017**, 492, 553–563. [Google Scholar] [CrossRef] - Lin, J. Network analysis of China’s aviation system, statistical and spatial structure. J. Transp. Geogr.
**2012**, 22, 109–117. [Google Scholar] [CrossRef] - Zhang, J.; Zhao, M.; Liu, H.; Xu, X. Networked characteristics of the urban rail transit networks. Phys. A Stat. Mech. Appl.
**2013**, 392, 1538–1546. [Google Scholar] [CrossRef] - Zhang, J.; Cao, X.B.; Du, W.B.; Cai, K.Q. Evolution of Chinese airport network. Phys. A Stat. Mech. Appl.
**2011**, 389, 3922–3931. [Google Scholar] [CrossRef] - Wang, C.; Wang, J. Spatial pattern of the global shipping network and its hub-and-spoke system. Res. Transp. Econ.
**2012**, 32, 54–63. [Google Scholar] [CrossRef] - Wang, J.; Mo, H.; Wang, F.; Jin, F. Exploring the network structure and nodal centrality of China’s air transport network: A complex network approach. J. Transp. Geogr.
**2011**, 19, 712–721. [Google Scholar] [CrossRef] - Lin, J.; Ban, Y. Complex network topology of transportation systems. Transp. Rev.
**2013**, 33, 658–685. [Google Scholar] [CrossRef] - Roth, C.; Kang, S.M.; Batty, M.; Barthélemy, M. Structure of urban movements: Polycentric activity and entangled hierarchical flows. PLoS ONE
**2011**, 6, e15923. [Google Scholar] [CrossRef] - Liu, X.; Gong, L.; Gong, Y.; Liu, Y. Revealing travel patterns and city structure with taxi trip data. J. Transp. Geogr.
**2015**, 43, 78–90. [Google Scholar] [CrossRef][Green Version] - Zhong, C.; Arisona, S.M.; Huang, X.; Batty, M.; Schmitt, G. Detecting the dynamics of urban structure through spatial network analysis. Int. J. Geogr. Inf. Sci.
**2014**, 28, 2178–2199. [Google Scholar] [CrossRef] - Patuelli, R.; Reggiani, A.; Gorman, S.P.; Nijkamp, P.; Bade, F.J. Network analysis of commuting flows: A comparative static approach to German data. Netw. Spat. Econ.
**2007**, 7, 315–331. [Google Scholar] [CrossRef] - Zhu, G.; Corcoran, J.; Shyy, P.; Pileggi, S.F.; Hunter, J. Analysing journey-to-work data using complex networks. J. Transp. Geogr.
**2018**, 66, 65–79. [Google Scholar] [CrossRef] - Yang, X.; Fang, Z.; Yin, L.; Li, J.; Zhou, Y.; Lu, S. Understanding the spatial structure of urban commuting using mobile phone location data: A case study of Shenzhen, China. Sustainability
**2018**, 10, 1435. [Google Scholar] [CrossRef] - Gonzalez, M.C.; Hidalgo, C.A.; Barabasi, A. Understanding individual human mobility patterns. Nature
**2008**, 453, 779–782. [Google Scholar] [CrossRef] [PubMed] - Li, M.X.; Jiang, Z.Q.; Xie, W.J.; Miccichè, S.; Tumminello, M.; Zhou, W.X.; Mantegna, R.N. A comparative analysis of the statistical properties of large mobile phone calling networks. Sci. Rep.
**2014**, 4, 5132. [Google Scholar] [CrossRef] [PubMed][Green Version] - Demsar, U.; Spatenkova, O.; Virrantaus, K. Identifying critical locations in a spatial network with graph theory. Trans. GIS
**2008**, 12, 61–82. [Google Scholar] [CrossRef] - Rui, Y.; Ban, Y. Exploring the relationship between street centrality and land use in Stockholm. Int. J. Geogr. Inf. Sci.
**2014**, 28, 1425–1438. [Google Scholar] [CrossRef] - Dai, L.; Derudder, B.; Liu, X.; Witlox, F. Transport network backbone extraction: A comparison of techniques. J. Transp. Geogr.
**2018**, 69, 271–281. [Google Scholar] [CrossRef] - Jiang, B.; Claramunt, C. Topological analysis of urban street networks. Environ. Plan. B Abstr.
**2003**, 31, 151–162. [Google Scholar] [CrossRef] - Sun, D.; Zhao, Y.; Lu, Q.C. Vulnerability analysis of urban rail transit networks: A case study of Shanghai, China. Sustainability
**2015**, 7, 6919–6936. [Google Scholar] [CrossRef] - Zhang, J.; Wang, S.; Wang, X. Comparison analysis on vulnerability of metro networks based on complex network. Phys. A Stat. Mech. Appl.
**2018**, 496, 72–78. [Google Scholar] [CrossRef] - Soh, H.; Lim, S.; Zhang, T.; Fu, X.; Lee, G.K.K.; Hung, T.G.G.; Di, P.; Prakasam, S.; Wong, L. Weighted complex network analysis of travel routes on the Singapore public transportation system. Phys. A Stat. Mech. Appl.
**2010**, 389, 5852–5863. [Google Scholar] [CrossRef] - Chen, Y.Z.; Li, N.; He, D.R. A study on some urban bus transport networks. Phys. A Stat. Mech. Appl.
**2007**, 376, 747–754. [Google Scholar] [CrossRef] - Rodrigue, J.P.; Comtois, C.; Slack, B. The geography of transport systems. J. Urban. Technol.
**2013**, 18, 127. [Google Scholar] - Feng, S.; Hu, B.; Nie, C.; Shen, X. Empirical study on a directed and weighted bus transport network in china. Phys. A Stat. Mech. Appl.
**2016**, 441, 85–92. [Google Scholar] [CrossRef] - Sienkiewicz, J.; Hołyst, J.A. Statistical analysis of 22 public transport networks in Poland. Phys. Rev.
**2005**, 72, 046127. [Google Scholar] [CrossRef][Green Version] - Háznagy, A.; Fi, I.; London, A.; Nemeth, T. Complex network analysis of public transportation networks: A comprehensive study. In Proceedings of the 2015 International Conference on MODELS and Technologies for Intelligent Transportation Systems, Budapest, Hungary, 3–5 June 2015; pp. 371–378. [Google Scholar]
- Tanuja, S.; Ho, I.W.H.; Chi, K.T. Spatial analysis of bus transport networks using network theory. Phys. A Stat. Mech. Appl.
**2018**, 502, 295–314. [Google Scholar] - Barabasi, A.; Albert, R. Emergence of scaling in random networks. Science
**1999**, 286, 509–512. [Google Scholar] [CrossRef] - Xu, X.; Hu, J.; Liu, F.; Liu, L. Scaling and correlations in 3 bus-transport networks of China. Phys. A Stat. Mech. Appl.
**2007**, 374, 441–448. [Google Scholar] [CrossRef] - Chatterjee, A.; Ramadurai, G. Scaling laws in Chennai bus network. In Proceedings of the International Conference on Complex Systems and Applications ICCSA 2014, Le Havre, France, 23–26 June 2014. [Google Scholar]
- Watts, D.J.; Strogatz, S.H. Collective dynamics of ‘small-world’ networks. Nature
**1998**, 393, 440–442. [Google Scholar] [CrossRef] [PubMed] - Latora, V.; Marchiori, M. Efficient behavior of small-world networks. Phys. Rev. Lett.
**2001**, 87, 198701. [Google Scholar] [CrossRef] [PubMed] - Barthelemy, M. Spatial networks. Phys. Rep.
**2010**, 499, 1–101. [Google Scholar] [CrossRef] - Yang, X.-H.; Chen, G.; Chen, S.-Y.; Wang, W.-L.; Wang, L. Study on some bus transport networks in China with considering spatial characteristics. Transp. Res. Part A Policy Pract.
**2014**, 69, 1–10. [Google Scholar] [CrossRef] - Fang, Z.; Yang, X.; Xu, Y.; Shaw, S.; Yin, L. Spatiotemporal model for assessing the stability of urban human convergence and divergence patterns. Int. J. Geogr. Inf. Sci.
**2017**, 31, 2119–2141. [Google Scholar] [CrossRef] - Amap Platform. Available online: https://www.amap.com/ (accessed on 29 October 2019).
- Sen, P.; Dasgupta, S.; Chatterjee, A.; Sreeram, P.A.; Mukherjee, G.; Manna, S.S. Small-world properties of the Indian railway network. Phys. Rev. E
**2003**, 67, 036106. [Google Scholar] [CrossRef][Green Version] - You, J.; Nedović-Budić, Z.; Kim, T.J. A GIS-based traffic analysis zone design: Technique. Transp. Plan. Technol.
**1998**, 21, 45–68. [Google Scholar] [CrossRef] - Dong, H.; Wu, M.; Ding, X.; Chu, L.; Jia, L.; Qin, Y.; Zhou, X. Traffic zone division based on big data from mobile phone base stations. Transp. Res. Part. C Emerg. Technol.
**2015**, 58, 278–291. [Google Scholar] [CrossRef] - Amaral, L.A.; Scala, A.; Barthelemy, M.; Stanley, H.E. Classes of small-world networks. Proc. Natl. Acad. Sci. USA
**2000**, 97, 11149–11152. [Google Scholar] [CrossRef][Green Version] - Sabidussi, G. The centrality index of a graph. Psychometrika
**1996**, 31, 581–603. [Google Scholar] [CrossRef] - Freeman, L.C. A set of measures of centrality based upon betweenness. Sociometry
**1977**, 40, 35–41. [Google Scholar] [CrossRef] - Brin, S.; Page, L. The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst.
**1998**, 30, 107–117. [Google Scholar] [CrossRef] - Liu, L.; Li, R.; Shao, F.; Sun, R. Complexity analysis of Qingdao’s public transport network. In Proceedings of the International Symposium on Intelligent Information Systems and Applications (IISA 2009), Nanchang, China, 21–22 November 2009; pp. 300–303. [Google Scholar]
- Ferber, C.V.; Holovatch, T.; Holovatch, Y.; Palchykov, V. Network harness: Metropolis public transport. Phys. A Stat. Mech. Appl.
**2007**, 380, 585–591. [Google Scholar] [CrossRef][Green Version] - Huang, Y.; Lu, S.; Yang, X.; Zhao, Z. Exploring railway network dynamics in China from 2008 to 2017. ISPRS Int. J. Geo Inf.
**2018**, 7, 320. [Google Scholar] [CrossRef] - Clauset, A.; Newman, M.E.J.; Moore, C. Finding community structure in very large networks. Phys. Rev. E
**2004**, 70, 066111. [Google Scholar] [CrossRef] [PubMed][Green Version] - Jenks, G.F. The data model concept in statistical mapping. Int. Yearb. Cartogr.
**1967**, 7, 186–190. [Google Scholar]

**Figure 10.**Statistical distribution of the six levels of groups. L1 represents the percentage of traffic analysis zones (TAZs) with level L1 in all TAZs.

**Figure 11.**Spatial distribution of closeness centrality, betweenness centrality, and PageRank score of the TAZs.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yang, X.; Lu, S.; Zhao, W.; Zhao, Z.
Exploring the Characteristics of an Intra-Urban Bus Service Network: A Case Study of Shenzhen, China. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 486.
https://doi.org/10.3390/ijgi8110486

**AMA Style**

Yang X, Lu S, Zhao W, Zhao Z.
Exploring the Characteristics of an Intra-Urban Bus Service Network: A Case Study of Shenzhen, China. *ISPRS International Journal of Geo-Information*. 2019; 8(11):486.
https://doi.org/10.3390/ijgi8110486

**Chicago/Turabian Style**

Yang, Xiping, Shiwei Lu, Weifeng Zhao, and Zhiyuan Zhao.
2019. "Exploring the Characteristics of an Intra-Urban Bus Service Network: A Case Study of Shenzhen, China" *ISPRS International Journal of Geo-Information* 8, no. 11: 486.
https://doi.org/10.3390/ijgi8110486