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

International Journal of Geo-Information

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

Xiping Yang 1,2,3 , Shiwei Lu 4,5,6,*, Weifeng Zhao 7 and Zhiyuan Zhao 8

1 School of Geography and Tourism, Shaanxi Normal University, Xi’an 710119, China; [email protected] 2 Geomatics Technology and Application key Laboratory of Qinghai Province, Xining 810001, China 3 Shaanxi Key Laboratory of Tourism Informatics, Xi’an 710119, China 4 School of Architecture and Urban Planning, Huazhong University of Science and Technology, Wuhan 430074, China 5 Key Laboratory of Urban Land Resources Monitoring and Simulation, Ministry of Land and Resources of China, Shenzhen 518034, China 6 Beijing Key Laboratory of Urban Spatial Information Engineering, Beijing 100038, China 7 College of Geology Engineering and Geomantics, Chang’an University, Xi’an 710054, China; [email protected] 8 Academy of Digital China (Fujian) and Fujian Collaborative Innovation Center for Big Data Applications in Governments, Fuzhou University, Fuzhou 350002, China; [email protected] * Correspondence: [email protected]

Received: 15 August 2019; Accepted: 28 October 2019; Published: 29 October 2019

Abstract: The urban bus service system is one of the most important components of a public transport system. Thus, exploring the spatial configuration of the urban bus service system promotes an understanding of the quality of bus services. Such an understanding is of great importance to urban transport planning and policy making. In this study, we investigated the spatial characteristics of an urban bus service system by using the complex network approach. First, a three-step workflow was developed to collect a bus operating dataset from a public website. Then, we utilized the P-space method to represent the bus service network by connecting all bus stop pairs along each bus line. With the constructed bus network, a set of network analysis indicators were calculated to quantify the role of nodes in the network. A case study of Shenzhen, China was implemented to understand the statistical properties and spatial characteristics of the urban bus network configuration. The empirical findings can provide insights into the statistical laws and distinct convenient areas in a bus service network, and consequently aid in optimizing the allocation of bus stops and routes.

Keywords: complex network; bus service system; spatial characteristic

1. Introduction A city can be considered as a place where people are more densely distributed, with developed industrial and commercial activities. Therefore, it is a place of aggregated people, resources, energy, and their interactions, and has been treated as a complex system since the 1950s. Recently, with the rapid growth of population and expansion of urban areas, the demand for urban mobility has been increasing. Consequently, big cities around the world have encountered a common challenge—traffic congestion. The development and improvement of urban public transport is an effective approach to alleviate urban traffic pressure. In a public transport system, the bus service system is a primary travel mode that attracts a large number of people because of its convenience and low cost. Therefore, when optimizing bus stops and lines, urban policy makers must understand the spatial configuration of urban bus systems to improve the service efficiency of these transport systems [1–3].

ISPRS Int. J. Geo-Inf. 2019, 8, 486; doi:10.3390/ijgi8110486 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2019, 8, 486 2 of 17

In a transport system, spatial interaction activity is a common phenomenon because people and cargo need to be transported from one place to another. Thus, different types of transport network systems are generated such as urban bus or metro networks, railroad networks, maritime networks, and aviation network systems. As a result, the network data model has become an effective tool for representing and extracting the latent topological properties of public transport networks [4–7]. In a network system, places and interaction activities can be modeled as nodes and edges, respectively. Complex network theory has been developed to investigate the network characteristics of the connections and interactions between elements in the last few decades [8,9]. More recently, this theory has been widely applied by researchers to urban transport-related studies for exploring urban polycentric spatial structures [10–12] or commuting structures [13–15], revealing human mobility patterns [16,17], identifying critical locations or the backbone of urban streets [18–21], and evaluating the vulnerability of urban metro networks [22–24]. Therefore, complex network analysis can be powerful for examining the underlying characteristics of systems that represent spatial interaction activities such as public transport systems. For urban bus service systems, a body of literature has utilized the sophisticated complex network theory to uncover the raw statistics of bus networks by calculating a set of indicators such as degree, centrality, and clustering coefficient [9,25–27]. For example, researchers can compare bus networks in different cities by quantifying their configurations with these indicators [28–30]. In statistical analysis, an important measurement method is to examine the degree distribution of nodes to determine whether the bus network is a scale-free network [31,32]. The scale-free property indicates that heterogeneity exists in the network [9,33]. Another important measurement is to analyze the small-world property of bus networks, which can be detected through the clustering coefficient and average path length [9,34–36]. For example, a spatial representation model based on the geographical location of bus stops and routes was proposed to perform a statistical study on the network features of the bus network in [37], however, the geographical spatial distribution characteristics (e.g., spatial interaction communities of bus networks) of the network indicators were not revealed. Obviously, these existing studies have mainly focused on investigating the statistical properties (e.g., degree distribution model, and small-world and scale-free laws) of urban bus networks, and the methods used in these studies were very similar; that is, some network indicators were defined to analyze the topological statistical laws of these indicators. Another study utilized the network analysis methods to detect the dynamics of urban structures, which mainly concentrated on identifying the temporal changes of an urban spatial structure by using big smart card data [12]. However, this study did not focus on the bus network configuration structure. Thus, the present study aimed to investigate the spatial characteristics of bus networks to determine nodes with dominant or low accessibility and connections in urban space, the spatial interaction structure generated by bus lines, and the relationship between the bus and road networks. Understanding these characteristics would provide a deep spatial insight of bus networks, which is meaningful to urban transportation and planners to optimize the original network such as by changing the route of some bus lines to improve the accessibility of areas with few buses passing through. In this study, we not only analyzed the statistical characteristics of the bus network, but also mapped these statistical indicators onto spatial areas to explore the spatial characteristics of the bus service system by using complex network methods. Like in previous studies, the typical degree distribution and small-world property were analyzed to quantify the whole topological features of the bus network. In addition, we also focused on the spatial distribution of three centrality indicators and the closely interacting communities formed by the bus service network. Specifically, we first developed a program to crawl the urban bus operating dataset from a public transport inquiry website and projected these bus stops onto a geographic space using a public map service platform. Next, the bus service spatial network was constructed using the P-space graph method to represent the linking relation between bus stops. Such a relation is implied in the configuration of bus lines. Finally, a set of network analysis indicators, namely, degree, clustering coefficient, average path length, and centrality, ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 3 of 17 to enhance our understanding of the statistical and spatial characteristics of the allocation of the bus service system on the basis of the spatial units of traffic analysis zones (TAZs). The contributions of this study are two-fold. First, it provides a deep insight into the statistical and spatial characteristics of an intra-urban bus service system in a metropolis of China through the ISPRS Int. J. Geo-Inf. 2019, 8, 486 3 of 17 classical complex network approach. Second, evaluation of the network properties and the importance of nodes in the bus service network can help urban governments, transportation and planningwere calculated departments, to evaluate and planners the network learn properties more about and intra-urban quantify the bus importance networks. of For nodes example, in the busby mappingservice network. the centrality A case of study the bus of Shenzhen,network onto China TAZs was, planners implemented could to identify enhance the our TAZs understanding with high or of lowthe accessibility, statistical and connectivity, spatial characteristics and influence of the on allocation others in ofthe the bus bus service service network. system on the basis of the spatial units of traffic analysis zones (TAZs). 2. StudyThe Area contributions and Dataset of this study are two-fold. First, it provides a deep insight into the statistical and spatial characteristics of an intra-urban bus service system in a metropolis of China through the classical 2.1.complex Study networkArea approach. Second, evaluation of the network properties and the importance of nodes in theThe bus case service study network area of this can work help urbanwas Shenzhen, governments, which transportation is located in the and southeast planning of departments, China, near Hongand planners Kong. It learn was moredesignated about intra-urbanas the first busspecial networks. economic For zone example, after by the mapping launch theof the centrality reform of and the opening-upbus network policy onto TAZs,of China. planners Shenzh coulden is identify considered the TAZs as a special with high economic or low accessibility,zone; this means connectivity, that it benefitsand influence from a on number others inof the welfare bus service policies network. in economic development (e.g., creating a favorable investment environment, reducing customs duty, and allowing the introduction of advanced 2. Study Area and Dataset technologies). This city has experienced tremendous change after being developed into a famous international2.1. Study Area metropolis from three fishing villages over the past four decades. Currently, it encompasses 10 administrative districts, which are further divided into downtown areas, suburbs, and ruralThe caseareas study according area ofto thisthe workeconomic was Shenzhen,development which (Figure is located 1). Shenzhen in the southeastcovers an of area China, of approximatelynear Hong Kong. 2000 km It was2 and designated has a population as the of first more special than economic15 million, zone making after it thethe most launch densely of the populatedreform and among opening-up Chinese policy cities of [15,38]. China. The Shenzhen unique is socioeconomic considered as aand special demographic economic zone;status thisof Shenzhenmeans that makes it benefits it an interesting from a number area for of welfarethe study policies of urban in bus economic networks. development (e.g., creating a favorableTo meet investment the massive environment, daily travel reducing demand customs of duty,citizens, and allowingthe government the introduction has constructed of advanced a multimodaltechnologies). public This transport city has service experienced system tremendous comprised changeof buses, after subways, being developedtaxis, and bicycles. into a famous This studyinternational focused metropolis on the bus from service three system. fishing The villages service over area the generated past four decades. by bus stops Currently,it has a radius encompasses of 500 m,10 accounting administrative for more districts, than which 80% of are the further entire divided area of Shenzhen. into downtown This coverage areas, suburbs, is outstanding and rural when areas 2 comparedaccording towith the economicother large development cities in (FigureChina. 1).Du Shenzhene to the coversconvenience an area ofand approximately low fare of 2000 buses, km approximatelyand has a population 55.6% of of passengers more than 15in million,Shenzhen making have itopted the most to travel densely by bus. populated Therefore, among Shenzhen Chinese wascities selected [15,38]. as The the uniquecase study socioeconomic to explore the and characte demographicristics of status a bus of service Shenzhen system. makes The it results an interesting of this studyarea for can the be studyreferenced of urban by other bus networks. cities to improve the efficiency of their bus services.

Figure 1. Study area and bus stops. Figure 1. Study area and bus stops. To meet the massive daily travel demand of citizens, the government has constructed a multimodal public transport service system comprised of buses, subways, taxis, and bicycles. This study focused on the bus service system. The service area generated by bus stops has a radius of 500 m, accounting for more than 80% of the entire area of Shenzhen. This coverage is outstanding when compared with other large cities in China. Due to the convenience and low fare of buses, approximately 55.6% of ISPRS Int. J. Geo-Inf. 2019, 8, 486 4 of 17 passengers in Shenzhen have opted to travel by bus. Therefore, Shenzhen was selected as the case study to explore the characteristics of a bus service system. The results of this study can be referenced by other cities to improve the eﬃciency of their bus services.

2.2. Dataset Collection The bus dataset used in this study was acquired from a public transport inquiry website (www.8684.cn/) that provides bus query services for most Chinese cities. The website updates in real time, that is, once the operation of buses (e.g., bus stops and bus lines) shows a change in the city. The website is linked to the homepage of the Shenzhen Bus Company (the company in charge of Shenzhen’s bus system) to provide a bus inquiry service for citizens. Thus, the dataset collected from this website is reliable for exploring characteristics of the urban bus system. A three-step workﬂow was proposed to collect the bus data based on this website. First, we developed a web crawler program to crawl all bus lines from the website including every bus line number and bus stop name that each bus passed. Consequently, we generated a set of bus stops. Second, we projected these stops onto a spatial map. To achieve this goal, we utilized the Amap platform, which is a famous map service operator in China to obtain the geographic coordinates of each stop [39]. The platform provides the service of a geocoding API (application programming interface) to interpret an address into the corresponding latitude and longitude on the basis of its coordinate system. Finally, we transformed the latitude and longitude into a universal WGS84 (World Geodetic System 1984) coordinate system to match the other geospatial data of the study area. Through this workﬂow, a total of 1016 bus lines were obtained in Shenzhen. Each bus line operates in a two-way fashion, which implies that the buses take the same route in outward and return directions. Thus, two bus stops are located on both sides of the road for the same stop. This study did not consider the directions of the bus lines, and pairs of bus stops with the same name on either side of the road were merged into one stop. Accordingly, a total of 5334 bus stops were generated. Figure1 shows the spatial distribution of the extracted bus stops, which were mainly distributed along the road network.

3. Complex Network Analysis In this section, the construction of the proposed complex network based on the bus lines and bus stops is initially described. Then, some network indicators are introduced to quantify the structure and centrality of the urban bus service network.

3.1. Network Construction Generally, two popular methods are used to represent transport network systems, namely, L-space and P-space methods. The L-space method directly connects the adjacent bus stops along the same bus line, as shown in Figure2b, which could only represent the original conﬁguration of the bus network. The P-space method connects all bus stop pairs that pass along the same bus line (Figure2c). Unlike the L-space method, this method is used to measure whether two stops are accessible by the same bus line, thus it generates a completely connected graph [9,40]. For example, bus line 3 in Figure2 passes three stops, namely I, G, and J. In L-space, there is no direct connection between stop I and stop J (Figure2b), but there is a direct connection between the two stops in the P-space because they can access each other through bus line 3 (Figure2c). Therefore, the P-space method is more suitable for analyzing the spatial transfer and correlation of bus stops. This study utilized the P-space method to construct the bus service network. In the P-space bus service network G = (V, E, W), a node vi is a bus stop i, and a weight is assigned to each link of a bus line. First, the weight wij of edge eij between vi and vj in the network is initialized as wij = 0. For every bus line, the speciﬁc rule to obtain the weight matrix W is as follows: ISPRS Int. J. Geo-Inf. 2019, 8, 486 5 of 17

(1) If two nodes vi and vj can be accessed without any transfer, it is considered that the two nodes are connected to each other, and the corresponding weight wij between vi and vj is set to plus 1. (2) For each pair of nodes on the same bus line, there is no need to make any transfer, as shown in Figure2c. For instance, bus line 1 passes through the four stops of A, B, C, and D. This line can be converted into six links: A–B, A–C, A–D, B-C, B–D, and C–D. Finally, the weight matrix of a bus service network derived from P-space method is W = {wij}. ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 5 of 17 ( wij + 1, i , j wij = +≠ wijwij , other1, w =  ij wother,  ij

Figure 2. Constructing the complex network based on bus lines. Figure 2. Constructing the complex network based on bus lines. The spatial analysis units in this study were the TAZs (traﬃc analysis zones). TAZs are the basic The spatial analysis units in this study were the TAZs (traffic analysis zones). TAZs are the basic spatial analysis units used in transportation planning to forecast the trip generation and travel demand. spatial analysis units used in transportation planning to forecast the trip generation and travel It is assumed that people living in the same TAZ show similar demographic characteristics [41,42]. demand. It is assumed that people living in the same TAZ show similar demographic characteristics The design of TAZs is usually implemented by urban planners or transport geographers. Therefore, [41,42]. The design of TAZs is usually implemented by urban planners or transport geographers. it is reasonable for planners and researchers to adopt the TAZ as a basic unit for researching urban Therefore, it is reasonable for planners and researchers to adopt the TAZ as a basic unit for transportation problems. In this study, we obtained the TAZ ﬁle from the local transport department. researching urban transportation problems. In this study, we obtained the TAZ file from the local We aggregated the constructed stop-based network by excluding the edges when both stops were transport department. We aggregated the constructed stop-based network by excluding the edges located in the same TAZ and generated the new TAZ-based network GTAZ = (V, E, W). In this network, when both stops were located in the same TAZ and generated the new TAZ-based network GTAZ = node Vi represents TAZ i, edge Eij represents the connection between TAZ i and TAZ j, and weight wij (V, E, W). In this network, node Vi represents TAZi, edge Eij represents the connection between TAZ represents the number of bus lines that pass through the two TAZs. Ultimately, a TAZ-based network i and TAZ j, and weight wij represents the number of bus lines that pass through the two TAZs. with more than 965 nodes and 71,000 links was constructed for use in the subsequent analysis. Ultimately, a TAZ-based network with more than 965 nodes and 71,000 links was constructed for use in3.2. the Topological subsequent Analysis analysis. of the Bus Service Network Structure

3.2. TopologicalIn the field Analysis of complex of the Bus network Service theory, Network a networkStructure can be classified into different types (e.g., random, small-world, and free-scale networks), according to their statistical characteristics such as degreeIn distribution,the field of complex clustering network coefficient, theory, and averagea networ pathk can length. be classified Therefore, into this different section presentstypes (e.g., the random,probe into small-world, the overall topologicaland free-scale features networks), of the according bus service to networktheir statistical by calculating characteristics the three such basic as degreeindicators. distribution, The weight clustering of edge coefficient, is not considered and aver in theage topologicalpath length. analysis. Therefore, this section presents the probe into the overall topological features of the bus service network by calculating the three basic indicators.(1) Degree The and weight degree of distribution edge is not considered in the topological analysis. (1) Degree and degree distribution Degree is a basic measurement index in network analysis and represents the total number of edges connectedDegree to is a nodea basic [8 ].measurement For an undirected index network,in network the analysis degree ofand node representsi can be definedthe total as number follows: of edges connected to a node [8].N For an( undirected network, the degree of node i can be defined as X aij = 1, i f node i connecting to node j follows: ki = aij, (1) aij = 0, otherwise j=1 N a =1 , if node i connecting to node j  ij , k=iij a  (1) a=0 , otherwise j=1  ij

In this study, N represents the total number of TAZs, and the degree ki 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: n pk() = k (2) N

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(2) Average path length

The average path length presents the average number of edges along the shortest paths between all possible node pairs in the network [43]. This parameter can be calculated as

1 X L = dij (3) 1 N(N 1) 2 − i,j where dij is the number of edges of the shortest path between nodes i and j. A small average path length indicates good network accessibility.

(3) Clustering coeﬃcient

The clustering coefficient is used to measure the extent of the local aggregation in the network [43]. The clustering coefficient of a node can be defined as the proportion of the actual edges Ei between nodes within its neighborhood divided by the maximal possible edges between them:

E C = i . (4) i k (k 1)/2 i i − The clustering coeﬃcient of the entire network is the average of all nodes in the network. The larger the clustering coeﬃcient of the network, the greater the local aggregation. This parameter can be expressed as follows: N 1 X C = C . (5) N i i=1

3.3. Nodes’ Centrality Measurement of the Weighted Bus Network Structure In this section, weight is considered in measuring the importance of nodes (TAZs) in the conﬁguration of the bus service network. Generally, centrality is used to quantify the extent of importance of the nodes in the network. Therefore, the node of closeness centrality, betweenness centrality, and PageRank score were used to represent the TAZs’ accessibility, connectivity, and inﬂuence on others in the network, respectively.

(1) Closeness centrality

The closeness centrality of a node is used to quantify how close the node is to others by using the shortest path [44], which is deﬁned as the reciprocal of the average shortest path length from the node to others: C N 1 Ci = P− (6) dij j V,j,i ∈ where dij 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.

(2) Betweenness centrality ISPRS Int. J. Geo-Inf. 2019, 8, 486 7 of 17

Betweenness centrality measures the connectivity of a node, which reﬂects the capacity of the intermediate transitivity of the node in the network [45]. The index is deﬁned as follows:

X n (i) B 1 jk Ci = (7) (N 1)(N 2) njk k,j V, k,j,i − − ∈ where njk represents the number of all shortest paths between TAZ j and TAZ k, and njk(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.

(3) PageRank score

PageRank score is used to measure the importance of nodes by comprehensively considering the importance of the nodes it connects [46]. It considers a strongly connected node to be more important than nodes with few connections. Therefore, a PageRank score can diﬀerentiate the importance of nodes with the same degree or strength. For an undirected and weighted network, the PageRank score can be calculated as follows: 1 X wij PRj PR = (1 λ) + λ × (8) i − N k e E i ij∈ i where λ is a free parameter, and the value of 0.85 was used in this study for the calculation [45]; Ei is the set of edges that connects with node i; ki represents the degree of node i; and PRi 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 Figure3 shows the degree of spatial distribution. On the basis of the method of network construction, the degree of a TAZ indicates the number of directly connected TAZs, that is, at least one bus line runs between the TAZ and others. Thus, the larger the degree of the TAZ, the greater the number of other TAZs that can be reached by taking a bus without transfer. As shown in Figure3, the TAZs located in the southern part of Shenzhen have more degree distributions than those in the northern part (downtown areas). Figure4a displays the statistical degree distribution, the minimum and maximum values of degree were 3 and 466, respectively, and the average value of degree was 148. For the cumulative degree distribution (Figure4b), the distribution appears as an approximate process of linear decline, and the decay process can be well ﬁtted by an exponential function, which is consistent with previous studies [28,32,47]. This result demonstrates that the degree does not follow the power law distribution in Shenzhen, indicating that the bus service network does not show a scale-free network property. Moreover, this observation is consistent with the results in [48], which implies that urban public transport systems rule out the law of scale-free because the stops are connected nearly randomly in P-space representation [9,31]. Furthermore, the results illustrate that the conﬁguration of the bus service system in Shenzhen is relatively fair in terms of the direct arrival of buses to few TAZs with enormous reachability. ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 7 of 17

B 1 nijk () C= (7) i --  (1)(2)N Nnk, j∈≠≠ V， k j i jk where njk represents the number of all shortest paths between TAZ j and TAZ k, and njk(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. (3) PageRank score

1 wPR× （） ij j PRi =1 - λ + λ  (8) Nk∈ eEij i i where λ is a free parameter, and the value of 0.85 was used in this study for the calculation [45]; Ei is the set of edges that connects with node i; ki represents the degree of node i; and PRi 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.ISPRS Degree Int. J. Geo-Inf. Distribution2019, 8, 486 8 of 17

ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 8 of 17 FigureFigure 3. 3. SpatialSpatial degree degree distribution. distribution.

Figure 4. Statistical degree distribution. Figure 4. Statistical degree distribution. 4.1.2. Small-World Property Figure 3 shows the degree of spatial distribution. On the basis of the method of network In complex network theory, the average path length and clustering coefficient are the two main construction, the degree of a TAZ indicates the number of directly connected TAZs, that is, at least measurements of small-world property network. A small-world network generally has a similar one bus line runs between the TAZ and others. Thus, the larger the degree of the TAZ, the greater average path length and a larger clustering coefficient compared to a random network of the same the number of other TAZs that can be reached by taking a bus without transfer. As shown in Figure size [43]. The average path length of the bus service network was 2.01, which indicates that people 3, the TAZs located in the southern part of Shenzhen have more degree distributions than those in only need one transfer on average to reach any TAZ of the city by taking buses. For the clustering the northern part (downtown areas). Figure 4a displays the statistical degree distribution, the coefficient of the entire network, the value of Shenzhen was 0.47. The average path length and minimum and maximum values of degree were 3 and 466, respectively, and the average value of clustering coefficient of a random network with the same size were 1.85 and 0.15, respectively. Thus, the degree was 148. For the cumulative degree distribution (Figure 4b), the distribution appears as an bus service network of Shenzhen presents the small-world property, which is beneficial for improving approximate process of linear decline, and the decay process can be well fitted by an exponential both robustness and stability in network planning and protection, and can be used to understand and function, which is consistent with previous studies [28,32,47]. This result demonstrates that the interpret the bus service network. Figure5 shows the spatial distribution of the clustering coe fficient degree does not follow the power law distribution in Shenzhen, indicating that the bus service of TAZs. The high clustering coefficient of TAZs are mainly located at the edge of the city. Such places network does not show a scale-free network property. Moreover, this observation is consistent with including mountains, forests and farmland are sparsely populated areas. In comparison with Figure3, the results in [48], which implies that urban public transport systems rule out the law of scale-free the TAZs with a large degree had a low clustering coefficient, and the correlation between degree and because the stops are connected nearly randomly in P-space representation [9, 31]. Furthermore, the clustering coefficient showed a nearly opposite tendency (Figure6). In other words, the larger the results illustrate that the configuration of the bus service system in Shenzhen is relatively fair in terms degree of the TAZ, the smaller the clustering coefficient, which is consistent with studies of the Chinese of the direct arrival of buses to few TAZs with enormous reachability. aviation system and railway network [4,49]. 4.1.2. Small-World Property In complex network theory, the average path length and clustering coefficient are the two main measurements of small-world property network. A small-world network generally has a similar average path length and a larger clustering coefficient compared to a random network of the same size [43]. The average path length of the bus service network was 2.01, which indicates that people only need one transfer on average to reach any TAZ of the city by taking buses. For the clustering coefficient of the entire network, the value of Shenzhen was 0.47. The average path length and clustering coefficient of a random network with the same size were 1.85 and 0.15, respectively. Thus, the bus service network of Shenzhen presents the small-world property, which is beneficial for improving both robustness and stability in network planning and protection, and can be used to understand and interpret the bus service network. Figure 5 shows the spatial distribution of the clustering coefficient of TAZs. The high clustering coefficient of TAZs are mainly located at the edge of the city. Such places including mountains, forests and farmland are sparsely populated areas. In comparison with Figure 3, the TAZs with a large degree had a low clustering coefficient, and the correlation between degree and clustering coefficient showed a nearly opposite tendency (Figure 6). In other words, the larger the degree of the TAZ, the smaller the clustering coefficient, which is consistent with studies of the Chinese aviation system and railway network [4,49].

ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 9 of 17 ISPRS Int. J. Geo-Inf. 2019, 8, 486 9 of 17 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 9 of 17

. . Figure 5. Spatial distribution of the clustering coefficient. Figure 5. Spatial distribution of the clustering coeﬃcient. Figure 5. Spatial distribution of the clustering coefficient.

Figure 6. Figure 6. Correlation of degree and clustering coecoefficient.fficient. 4.2. Spatial Characteristic ofFigure the Bus 6. Correlation Service Network of degree and clustering coefficient. 4.2. Spatial Characteristic of the Bus Service Network 4.2.1.4.2. Spatial Charactering Characteristic Edge Weightof the Bus of Service Bus Service Network Network 4.2.1. Charactering Edge Weight of Bus Service Network In this section, the weight of edges is considered in analyzing the importance of each TAZ in 4.2.1. Charactering Edge Weight of Bus Service Network a busIn service this section, network. the weight As described of edges in is Section consider 3.1ed, thein analyzing weight w ijtherepresents importance the of number each TAZ of busin a In this section, the weight of edges is considered in analyzing the importance of each TAZ in a lines.bus service Figure network.7 shows theAs constructeddescribed in weighted Section 3.1, network, the weight and thewij color represents represents the number the weight of bus of edges. lines. Figure8 shows the statistical distribution of weight. The weight exhibits a long-tailed distribution Figurebus service 7 shows network. the constructed As described weighted in Section network, 3.1, the weightand the wcolorij represents represents the the number weight of ofbus edges. lines. (Figure8a); that is, only a few TAZ pairs have an extremely large number of bus lines that pass through, FigureFigure 87 showsshows the the statistical constructed distribution weighted of network, weight. andThe weightthe color exhibits represents a long-tailed the weight distribution of edges. whereas the majority of TAZ pairs have few bus lines. We utilized a typical power law function (FigureFigureβ 88a); shows that theis, onlystatistical a few distribution TAZ pairs ofhave weight. an extremely The weight large exhibits number a long-tailed of bus lines distribution that pass p w− to capture the long-tailed distribution, where p represents the cumulative probability of weight through,(Figure∝ 8a); whereas that is,the only majority a few of TAZ TAZ pairs pairs have have an few extremely bus lines. large We number utilized of a typicalbus lines power that passlaw w, and β represents the friction coefficient of decay. As shown in Figure8b, the distribution can be through, whereas∝ - theβ majority of TAZ pairs have few bus lines. We utilized a typical power law approximatelyfunction p fittedw using to capture a straight the linelong-tailed on a log–log distribution, scale, which where impliesp represents that the weight the cumulative follows a -β powerprobabilityfunction law p distributionof ∝weightw wto and ,capture and the frictionβ representsthe long-tailed coeffi cientthe friction βdistribution,is 1.764. coefficient Detecting where of decay. thep represents distribution As shown the decayin cumulative Figure in bus 8b, servicetheprobability distribution network of weight connectionscan be wapproximately, and is a prerequisiteβ represents fitted for usingthe understanding friction a straight coefficient line constrained on of a decay. log–log complex As scale, shown networks which in Figure implies from 8b, a geospatialthatthe thedistribution weight perspective. follows can be a approximately power law dist fittedribution using and a the straight friction line coefficient on a log–log β is scale, 1.764. whichDetecting implies the distributionthat the weight decay follows in bus a servicepower lawnetwork distribution connections and theis a friction prerequisite coefficient for understanding β is 1.764. Detecting constrained the complexdistribution networks decay fromin bus a servicegeospatial network perspective. connections is a prerequisite for understanding constrained complex networks from a geospatial perspective.

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Figure 7. Weight of edges. FigureFigure 7.7. Weight ofof edges.edges.

FigureFigure 8.8. Statistical distributiondistribution ofof thethe weightweight ofof edges.edges. Figure 8. Statistical distribution of the weight of edges. In addition, it is apparent that distance decay also exists in the bus service network. As shown In addition, it is apparent that distance decay also exists in the bus service network. As shown in Figure7, most edges with larger weights usually have a shorter distance between the two TAZs, in Figure 7, most edges with larger weights usually have a shorter distance between the two TAZs, which follows a typical geographical phenomenon, namely, distance decay. Moreover, community which follows a typical geographical phenomenon, namely, distance decay. Moreover, community detection is implemented for the bus service network in order to check whether adjacent TAZs can detection is implemented for the bus service network in order to check whether adjacent TAZs can be classified into the same community. In complex networks, community detection can partition be classified into the same community. In complex networks, community detection can partition the the whole network into several densely connected subnetworks based on the weight of edges, and whole network into several densely connected subnetworks based on the weight of edges, and a a community is constituted by some tightly connected nodes. Therefore, community detection has community is constituted by some tightly connected nodes. Therefore, community detection has been been introduced into geographical research to divide the spatial interaction of cohesive communities. introduced into geographical research to divide the spatial interaction of cohesive communities. In In this study, TAZs within the same community represent those that can be closely connected by bus this study, TAZs within the same community represent those that can be closely connected by bus lines. The community detection algorithm utilized in this study was the fast modularity maximization lines. The community detection algorithm utilized in this study was the fast modularity algorithm, which shows better performance in detecting weighted and undirected networks; a detailed maximization algorithm, which shows better performance in detecting weighted and undirected description of this algorithm can be found in [50]. networks; a detailed description of this algorithm can be found in [50]. The result of community detection is shown in Figure9, in which all TAZs were grouped into six communities. It can be seen that spatially adjacent TAZs have been classified as the same community, which indicates that spatial distance influences the connection relationships of an intra-urban bus network. Through a comparison with Figure1, the detected communities were similar to Shenzhen’s administrative divisions. For example, communities C1, C2, and C4 cover most of the TAZs in the

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Guangming, Baoan, and Nanshan districts, respectively. The community C3 mainly includes the TAZs of the Longhua district. However, the three districts (Futian, Luohu, and Yantian) in the south of Shenzhen were identiﬁed as community C5, which indicates that the bus lines could connect bus stops between the three districts very well. Similarly, the bus lines also tightly connect the bus stops in ISPRSDapeng, Int. J.Pingshan, Geo-Inf. 2019 and, 8, x theFOR northPEER REVIEW of Longgang (Community C6). 11 of 17

FigureFigure 9. 9. TheThe result result of of community community detection; detection; one one color color represents represents one one community. community.

4.2.2.The Charactering result of community Centrality ofdetection Traffic Analysisis shown Zones in Figure in Bus 9, in Service which Network all TAZs were grouped into six communities.We calculated It the can closeness be seen centrality, that spatially betweenness adjacent centrality, TAZs have and been PageRank classified score as based the onsame the community,weighted bus which service indicates network that to measure spatial distance the centrality influences of the the TAZs connection in the bus relationships service system. of an In intra- order urbanto visualize bus network. the spatial Through distribution a comparison of the three with centrality Figure 1, indicators, the detected for communities each centrality were indicator, similar the to Shenzhen’sfamous approach administrative of natural divisi breaksons. classification For example, was communities utilized to classify C1, C2, TAZs and into C4 six cover classes most according of the TAZsto their in statistical the Guangming, characteristics. Baoan, Naturaland Nanshan breaks districts, are designed respectively. to determine The thecommunity best arrangement C3 mainly of includesvalues into the di TAZsfferent of classes the Longhua according district. to their However, statistical the characteristics; three districts their (Futian, determination Luohu, and requires Yantian) an initerative the south process of Shenzhen that seeks were to minimize identified the as variance commu withinnity C5, classes which and indicates maximize that the the variance bus lines between could connectclasses ofbus groups stops withbetween similar the elementsthree districts according very towe theirll. Similarly, statistical the features bus lines [51 ].also Thus, tightly this connect method thehas bus been stops extensively in Dapeng, used Pingshan, to classify and and the visualize north of geographicLonggang (Community data. After classification, C6). the dataset can be classified into different groups in ascending order. Therefore, the six classes are hierarchical 4.2.2.levels, Charactering and were denoted Centrality as L1 of, L2Traffic, L3, L4Analysis, L5, L6 Zones, where inL1 Busand ServiceL6 represent Network the lowest and highest classes, respectively. Figures9 and 10 show the statistical and spatial distributions of the six levels of groups for the closeness centrality, betweenness centrality, and PageRank score of TAZs, respectively. Note that this study did not use the same standard for classifying the three indicators; we executed the natural breaks for each centrality indicator separately. Therefore, the natural breaks method was used to help visualize the spatial hierarchical differences of TAZs for each centrality indicator. As previously mentioned, closeness measures the extent of ease in accessing other TAZs by taking a bus. The percentage of closeness in the six groups was close to a normal distribution, and the number of TAZs equal and greater than level L4 accounted for more than 55% of the total (Figure 10). TAZs with high bus accessibility were mainly concentrated in the southern areas of Shenzhen (Figure 11). For betweenness centrality, the distribution in the six groups showed a declining trend, and the number of TAZs in level L1 accounted for approximately 50% of all TAZs. The betweenness index quantifies the connectivity and transitivity capabilities of the TAZ in the bus service network, and the percentage of TAZs with high bus connectivity (being equal and greater than L4) only accounted for less than 17%Figure of all TAZs10. Statistical (Figure distribution 10). As shown of the in six Figure levels 11of ,groups. these high L1 represents bus connectivity the percentage areas of were traffic mainly scatteredanalysis over zones diff erent(TAZs) districts with level of L1 the in city all TAZs to connect. various urban areas. The statistical distribution of the PageRank score was similar to that of the closeness centrality; the main difference is that the numberWe calculated of TAZs lying the closeness in less than centrality, level L4 betweennesswas dominant centrality, and accounted and PageRa for approximatelynk score based 60%on the of weighted bus service network to measure the centrality of the TAZs in the bus service system. In order to visualize the spatial distribution of the three centrality indicators, for each centrality indicator, the famous approach of natural breaks classification was utilized to classify TAZs into six classes according to their statistical characteristics. Natural breaks are designed to determine the best arrangement of values into different classes according to their statistical characteristics; their determination requires an iterative process that seeks to minimize the variance within classes and maximize the variance between classes of groups with similar elements according to their statistical features [51]. Thus, this method has been extensively used to classify and visualize geographic data.

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Figure 9. The result of community detection; one color represents one community.

The result of community detection is shown in Figure 9, in which all TAZs were grouped into six communities. It can be seen that spatially adjacent TAZs have been classified as the same ISPRS Int. J.community, Geo-Inf. 2019 which, 8, 486 indicates that spatial distance influences the connection relationships of an intra- 12 of 17 urban bus network. Through a comparison with Figure 1, the detected communities were similar to Shenzhen’s administrative divisions. For example, communities C1, C2, and C4 cover most of the all TAZs (FigureTAZs in 10the). Guangming, The PageRank Baoan, score and Nanshan evaluates districts, the importance respectively. andThe community inﬂuence C3 of mainly TAZs in the bus includes the TAZs of the Longhua district. However, the three districts (Futian, Luohu, and Yantian) service network.in the south The of spatial Shenzhen distribution were identified of PageRankas community was C5, similarwhich indicates to the closenessthat the bus centrality. lines could The TAZs with a highconnect PageRank bus stops score between were the mainly three districts concentrated very well. inSimilarly, the Southern the bus lines Nanshan, also tightly Futian, connect and Luohu administrativethe bus districts stops in Dapeng, (Figure Pingshan, 11). Moreover, and the north the important of Longgang TAZs (Community were those C6). that play important roles in the geospatial bus network and represent regions that need to be protected, which could further 4.2.2. Charactering Centrality of Traffic Analysis Zones in Bus Service Network assist decision makers in identifying potentially important areas.

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After classification, the dataset can be classified into different groups in ascending order. Therefore, the six classes are hierarchical levels, and were denoted as L1, L2, L3, L4, L5, L6, where L1 and L6 represent the lowest and highest classes, respectively. Figures 9 and 10 show the statistical and spatial distributions of the six levels of groups for the closeness centrality, betweenness centrality, and PageRank score of TAZs, respectively. Note that this study did not use the same standard for classifying the three indicators; we executed the natural breaks for each centrality indicator Figure 10.FigureStatistical 10. Statistical distribution distribution of theof the six six levels levels of of groups. groups. L1 representsL1 represents the percentage the percentage of traffic of traﬃc separately. Therefore, the natural breaks method was used to help visualize the spatial hierarchical analysis zonesanalysis (TAZs) zones (TAZs) with levelwith levelL1 in L1 allin all TAZs. TAZs. differences of TAZs for each centrality indicator. We calculated the closeness centrality, betweenness centrality, and PageRank score based on the weighted bus service network to measure the centrality of the TAZs in the bus service system. In order to visualize the spatial distribution of the three centrality indicators, for each centrality indicator, the famous approach of natural breaks classification was utilized to classify TAZs into six classes according to their statistical characteristics. Natural breaks are designed to determine the best arrangement of values into different classes according to their statistical characteristics; their determination requires an iterative process that seeks to minimize the variance within classes and maximize the variance between classes of groups with similar elements according to their statistical features [51]. Thus, this method has been extensively used to classify and visualize geographic data.

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

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As previously mentioned, closeness measures the extent of ease in accessing other TAZs by taking a bus. The percentage of closeness in the six groups was close to a normal distribution, and the number of TAZs equal and greater than level L4 accounted for more than 55% of the total (Figure 10). TAZs with high bus accessibility were mainly concentrated in the southern areas of Shenzhen (Figure 11). For betweenness centrality, the distribution in the six groups showed a declining trend, and the number of TAZs in level L1 accounted for approximately 50% of all TAZs. The betweenness index quantifies the connectivity and transitivity capabilities of the TAZ in the bus service network, and the percentage of TAZs with high bus connectivity (being equal and greater than L4) only accounted for less than 17% of all TAZs (Figure 10). As shown in Figure 11, these high bus connectivity areas were mainly scattered over different districts of the city to connect various urban areas. The statistical distribution of the PageRank score was similar to that of the closeness centrality; the main difference is that the number of TAZs lying in less than level L4 was dominant and accounted for approximately 60% of all TAZs (Figure 10). The PageRank score evaluates the importance and influence of TAZs in the bus service network. The spatial distribution of PageRank was similar to the closeness centrality. The TAZs with a high PageRank score were mainly concentrated in the Southern Nanshan, Futian, and Luohu administrative districts (Figure 11). Moreover, the important TAZs were those that play important roles in the geospatial bus network ISPRS Int. J. Geo-Inf. 2019, 8, 486 13 of 17 and represent regions that need to be protected, which could further assist decision makers in identifying potentially important areas. 4.2.3. Correlation of Centrality between Bus Network and Road Network 4.2.3. Correlation of Centrality between Bus Network and Road Network As previously described, the degree reflects the number of TAZs that can be reached by taking a busAs without previously any transfers.described, Meanwhile,the degree reflects the closeness, the number betweenness, of TAZs that and can PageRank be reached measure by taking the TAZs’a bus accessibility,without any connectivity,transfers. Meanwhile, and influence the oncloseness, others inbetweenness, the network, and respectively. PageRank In measure this section, the weTAZs’ further accessibility, examined connectivity, the relationship and influence between theon others degree in and the the network, three centrality respectively. indexes, In this as section, shown inwe Figure further 12 examined. The Pearson’s the relationship correlation between coefficients the degree of closeness, and the betweenness,three centrality and indexes, PageRank as shown were 0.953,in Figure 0.761, 12. and The 0.995, Pearson’s respectively, correlation which coefficien demonstratests of closeness, the strong correlationbetweenness, between and PageRank the degree were and these0.953, three0.761, indexes. and 0.995, Therefore, respectively, in the buswhich service demonstrates network, athe TAZ strong with correlation a high degree between usually the has degree great accessibility,and these three connectivity, indexes. Therefore, and influence. in the bus service network, a TAZ with a high degree usually has great accessibility, connectivity, and influence.

Figure 12. Correlation between degree and centrality. Figure 12. Correlation between degree and centrality. In a city, because the bus travels along the urban network of roads, it is of interest whether the structure of the urban road network is correlated with the bus service network. In order to address this gap, we examined the correlation of the three centrality indicators between the bus service network and road network. Based on the theory presented in Section 3.3, we calculated the closeness, betweenness, and PageRank of urban road nodes and aggregated the average value for each TAZ. Similarly, Pearson’s correlation coefficient was used to measure the correlation between the bus network and road network, and we normalized the centrality indicators by using the maximum and minimum before calculating the correlation coefficient. As shown in Figure 13, the correlation coefficients of closeness, betweenness, and PageRank were 0.452, 0.104, and 0.003, respectively. The correlation coefficient indicates that there was some correlation of closeness between the bus network and road network, which indicates that the convenience of the road network may be correlated with the bus network in some TAZs. For betweenness, the coefficient indicates that the connectivity of the bus network has a low correlation with the intermediate transitivity of the urban road network. However, the PageRank of the bus network was nearly unrelated with that of the road network. In the road network, the nodes connect with their adjacent nodes by road segments; usually the influence of road nodes is very small, which results in a relatively concentrated PageRank score (about 0.45 in Figure 13c) of nodes in the road network. In contrast, in the bus network, a bus stop can connect with many other stops only if there are bus lines passing through these stops. Therefore, the PageRank of the bus network is more dispersed. ISPRS Int. J. Geo-Inf. 2019, 8, 486 14 of 17 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 14 of 17

FigureFigure 13.13. CorrelationCorrelation ofof centralitycentrality betweenbetween thethe busbus networknetwork andand roadroad network.network.

5. ConclusionsIn a city, because and Future the bus Work travels along the urban network of roads, it is of interest whether the structureThis studyof the aimed urban to road investigate network the is spatial correlated structure withof the urban bus busservice networks network. using Incomplex order tonetwork address theory.this gap, We we took examined Shenzhen the as correlation a case study of andthe th developedree centrality a three-step indicators workflow between to the collect bus theservice bus servicenetwork dataset and road from network. a public Based transport on the inquiry theory website. presented On in the Section basis 3. of3, thewe operatingcalculated configuration the closeness, ofbetweenness, bus lines, the and P-space PageRank graph of principle urban road was nodes used toand establish aggregated the busthe serviceaverage network value for to each represent TAZ. theSimilarly, relationship Pearson’s among correlation bus stops. coefficient Then, network was used analysis to measure indicators the were correlation calculated between to analyze the thebus statisticalnetwork and properties road network, of the network and we and normalized quantify the accessibility,centrality indicators connectivity, by using and influencethe maximum of nodes and inminimum the network. before We calculating found that thethe buscorrelation network coeffi of Shenzhencient. As follows shown a small-worldin Figure 13, property, the correlation with an averagecoefficients path of length closeness, of 2.01 betweenness, and clustering and coe PageRankfficient of 0.47.were This0.452, means 0.104, that and people 0.003, needrespectively. one transfer The oncorrelation average coefficient to reach any indicates TAZ of that the there city bywas taking some buses.correlation The of clustering closeness coe betweenfficient the represents bus network the extentand road of the network, local aggregation which indicates in the that network, the convenience so it indicates of the the road connectivity network of may the be TAZ correlated with its localwith adjacentthe bus network TAZs. The in twosome indicators TAZs. For could betweenness, be used to the design coefficient an urban indicates bus network, that the and connectivity a well-designed of the busbus networknetwork shouldhas a low try tocorrelation achieve a with small the average intermed pathiate length transitivity and high of clustering the urban coe roadfficient. network. The weightHowever, of edges the PageRank represents of the the spatial bus network interaction was between nearly unrelated the TAZs, with and thethat heavy-tailed of the road distributionnetwork. In ofthe weight road indicatesnetwork, that the only nodes a few connect edges havewith antheir extremely adjacent large nodes weight. by Basedroad segments; on the weight usually of edges, the weinfluence identified of road six spatially nodes is interacting very small, communities which results from in the a relatively bus service concentrated network, and PageRank discussed score the similarity(about 0.45 and in diFigurefference 13c) between of nodes detected in the communitiesroad network. and In contrast, administrative in the districts,bus network, which a providesbus stop ancan understanding connect with many of the other spatial stops interaction only if there structure are bus formed lines passing by urban through bus lines.these stops. In addition, Therefore, we classifiedthe PageRank the TAZs of the into bus six network classes is based more on dispersed. the value of closeness, betweenness and PageRank score, and found that the TAZs in southern area have high accessibility, connectivity, and influence. Finally, we5. Conclusions investigated theand correlation Future Work of centrality between the bus service network and urban road network and foundThis study that closeness aimed to showed investigate the highest the spatial correlation structure and of that urban PageRank bus networks was not using related. complex These empiricalnetwork theory. results We provide took anShenzhen insight intoas a thecase laws study and and significant developed accessible a three-step areas workflow of a bus network,to collect whichthe bus promotes service thedataset understanding from a public of the transport characteristics inquiry of configuration website. On in the urban basis bus of service the operating systems. configurationHowever, of limitations bus lines, the still P-space exist, which graph canprinciple be improved was used upon to establish in future the works. bus service The network dataset acquiredto represent from the the relationship website lacks among the detailed bus stops. operating Then, network information analysis of bus indicators lines such were as the calculated timetables to andanalyze number the ofstatistical buses for properties each line, whichof the isnetwork of great importanceand quantify to assessthe accessibility, the efficiency connectivity, of a bus service. and Moreover,influence of passenger nodes in trajectoriesthe network. can We reveal found the that usage the bus patterns network of citizens of Shenzhen who takefollows buses, a small-world which has greatproperty, referential with an meaning average in path optimizing length of the 2.01 configuration and clustering of acoefficien bus networkt of 0.47. system. This Therefore,means that we people will workneed onone both transfer issues on byaverage combining to reach other any datasets TAZ of (e.g.,the city smart by taking card dataset) buses. The to help clustering urban managerscoefficient establishrepresents a bus-friendlythe extent of city the andlocal improve aggregation the residents’ in the network, green travel so it behavior.indicates the connectivity of the TAZ with its local adjacent TAZs. The two indicators could be used to design an urban bus network, Author Contributions: The research was mainly conceived and designed by Xiping Yang and Shiwei Lu. Xiping Yangand anda well-designed Weifeng Zhao bus performed network the experiments.should try to Xiping achieve Yang a andsmall Zhiyuan average Zhao path wrote length the manuscript. and high Shiweiclustering Lu and coefficient. Zhiyuan Zhao The reviewedweight of the edges manuscript repres andents provided the spatial comments. interaction between the TAZs, and Funding:the heavy-tailedThis study distribution was jointly supported of weight by indicates the National that Natural only Sciencea few Foundationedges have of an China extremely (No. 41801373, large 41901390),weight. Based the Fundamental on the weight Research of edges, Funds for we the identified Central Universities six spatially (No. interacting GK201803049), communities the China Postdoctoral from the bus service network, and discussed the similarity and difference between detected communities and administrative districts, which provides an understanding of the spatial interaction structure formed

ISPRS Int. J. Geo-Inf. 2019, 8, 486 15 of 17

Science Foundation (Nos. 2017M623112, 2019T120876), the Foundation of Geomatics Technology and Application Key Laboratory of Qinghai Province (No. QHDX-2018-08), the Open Fund of Key Laboratory of Urban Land Resources Monitoring and Simulation, the Ministry of Land and Resources (KF-2018-03-006), the Open fund of Beijing Key Laboratory of Urban Spatial Information Engineering (No. 2019206), the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2018JM4041), and Shannxi Science and Technology Program (No. 2019ZDLSF07-04). Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Pittschieler, K. Performance improvement of urban bus system: Issues and solution. Int. J. Eng. Sci. Technol. 2010, 2, 21–23. 2. 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. 3. 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. [CrossRef] 4. Lin, J. Network analysis of China’s aviation system, statistical and spatial structure. J. Transp. Geogr. 2012, 22, 109–117. [CrossRef] 5. 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. [CrossRef] 6. 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. [CrossRef] 7. Wang, C.; Wang, J. Spatial pattern of the global shipping network and its hub-and-spoke system. Res. Transp. Econ. 2012, 32, 54–63. [CrossRef] 8. 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. [CrossRef] 9. Lin, J.; Ban, Y. Complex network topology of transportation systems. Transp. Rev. 2013, 33, 658–685. [CrossRef] 10. Roth, C.; Kang, S.M.; Batty, M.; Barthélemy, M. Structure of urban movements: Polycentric activity and entangled hierarchical ﬂows. PLoS ONE 2011, 6, e15923. [CrossRef] 11. 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. [CrossRef] 12. 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. [CrossRef] 13. 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. [CrossRef] 14. 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. [CrossRef] 15. 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. [CrossRef] 16. Gonzalez, M.C.; Hidalgo, C.A.; Barabasi, A. Understanding individual human mobility patterns. Nature 2008, 453, 779–782. [CrossRef][PubMed] 17. 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. [CrossRef] [PubMed] 18. Demsar, U.; Spatenkova, O.; Virrantaus, K. Identifying critical locations in a spatial network with graph theory. Trans. GIS 2008, 12, 61–82. [CrossRef] 19. Rui, Y.; Ban, Y. Exploring the relationship between street centrality and land use in Stockholm. Int. J. Geogr. Inf. Sci. 2014, 28, 1425–1438. [CrossRef] 20. Dai, L.; Derudder, B.; Liu, X.; Witlox, F. Transport network backbone extraction: A comparison of techniques. J. Transp. Geogr. 2018, 69, 271–281. [CrossRef] 21. Jiang, B.; Claramunt, C. Topological analysis of urban street networks. Environ. Plan. B Abstr. 2003, 31, 151–162. [CrossRef] ISPRS Int. J. Geo-Inf. 2019, 8, 486 16 of 17

22. 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. [CrossRef] 23. 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. [CrossRef] 24. 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. [CrossRef] 25. 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. [CrossRef] 26. Rodrigue, J.P.; Comtois, C.; Slack, B. The geography of transport systems. J. Urban. Technol. 2013, 18, 127. 27. 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. [CrossRef] 28. Sienkiewicz, J.; Hołyst, J.A. Statistical analysis of 22 public transport networks in Poland. Phys. Rev. 2005, 72, 046127. [CrossRef] 29. 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. 30. 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. 31. Barabasi, A.; Albert, R. Emergence of scaling in random networks. Science 1999, 286, 509–512. [CrossRef] 32. 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. [CrossRef] 33. 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. 34. Watts, D.J.; Strogatz, S.H. Collective dynamics of ‘small-world’ networks. Nature 1998, 393, 440–442. [CrossRef][PubMed] 35. Latora, V.; Marchiori, M. Efficient behavior of small-world networks. Phys. Rev. Lett. 2001, 87, 198701. [CrossRef][PubMed] 36. Barthelemy, M. Spatial networks. Phys. Rep. 2010, 499, 1–101. [CrossRef] 37. 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. [CrossRef] 38. 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. [CrossRef] 39. Amap Platform. Available online: https://www.amap.com/ (accessed on 29 October 2019). 40. 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. [CrossRef] 41. You, J.; Nedović-Budić,Z.; Kim, T.J. A GIS-based traffic analysis zone design: Technique. Transp. Plan. Technol. 1998, 21, 45–68. [CrossRef] 42. 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. [CrossRef] 43. Amaral, L.A.; Scala, A.; Barthelemy, M.; Stanley, H.E. Classes of small-world networks. Proc. Natl. Acad. Sci. USA 2000, 97, 11149–11152. [CrossRef] 44. Sabidussi, G. The centrality index of a graph. Psychometrika 1996, 31, 581–603. [CrossRef] 45. Freeman, L.C. A set of measures of centrality based upon betweenness. Sociometry 1977, 40, 35–41. [CrossRef] 46. Brin, S.; Page, L. The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 1998, 30, 107–117. [CrossRef] 47. 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. 48. Ferber, C.V.; Holovatch, T.; Holovatch, Y.; Palchykov, V. Network harness: Metropolis public transport. Phys. A Stat. Mech. Appl. 2007, 380, 585–591. [CrossRef] ISPRS Int. J. Geo-Inf. 2019, 8, 486 17 of 17

49. 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. [CrossRef] 50. Clauset, A.; Newman, M.E.J.; Moore, C. Finding community structure in very large networks. Phys. Rev. E 2004, 70, 066111. [CrossRef][PubMed] 51. Jenks, G.F. The data model concept in statistical mapping. Int. Yearb. Cartogr. 1967, 7, 186–190.

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