Hindawi Complexity Volume 2018, Article ID 4860531, 11 pages https://doi.org/10.1155/2018/4860531

Research Article Establishment and Analysis of the Supernetwork Model for Metro Transportation System

Yu Wei and Sun Ning

College of Automobile and Transport Engineering, Nanjing Forestry University, Nanjing , China

Correspondence should be addressed to Yu Wei; [email protected]

Received 7 August 2018; Revised 3 October 2018; Accepted 15 October 2018; Published 2 December 2018

Guest Editor: Katarzyna Musial

Copyright © 2018 YuWei and Sun Ning. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In recent years, many researchers have applied complex network theory to urban public transport network to construct complex network and analyze its network performance. Te original analysis method generally uses the Space L and Space R model to establish a simple link between public sites but ignores the organic link between the overall network system and the line subsystem. As an important part of urban public transport system, subway plays an important role in alleviating trafc pressure. In this paper, a supernetwork model of network is established by using the supernetwork method. Tree parameters, node- hyperedge degree, hyperedge-node degree, and hyperedge degree, are proposed to describe the model. Te model is compared with the traditional Space L and Space P models. Te study on the supernetwork model of Nanjing metro complex network shows that the network density, network centrality, and network clustering coefcient are large, and the average network distance is small, which meets the requirements of trafc planning and design. In this study, the subway line is considered as a subsystem and further simplifed as a node, so that the complex network analysis method can be applied to the new supernetwork model, expanding the thinking of complex network research.

1. Introduction of public transport system in Curitiba, and compares it with the structure of public transport system in three big cities With the rapid development of urban construction, more and of China, including Shanghai, Beijing, and Guangzhou [4]. more cities in China have opened the subway. As an impor- Manitz J proposes two methods for the cause estimation of tant part of urban public transport system, subway plays delay in public transport networks. Te application of the an important role in relieving trafc pressure. Urban public two methods in simulation research and in German railway transport system can be abstracted as complex network com- system is examined [5]. posed of stations and routes. Te study of subway network is helpful to understand the evolution mechanism of public Ouyang M takes China Railway System as an example, transport system and solve the problem of urban congestion. chooses three typical models based on complex network, Complex networks are characterized by complex struc- and analyzes railway accessibility and virtual users based on ture and huge number of nodes. Watts and Strogatz were trafc [6]. Zhang L has established a complex network of frst proposed to have small world characteristics for complex Jinan public transport lines by using the Space R method. networks [1]. Barabasi and Albert proposed scale-free power- It is found that the network has small world characteristics law distribution properties [2]. Complex networks are applied and large average clustering coefcient [7]. Mohmand Y T to the construction and analysis of public transport network. studied the structural characteristics of the Pakistani railway An X L takes the bus line as the network node and uses network, whose complex network shows the properties of the Space R method to establish a multiweight bus road network small world [8]. Tese studies include constructing complex model. By changing the diferent weights, the balance of networks of public transport networks and analyzing their the whole public transport network system is discussed [3]. structure and performance. From the static point of view of network topology, Bona A Complex network theory is also used to analyze the urban A D uses complex network theory to analyze the structure subway network. Based on the complex network theory, Ding 2 Complexity

R explores the evolution process of Kuala Lumpur public limited to abstract network and simulation research, and the rail transit network and evaluates the network performance important parameters of metro supernetwork are not put changes in the face of diferent attack strategies [9]. Based forward and have not been applied to actual cases. on the trip data and operation schedule of Beijing subway Te complex network theory is used to model and analyze system, Yang Y proposed a multilayer model to analyze the urban subway network, generally using the Space L the trafc fow pattern of subway network [10]. Feng J and Spacer methods. Both methods use subway stations as establishes a multilayer model of the workday and weekend nodes, the Space L method establishes the links between fow distribution of the subway network based on the Beijing adjacent stations on diferent lines, and the Space R method subway trip data and operation schedule [11]. establishes the links between stations on the same line. Te Wu X established six metro complex networks in Beijing, complex network model of urban subway is composed of London, Paris, Hong Kong, Tokyo, and New York and the links between stations, and then the performance of the evaluated their topological efciency and robustness [12]. complex network can be analyzed. Once these two models are Cats O establishes an evaluation model of public transport established, the relationship between the station and the line robustness and applies the model to Amsterdam urban rail is neglected, and the change of the relationship between the transit network and evaluates the robustness of the network stations is simply analyzed. [13].Zhang J analyzed the complex network characteristics of Te supernetwork model can make up for this defciency. the subway network in Beijing, Guangzhou, and Shanghai Urban subway supernetwork is composed of main system and studied the vulnerability of the subway network [14]. and subsystem. Te stations between the main systems are Tese studies include the construction of complex urban connected by some rules, which refects the overall structure subway network, the analysis of its structural performance and performance of urban subway network. At the same and robustness, and the establishment of subway network time, the nodes in each subsystem are connected according trafc fow model. to some rules, refecting the connection between the lines Supernetwork theory has been applied to various indus- and stations. When analyzing the performance of the main tries. Wang J P presents an improved hypernetwork model of network of the metro supernetwork, the control rules of the knowledge difusion algorithm and analyzes the performance line subsystem must be taken into account. In some cases, of knowledge difusion [15]. Zhao L constructs the knowledge the line subsystem can be further simplifed as a supernode, supernetwork model of business incubators and studies the thus refecting the overall relationship between lines. As an performance diferences of knowledge services of diferent upgraded version of complex network, supernetwork can incubators by simulation [16]. Suo Q applies hypernetwork more efectively refect the real structure and performance of method to analyze user ratings in social networks and puts urban subway network. forward suggestions for collaboration in hypernetworks [17]. In recent years, Nanjing’s public transport system has Cheng Q proposes a new method to reveal the community of developed rapidly, opening a number of subway lines, more supernetworks, which transforms the problem of community and more subway lines are also under construction. As an detection into the problem of DOT partitioning [18]. important part of public transport network system, subway Wang F, taking WeChat as a sample, proposes an attrac- can not only save trafc resources, but also provide a strong tive and node-age inhomogeneous hypernetwork model guarantee for the convenience of passengers. In this paper, [19]. Cheng Y puts forward the concept of supply-demand the complex network of Nanjing metro is selected as the matching hypernetwork for manufacturing services in SOM object. On the basis of the traditional complex network model system and reveals the matching relationship between each SpaceLandSpaceP,thetopologymodelofthesupernetwork service and each task [20]. Lv T proposes a three-tier is constructed. In this paper, the subway supernetwork petroleum emergency dispatching network based on super- is described with the parameters of node degree, node- network model, which enhances regional emergency corre- hyperedge degree, hyperedge-node degree, and hyperedge lation by adding transfer management process [21]. Yamada degree, and the network density, center degree, average T proposes a discrete network design problem based on distance, and clustering coefcient in complex network are supernetwork optimization of freight network [22]. Te extended to the theory of supernetwork, and the comparison application of supernetwork analysis is focused on knowledge with the traditional subway complex network model is made. propagation model, community network analysis, and supply Te subway can also be called the metro. In the general chain management. description of this article, it is called the subway. And Supernetwork analysis can also be seen in the subway according to the ofcial name of Nanjing, it is called the network. Du W J puts forward a supernetwork model of metro. Te supernetwork can also be called a hypernetwork. urban public transport composed of conventional public In the general description of this article, it is called the super- transport network and urban rail transit network. Based on network. In the specifc model, it is called hypernetwork, and the external synchronization theory of coupled complex net- its corresponding edge is also called hyperedge. works, the synchronization problem of urban public trans- port supernetwork model is studied [23]. Suo Q takes station 2. Nanjing Metro Network representation as node and line representation as superedge. Tis paper presents a supernetwork model to describe the Te data of the Nanjing metro network mainly comes from evolution mechanism of high-speed railway system [24]. At thelatestNanjingbuslinemapissuedbytheNanjingpassen- present, the analysis of supernetwork in metro network is ger transport management ofce and the latest tourism trafc Complexity 3

Figure 1: Space L spatial model of Nanjing metro complex network.

Figure 2: Space P spatial model of Nanjing metro complex network. map of 2018 and the city map of Nanjing. Te basic assump- the number of nodes in the network is not much, and the tions of Nanjing metro network topology are as follows. topologymapisnotcomplex.Tisisbecausethesubway Te subway network is abstracted as an undirected network in Nanjing is still in the process of construction, and network. Tere are diferences between the upstream and there are still more lines to be opened in the future to meet downstream stations due to trafc control and other routes. the needs of the residents. Te network presents an obvious Without considering the frequency of departure, the network star structure extending from the center to the periphery. At is abstracted as a nonweighted network. Te same name the core of the network is the core residential area of the city, site is regarded as a docking site, ignoring the diferences surrounded by suburbs and further county towns. caused by the same location of individual sites but diferent Figure 2 shows the Space P spatial model of Nanjing locations. Te temporary bus route diversion caused by road metro complex network. It can be seen from the model that construction or other reasons, the cancellation or increase of because the model represents all sites on the same line, there subway stations, etc. shall not be considered. are ten distinct clustering subgraphs, which actually represent Tere are two ways to describe the traditional trafc 10 subway lines. Tese lines are linked by important nodes. network topology: one is the Space L method, that is, the trafc site is regarded as a node, and if the two sites on a trafc 3. Hypergraph and Supernetwork Model line are adjacent, there is a link between them. Another is the Space P method, that is, the trafc network site as a node, Te concept of hypergraph is proposed by BERGE in 1970. if there is a direct trafc line between the two stations, they Tis is the frst time that the theory of undirected hyper- have a connection. From the defnition, we can see that the graph is established systematically, and the application of network constructed by Space L method is the subnetwork hypergraph theory in operational research is studied by using constructed by Space P method [25]. matroids. Nodes in a supernetwork represent a given set of Figure 1 shows the Space L spatial model of Nanjing networks, while edges and arcs represent a combined move- metro complex network. It can be seen from the model that ment and a combination of preferences in a given set, and 4 Complexity

Line1 Line2 Line3

Stations

Figure 3: Supernetwork topology map of Nanjing metro. the supernetwork uniquely represents all the combination of main system network of a metro network are associated with mobile and preference dominated by the rules [26]. certain rules, such as the Space L and Space R methods for Te defnition of hypergraph is as follows: suppose V is a general complex network models. However, the constraints of fnite set. subsystem networks are neglected once the complex network If e� =�(�=1,2,...,�)̸ , models using these two methods are established. Te supernetwork model of metro network is diferent, � and the organic connection between the main system net- (1) � �� =� (1) �=1 work and the subsystem network is always considered. Tere- fore, in the analysis of the supernetwork model of subway net- Te two element relation �=(�,�)is called a work, the relationship between nodes-hyperedge, hyperedge- hypergraph. node, and hyperedge-hyperedge is included. When each Te element of V, {V1, V2,⋅⋅⋅ ,V�} is called the vertex subway line is simplifed into a supernode, a new superedge of hypergraph, �={�1,�2,⋅⋅⋅ ,��} istheedgesetof network model is formed. Unlike Space L and Space R, hypergraph, and the set is called the edge of hypergraph. each node of the hyperedge network model represents a Figure 3 shows the supernetwork topology map of Nan- specifc subway line. A general complex network analy- jing metro. Te supernetwork model of the subway network sis method is also applicable to the superedge network consists of two parts, one is the subsystem network, which model. refers to the local railway lines, the other is the main system In the hypergraph of the supernetwork of Nanjing metro, network, which refers to the overall network established the neighborhood matrix A refects the relationship between between the railway stations. Te main system and subsys- the subway station and the hyperedge of the subway line. Te tems are independent and interrelated. Subsystem networks line of the A represents the subway station, and the column of the subway network include , , and . Te of the A is the subway line. If the site belongs to a certain line, site on each route forms a line with certain rules. Lines, there is a relationship between the two, and the assignment is sites, and rules form the so-called hyperedge. Stations in the 1 or 0. A is a symmetric matrix.

V1 V2 V3 V4 ⋅⋅⋅ V�

�1 0 �12 �13 �14 ⋅⋅⋅ �1� [ ] [ ] �2 [ �21 0 �23 �24 ⋅⋅⋅ �2� ] [ ] [ ] � = �3 [ �31 �32 0 �34 ⋅⋅⋅ �3� ] �×� [ ] (2) [ ] �4 [ �41 �42 �43 0 ⋅⋅⋅ �4� ] [ ] . [ . . . . . ] . [ . . . . ⋅⋅⋅ . ] . [ . . . . . ] ⋅⋅⋅ �� [ ��1 ��2 ��3 ��4 0 ]

where N is the number of stations on the subway network represents the subway line. ��� (� = 1,2,3,4,⋅⋅⋅�;� = and M is the number of subway lines. V�(�= 1,2,3,4,⋅⋅⋅ ,�) 1, 2, 3, 4, ⋅ ⋅ ⋅ , �) represents the relationship between the site stands for the subway station,. ��(� = 1,2,3,4,⋅⋅⋅,�) and the line. Complexity 5

S8

S9 Line4 Line3

S1 S7

Line2 Line1 S3

Line10

Figure 4: Topology of hyperedge-hyperedge relation in supernetwork of Nanjing metro.

Te study in this paper further simplifes the sub- subway hyperedges. Te rows and columns of B represent the way supernetwork and establishes the relationship between metro lines. If there is the same station between the two lines, hyperedge and hyperedge. In hypergraph �=(�,�),the there is a relationship between them. Te assignment value is neighborhood matrix B refects the relationship between the 1, otherwise it is 0. B is a symmetric matrix.

�1 �2 �3 �4 ⋅⋅⋅ ��

�1 0 �12 �13 �14 ⋅⋅⋅ �1� [ ] � [ � 0 � � � ] 2 [ 21 23 24 ⋅⋅⋅ 2� ] [ ] �3 [ �31 �32 0 �34 �3� ] ��×� = [ ⋅⋅⋅ ] (3) [ ] � [ � � � 0 � ] 4 [ 41 42 43 ⋅⋅⋅ 4� ] [ ] . [ . . . . ⋅⋅⋅ . ] . [ . . . . . ] ⋅⋅⋅ �� [ ��1 ��2 ��3 ��4 0 ]

where M is the number of subway lines. ��(� = 1, 2, outlier. Te node degree distribution can be described by the 3, 4, ⋅ ⋅ ⋅ , �) stands for subway lines, ��(�= 1,2,3,4,⋅⋅⋅,�) distribution function p (k), which indicates the probability represents subway lines, and ��� (� = 1,2,3,4,⋅⋅⋅,�;� = that a randomly selected node is exactly k. 1,2,3,4,⋅⋅⋅,�)represents the relationship between the lines. Figure 5 shows the probability distribution of node degree Figure 4 shows the topology of hyperedge-hyperedge in Space L space of complex network in Nanjing metro. Te −1.64 relation in supernetwork of Nanjing metro. By comparing formula is ftted to y = 0.271x through the data. It can Figure 4 with Figure 2, we can see that the model is a sim- be seen that the node degree distribution in the bus network plifed version of the Space P spatial model. In supernetwork Space L of Nanjing is close to the power-law distribution, model, the nodes are juxtaposed. Afer simplifcation, the which indicates that the subway network in Nanjing is a scale- hyperedge space model also forms a new complex network in free network in Space L. which the nodes represent a line, the edges of which represent According to the observation and analysis of the pub- a common site between the lines. Te method of analyzing lic transport network, the urban public transport network general complex networks is applicable to the hyperedge has the characteristics of growth and priority connectivity. space model. Terefore, the public transport network will eventually form a scale-free network, and the distribution of the node degree 4. The Degree of Complex Network in Figure 5 confrms this theory. In general, the greater the degree of a node means the more important the node is. As .. Node Degree. Tose points adjacent to a point become can be seen from Figure 5, the degree of most of the nodes is a node's adjacent point; the number of adjacent points of less than 6, and the node degree is basically 2. Tis is because a point is called the degree of the point, also known as the subway network structure is relatively simple and can not the degree of association. Te node degree is defned as form a very complex network structure. the number of other nodes connected to the node. In fact, Figure 6 shows the probability distribution of node degree the degree of a point is also the number of lines connected in Space P space of complex network in Nanjing metro. −0.89 to that point. If the degree of a point is 0, it is called an Te formula is ftted to y = 0.421x through the data. 6 Complexity

0.9 1 0.8 0.9 0.7 0.8 0.6 0.7 0.6 0.5 0.5 p(K)

p(K) 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 01234567 012345 K K

Figure 5: Probability distribution of node degree in Space L space Figure 7: Probability distribution of hypernetwork node-hyperedge of complex network in Nanjing metro. degree in Nanjing metro.

0.16 35 29 0.14 30 27 26 19 17 0.12 25 18 0.1 20 14 10 0.08 6 8

p(K) 15 0.06 10 0.04 Number of stations Number 0.02 5 0 0 0 20406080100 12345678910 K Metro Name

Figure 6: Probability distribution of node degree in Space P space Figure 8: Distribution of hyperedge-node degree of hypernetwork of complex network in Nanjing metro. in Nanjing metro.

Itcanbeseenthatthenodedegreedistributioninthe is determined by the nature of the subway network, the subway network Space P of Nanjing is close to the power- structure presents star type radiation, and the overlapping law distribution. As can be seen from Figure 6, the degree sites are few. of most of the nodes is less than 60 and the degree of node concentration is between 10 and 30, which indicates the .. Hyperedge-Node Degree. Te hyperedge-node degree is number of other sites connected by the node through the defned as the number of nodes contained in a superedge. In subway line. subway hypernetwork, this parameter represents the number of subway stations contained in a line. .. Node-Hyperedge Degree. Node-hyperedge degree is Figure 8 shows the distribution of hyperedge-node degree defned as the number of hyperedges that contain the node. of hypernetwork in Nanjing metro. Te name of the subway As shown in Figure 3, we can see that there is a node is 1 to 10, representing Nanjing metro 1, 2, 3, 4, 10, and belonging to line 1 and line 2, and the node's node-hyperedge suburban railway lines s1, s3, s7, s8, and s9. Te degree of degree is 2. Te node-hyperedge degree distribution can be hyperedge-node is between 6 and 29. Te subway lines in described by the distribution function P (k), which represents the center of the city usually have more stations, and the the probability that the node-hyperedge degree of a randomly distance between stations is shorter, which efectively meets selected node is exactly K. the needs of the residents in the central area. Te suburban Figure 7 shows the probability distribution of hypernet- subway lines have fewer stations, and the distance between work node-hyperedge degree in Nanjing metro. Te formula stations is longer, connecting the suburbs, remote counties, −3.59 is ftted to y = 0.916x through the data. It can be seen and airports. that the probability distribution of node-hyperedge degree of Nanjing metro network is close to power-law distribution. .. Hyperedge Degree. Te hyperedge degree refers to the From Figure 7, we can see that node-hyperedge degree is number of other hyperedges adjacent to the hyperedge, actually 1, 2, and 4. Te number of stations containing that is, the number of other hyperedges that have common stations is usually 1, meaning that most subway stations only nodes with the hyperedge. In subway hyperedge network, have one route to go through. A few subway stations, as this parameter represents the number of other subway lines important transfer sites, have two routes to go through. Tis connected by a subway line. Complexity 7

Table 1: Degree distribution of main sites in Nanjing metro.

Space Space L Space P Node-hyperedge Ranking Node Degree Node Degree Node Degree 1 Nanjing south 6 Nanjing south 78 Nanjing south 4 railway station railway station railway station NanJing Railway 2 Yuantong 4 53 Yuantong 2 Station 3 Jimingsi 4 Daxinggong 53 Youfangqiao 2 NanJing Railway 4 4 Xinjiekou 51 Xinjiekou 2 Station Xiangyu Road 5 Jinma Road 4 Jimingsi 45 2 South 6 Taifeng Road 4 Taifeng Road 44 Taifeng Road 2 NanJing Railway 7 Xinjiekou 4 Youfangqiao 43 2 Station 8 Gulou 4 Gulou 43 Lukou airport 2 9 Daxinggong 4 Jinma Road 42 Jinma Road 2 Xiangyu Road 10 3 Andemen 39 Jimingsi 2 South 11 Andemen 3 Yuatong 38 Gulou 2 12 Youfangqiao 3 Chengxin Road 28 Daxinggong 2

12 0.35 5 4 1 1 0.3 10 6 1 0.25 8 0.2

6 3 2 p(K) 5 0.15 6 0.1 0.05 4 0 Number of stations Number 01234567 2 K 0 12345678910 Figure 10: Probability distribution of hypernetwork hyperedge degree in Nanjing metro. Metro Name Figure 9: Hyperedge degree distribution of the hypernetwork in Nanjing metro. .. Analysis of Public Hub Sites. Table 1 shows the highest degree of 12 nodes in Space L, Space P, and node-hyperedge space. Tese sites, known as public pivot points, play a vital Figure 9 shows the hyperedge degree distribution of the role in the urban public transport network, connected to not hypernetwork in Nanjing metro. Te name of the subway is 1 only a large number of subway stations, but also a number of to10,representingNanjingmetro1,2,3,4,10,andsuburban bus stations and many of the lines through the site. railway lines s1, s3, s7, s8, and s9. Te value of the superedge It can be seen from Table 1 that the node degree of Space is between 1 and 6. Metro lines 1, 2, and 3 have a higher node- P space is 6. Te maximum node degree of Space P space hyperedge degree and have a better switching function. Te is 78, and the range of numerical fuctuation is large. Te suburban subway s1 has a superedge of 5, because it connects node-hyperedge space is 2 except for one node with 4. In the the suburbs, airports, railway stations, and remote county three spaces, the most important is the Nanjing south railway towns. Metro line s3 has a superedge of 4, because it connects station, which connects the suburban, railway station, and the some suburban lines. airport's subway lines, which has played an important role Figure 10 shows the probability distribution of hypernet- in the transfer. In the three spaces, the top ranking sites are work hyperedge degree in Nanjing metro. If the hyperedge basically unchanged. Tese are important public hub sites. degree distribution is described by the distribution function p(k),theprobabilityofahyperedgeofarandomlyselected 5. Spatial Characteristics of Metro Network hyperedge is exactly k. From the probability distribution map, the hyperedge does not obey the power-law distribution, but In this paper, three spatial models of urban subway network it is similar to the two power function afer ftting. are constructed by using the space L, space R and superedge 8 Complexity

Table 2: Spatial characteristics of the complex network of Nanjing metro. characteristics Space L Space P Hyperedge Space Network size 159 159 10 Network density (%) 1.31 13.69 37.78 Network centrality (%) 2.52 36.13 36.11 Network average distance 16.77 2.34 1.82 Network clustering coefcient (%) 0 95.8 67.6 space methods. Te superedge network model simplifes of centralization of the entire network, that is, the extent to each subway line into a supernode. If each line has the which the entire network organizes the operation around a same station, the supernodes are connected. When analyzing node or a group of nodes. Te degree centrality �� (v�)of theperformanceofSpaceLandSpaceRmodelsinsub- node v� is defned as way networks, the general spatial characteristic parameters �� include network size, network density, network center degree, �� (��)= (5) network average distance, and network clustering coefcient �−1 [9, 10]. Te analysis method is also applicable to the superedge In all networks containing N nodes, assume that network network model. Goptimal maxims the following formula: Table 2 shows the spatial characteristics of Nanjing metro complex network and uses the network size, network � density, network center degree, network average distance, and �=∑ [�� (�max)−�� (��)] (6) network clustering coefcient of fve indicators. In this paper, �=1 threemodelsofSpaceL,SpaceP,andhyperedgespaceare G selected for comparison. Te hyperedge space model is shown In the formula, v� isthenodeofthenetwork optimal ,and V max represents the node with the largest degree of centrality inFigure4.TenetworksizeofSpaceLandSpacePspaceis G 159, which means that there are 159 subway stations. Te size in the network optimal . For a network G containing N nodes, Vmax means that of the network in the hyperedge space is 10, which means that G there are 10 subway lines. it has the largest degree of centrality. Figure optimal for star network, the degree centrality �� of network G is defned as

.. Network Density. Network density refers to the degree of 1 � � = ∑ [� (� )−� (�)] closeness between nodes in a network. Network G's network � �−2 � max � � (7) density d (G) is defned as �=1 2� As can be seen from Table 2, the network centrality of � (�) = [� (�−1)] (4) Space L is relatively small, which is due to loose structure; no node has a larger degree of node. Te network center of Space where M is the number of connections actually owned in P is relatively large, because the connection between lines is the network and N is the number of network nodes. Te range associated with all sites on diferent lines and thus presents of network density is [0, 1]. When the network is completely better centrality. Te network center of the hyperedge space connected, the network density is 1, while the actual network is relatively large, because some important metro lines are density is usually much less than 1. efectively connected to other suburban metro lines, such as As can be seen from Table 2, the network density of line 1, line 2, and line 3 of the Nanjing metro. Space L is relatively low, because the subway lines are still relatively small, and the structure presents a star-shaped loose .. Network Average Distance. In mathematics, physics, and structure. Te network density of Space P is the result of sociology, the small world network is a type of mathematical the characteristics of the structure model, so the connection graph, in which most of the nodes are not adjacent to each between the stations on each line has been established, and other,butmostofthenodescanarriveatafewstepsfrom the density value of the network is improved. In fact, there any other point. Small world networks are usually measured are relatively few links between the lines. Te density of by means of two parameters: average distance and clustering network in hyperedge space is relatively high, because the coefcient. Te small world standard has a small network model refects the relationship between subway lines, and the average distance L and a high clustering coefcient C. distribution is more balanced in the whole region. Distance refers to the total number of lines that a node must pass through in its path to another node, i.e., the length .. Network Centrality. Degree centrality is divided into of the shortcut between two points. Mean distance represents node centrality and network centrality. Te former refers to the average distance between all pairs of points in a graph. Te the degree of centrality among the nodes in which the nodes overall reachability of the network is better than the average are directly connected to them, while the latter focuses on the distance, but the connectivity of the whole network cannot be central degree of the whole network, representing the degree truly refected by the connected distance in the case that the Complexity 9 whole network is not in the connected state, but in the case of ignoring the small group efect of the network. Hypergraph multiple subgraphs. Although many real networks have large and hypernetwork method make up for this defciency to a number of nodes, the average distance is surprisingly small. certain extent. Tis paper chooses Nanjing metro complex Tis is the so-called small world efect. network as the research object, establishes the space L, For the undirected simple graph, the formula is as follows: space P, and hypernetwork model, and compares the three network structures. Te hypernetwork model refects the 2 � � relationship between the subway station and the subway �= ∑ ∑ � �� (8) lines and the relationship between the subway lines. Te � (�−1) �=1 �=�+1 analysis shows that the network density, network centrality, where L is the average distance of the network, N is the and network centrality of the metro hypernetwork in Nan- total number of nodes, and the distance from node i to node jing are large, and the average distance of the network is j. small, which is in line with the ideal trafc planning and As you can see from Table 2, the network average distance design. of Space L is larger because it represents the length between Te public transport hub sites extracted from the hyper- one site and another, and the space model’s star structure network model are similar to the other two models. Tis determines the distance to the suburb. Te average distance of paper only analyzes the complex network of Nanjing metro Space P is 2.34, which means the average transfer is 2.34 times and can further expand to the bus system, shared bicycle sys- from one subway station to another. Considering the shortcut tem, and uses the hypernetwork model to establish a higher of the subway, the transfer efciency is still high. Te average level, more complex system, and analyze the connection. Te distance in the hyperspace is 1.82, which means that it is more application of the hypernetwork model is only an undirected efcient to transfer from one subway line to another through simple network, and the relationship established is only a 1.82. subordinate relationship between the line and the site. Te future hypernetwork model can be extended to a directed weighted network, to establish a more complex model to .. Network Clustering Coefficient. According to the graph consider travel costs and travel preferences and to apply to theory, the clustering coefcient is the coefcient that repre- solving other trafc problems. sents the degree of node clustering in a graph. Evidence shows that in the real network, especially in a specifc network, the nodes tend to establish a set of close organizational systems Appendix because of the relative high density connection points. In real-world networks, this probability is ofen greater than Nanjing Metro Data the average probability of randomly setting up a connection Te data of the Nanjing metro network mainly comes from between two nodes. thelatestNanjingbuslinemapissuedbytheNanjing First of all, we look at the defnition of the clustering passenger transport management ofce and the latest tourism coefcient of the nodes. If the node v� is connected directly trafc map of 2018 and the city map of Nanjing. Te basic with the �� node, the maximum number of possible edges assumptions of Nanjing metro network topology are as between the �� nodes for the undirected network is �� (�� − follows. 1)/2, while the actual number of edges is ��. By May 2018, Nanjing metro network has opened 10 lines, � � 2� 1, 2, 3, 4, and 10 and the suburban railway lines S1, S3, S7, S8, �=∑� = ∑ � � � (� −1) (9) S9, which are composed of 159 subway stations. Te opening �=1 �=1 � � order is 1, 2, 10, S1, S8, 3, 4, S3, S9, and S7. Te network clustering coefcient C is the average clus- Te metro data are as follows: 0≤ ≤1 tering coefcient Ci of all nodes i. It is obvious C , Line 1: maigaoqiao, hongshandongwuyuan, nanjingzhan, where �� represents the number of all adjacent nodes of node xinmofanmalu, xuanwumen, gulou, zhujianglu, xinjiekou, i and N represents the number of all nodes. zhangfuyuan, sanshanjie, zhonghuamen, andemen, tianlon- It can be seen from Table 2 that the clustering coefcient gsi, ruanjiandadao, huashenmiao, nanjingnanzhan, shuan- ofSpaceLiszerobecauseoftheloosetopologyofspace.Space glongdadao, hedingqiao, shengtailu, baijiahu, xiaolongwan, P's network clustering coefcient is large because the sites zhushanlu, tianyindadao, longmiandadao, nanyidajiangsu- on each line are set up to connect when building the model. jingmaoxueyuanzhan, nanjingjiaoyuan, zhongguoyaokedax- Te network clustering coefcient of the hyperedge space is ue relatively large, because the subway lines in some urban areas Line 2: youfangqiao, yurundajie, yuantong, aotidong, xin- have played an important connection with the lines of the glongdajie, jiqingmendajie, yunjinlu, mochouhu, hanzhong- suburbs, airports, and railway stations. men, shanghailu, xinjiekou, daxinggong, xianmen, minggu- gong, muxuyuan, xiamafang, xiaolingwei, zhonglingjie, maq- 6. Conclusions un,jinmalu,xianhemen,xuezelu, xianlinzhongxin, yang- shangongyuan, nandaxianlinxiaoqu, jingtianlu When using the general complex network method to analyze Line 3: linchang, xinghuolu, dongdachengxianxueyuan, the network, the nodes are ofen regarded as independent, taifenglu, tianruncheng, liuzhoudonglu, shangyuanmen, 10 Complexity wutangguangchang, xiaoshi, nanjingzhan, nanjinglinyedax- the P-Space,” Mathematical Problems in Engineering,vol.2016, uexinzhuang, jimingsi, fuqiao, daxinggong, changfujie, fuz- Article ID 3898762, 12 pages, 2016. imiao, wudingmen, yuhuamen, qiazimen, daminglu, ming- [5] J. Manitz, J. Harbering, M. 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