Analyzing the Direction of Urban Function Renewal Based on the Complex Network

Abstract

Urban function renewal is essential for modern megacities’ urban planning and economic developments. This paper investigates the urban function renewal in Shenzhen, China based on a complex network method. According to the points of interest and the location quotient, the dominant urban functions in each district are discussed. After computing conditional probability, the interdependence of urban functions is analyzed. The complex networks of the functions and the corresponding clusters are presented to examine the relationship and the overall features of the functions, and the features of the function clusters, respectively. The average degree and average weighted degree of the main function categories of the functions are computed to explore the features of the function classification. The urban functions’ renewal potential index is calculated to show the potential of the non-dominant functions renewing to the dominant ones in the coming years. The difficulty index of the urban function renewal in each district is presented, and the difficulty degree of the original d-ominant function group renewing to a new one is obtained. The results show that more dominant urban functions have a significant probability of being dominant ones in a district; the functions of hotels and life services are essential in the planning and development in Shenzhen; and the districts with better economic levels have greater values of the difficulty of the urban function renewal. Then, the function renewal direction in Shenzhen is analyzed, and some policy implications are given.

1. Introduction

A city is a gathering center for various industries, sectors, trades, and facilities. Different urban functions refer to the city’s role in a country or regional economic, political, and cultural life in a certain period. Urban functions are fundamental to a city, and they can reflect the unique characteristics of the city. The change or renewal of urban functions affects the development direction of a city. Under the influences of social, economic, political, cultural, and other factors, the urban functions of a city can promote urbanization and urban transformation [1]. Urban function renewal is an aspect of urban renewal [2,3]. With the development of a city, urban functions change gradually [4]. The renewal of urban function can promote industrial structure upgrading and sustainable land development, and urban–rural harmonious development, even urban renewal. Coordinated development of different urban functions can promote the sustainable development of a city [5].

Urban function renewal is a critical component of urban development and is essential for modern cities. Urban function renewal can improve citizens’ quality of life by improving transportation systems, providing more green spaces, and improving housing and infrastructure. It contributes to improving urban sustainability through adopting renewable energy, improving waste and water management, and reducing carbon emissions. It can promote economic growth by attracting businesses, creating more jobs, improving education, and providing innovative infrastructure. By better planning land use, improving transportation systems, and reducing resource waste, urban renewal can help improve resource efficiency. Urban function renewal can contribute to more significant social equity and inclusion, such as improving access to education, health care, and housing services, and reducing social inequality. By optimizing urban functions, cities can be more attractive, attract more investment and talent, and improve urban competitiveness. Therefore, urban function renewal plays an indispensable role in modern urban management.

Complex network methods have been applied in many fields of science and engineering. Based on complex networks, urban function structure can be quantitatively analyzed. However, from the extant literature, most research mainly focuses on the spatial distribution, classification, mixed degree, and the evolution process of urban functions. Moreover, research on urban function renewal has yet to be carried out based on the interdependence of the functions, renewal potential, and difficulty of urban function renewal.

In recent years, China’s urban development has changed from ‘incremental expansion’ to ‘inventory optimization’, and it is very important to explore the upgrading of urban functions and space. Effective identification of urban dominant functions, urban function relationships, and functions that have the potential to update from non-dominant functions to dominant ones is conducive to expanding urban spatial layout, promoting the aggregation of urban elements, enhancing urban vitality and operational efficiency, and creating a multi-dimensional urban pattern [6]. Shenzhen is an emerging megacity in China, and it has developed rapidly in recent years. It is focusing on developing its economy, finance, and technology industries developments while neglecting other aspects such as culture, education, and infrastructure [7]. Based on the Statistical Yearbook of Shenzhen in 2020, the value-added of the secondary industry was 1045.401 billion CNY, which accounts for 37.8% of the total gross domestic product (GDP), and that of the tertiary sector was 1719.044 billion CNY, which takes up 62.1%. The value-added of the tertiary sector far exceeds that of the secondary one. With the increase in the tertiary industry, Shenzhen must consider the urban function renewal to achieve long-term sustainability, have a better and balanced comprehensive development, and improve the city’s attraction.

Urban function renewal is essential for modern megacities’ urban planning and economic developments. This paper investigates the urban function renewal in Shenzhen, China based on a complex network method. According to the points of interest (POI) and the location quotient, the dominant urban functions in each district are discussed. After computing conditional probability, the interdependence of urban functions is analyzed. The complex networks of the functions and the corresponding clusters are presented to examine the relationship and the overall features of the functions, and the features of the function clusters, respectively. The average degree and average weighted degree of the main function categories of the functions are computed to explore the features of the function classification. The urban functions’ renewal potential index is calculated to show the potential of the non-dominant functions renewing to the dominant ones in the coming years. The difficulty index of the urban function renewal in each district is presented, and the difficulty degree of the original dominant function group renewing to a new one is obtained. The results show that more dominant urban functions have a significant probability of being dominant ones in a district; the functions of hotels and life services are essential in the planning and development in Shenzhen; and the districts with better economic levels have greater values of the difficulty of the urban function renewal. Then, the function renewal direction in Shenzhen is analyzed, and some policy implications are given.

This study provides suggestions for the government to renew the urban functions and optimize the industrial structure of a city. It is also helpful to promote proper urban planning, which can improve a city’s overall development, sustainability, and competitiveness.

The contributions in this paper are as follows: (1) The urban function renewal of Shenzhen is explored based on the complex network method; (2) The interdependence of urban functions is analyzed; (3) The complex network is presented to analyze the relationship between functions and the corresponding overall features; (4) The complex network of urban function clusters is obtained to discuss the features of the function clusters; (5) The renewal potential and renewal difficulty indices of the urban functions are proposed to evaluate the potential of the non-dominant functions renewing to dominant ones in the coming years and the degree of the difficulty of the original dominant urban function group renewing to a new one.

2. Literature Review

The literature on urban function renewal and the corresponding complex network method used for this problem is reviewed in this section. Moreover, the related research gaps are identified and discussed.

2.1. Urban Function

The research on urban function mainly includes spatial distribution classification, identification, the mixed degree, and evolution process, of the functions.

About the spatial distribution and evolution process, Myint investigated the spatial distribution and correlation between the socio-economy, polity, and culture sectors for urban structures and activities [8]. Chen et al. applied principal component and cluster analysis methods to discuss the urban economic functions and industries in terms of urban scale, industrial gradient differences, and dominant sectors [9]. The urban functions of each city in North Xinjiang, China, are identified, and the deficiencies of similar urban functions are presented. Tian et al. analyzed the spatial distribution of urban functions in Beijing and determined five concentric zones in Beijing [10]. Through the latest progress in comprehensive open-source data analysis, Crooks et al. analyzed the evolution process of urban function and urban pattern using social media data, trajectory, and traffic [11]. Mozuriunaite studied the critical transformation of Lithuanian urban functions and the technical factors that influence the mutation of the functions considering various aspects, such as economy, new technology, and people’s lifestyle, and presented a method to identify the transformation of the functions [1]. Zhou et al. considered Changchun City as an example to discuss the spatial patterns of urban functions, which is explained by utilizing urban land development [12]. Tao et al. presented a probability factor model to analyze the population flows with high-order interactivity and how it affects the urban structure and inferred the connection level of the regions [13]. Zhen et al. discussed the comprehensive situation in Hebei Province based on the flows of urban economy, transportation, information, and finance between cities in the provinces in China [14]. Zhou et al. analyzed the enhancement and weakening of urban functions and their spatial differences based on overlay analysis and transition matrix [15]. Chai et al. discussed the differences in urban functions among the cities in the economic belt of the Yangtze River. They investigated how it impacts land prices by using regression of fixed effect and two-stage least squares from 2009 to 2016 [16]. The results showed that noticeable differences exist between these cities, and the urban functions of central cities are higher than those of other cities. Stanković et al. analyzed the main urban functions of the cities worldwide and how these functions affect the urban scale [17]. Based on social media data from the perspective of the physical environment, Ye et al. presented a deep learning method to predict the change and pattern of urban functions [18]. Cheng et al. investigated the urban function characteristics under the COVID-19 lockdown by using complex network analysis [19].

Regarding urban function identification and classification, using the Nelson method, Tian et al. analyzed the structure and the characteristics of urban functions in China to classify urban functions. They discussed the impacts of urban scale on urban functional structure [20]. In conjunction with the landscape index and population density, Lin et al. delineated urban functional zones across the urban-rural spectrum, scrutinizing the attributes of urban functional landscape patterns, population density, and their interconnections [21]. Tu et al. applied the hidden Markov model to aggregate human activity inferred from mobile phone location and social media data to reveal urban functions [4]. Gao et al. proposed a statistical framework to confirm functional areas according to the co-occurrence pattern of the POI types by using a latent Dirichlet allocation topic model and extracted urban functional areas through K-means clustering and Delaunay triangulation spatial constraint clustering [22]. Using social media data, Chen et al. presented a new method of urban functional area division [23]. Using remote sensing images and mobile phone positioning data, Tu et al. analyzed urban functional areas with landscape and human activity indicators and divided the functional areas into classes. [24]. From the urban form and human activities perspective, Xing et al. classified the urban functional areas. They fused these features using the random forest to measure different functions [25]. Gao et al. developed a clustering method of the Gaussian mixture model to confirm the specific functions in urban areas and distinguished urban functional regions [26]. Zhai et al. proposed a neighborhood (NA) scale functional area detection method that combines POI data and a simplified Place2vec model based on the first law of geography [27]. Yu et al. presented a three-tier theoretical framework for urban center identification, and proposed a density-based spatial clustering technique, which combined with a noise algorithm to cluster POI to the urban center according to their distance and urban function [28]. Qian et al. applied hierarchical cluster method to study the spatial distribution and structure of urban functions in 200 Chinese cities on different time scales [29]. Luo et al. identified a relationship diagram of POI data and classification of urban spatial functions, calculated the densities of each type of POI, and used the density values of various POIs in the research unit as feature vectors to recognize urban spatial function by the Kstar algorithm [30].

The mixed degree of urban functions is studied to understand the urban structure and pattern. Chen et al. investigated the urban activities and the commonness and characteristics in the urban functional structure of the cities in China [31]. They found that the urban functions of most cities are mixed in space. Yuan et al. established the entropy model of spatial information to explore the mixed degree of various urban functions in Xi’an, China, and discussed the evolution process and the distribution of residents’ demand for taxi travel [32]. The spatiotemporal effect of the mixed degree of urban internal function on residents’ need for taxi travel was explored using the geographic weighted regression model. Based on urban POI and taxi GPS track data, Xia et al. calculated the spatial entropy of urban POI and the time entropy of taxis by information entropy to measure the mixed degree of urban functions [33]. The coupling coordination degree model was used to analyze the coupling coordination degree between the mixing degree of urban functions and the level of urbanization development. Hu et al. proposed a framework that extracts deep features of human activities through representation learning methods. Based on taxi traffic and social media data, they used fuzzy clustering methods to identify urban functional mixtures and their correlation with land use in Beijing, China [34]. Evaluating the urban function is essential to improve urban management and land use utilization. Hu et al. proposed an adaptive urban function detection model and LDA theme modeling to extract semantic urban functions and evaluate street quality from the perspective of urban functional changes [35].

From previous publications on urban functions, most research mainly focuses on spatial distribution, evolution process, classification, and mixed degree. There are no studies on the correlation between urban functions and the corresponding characteristics based on the interdependence of the functions. In addition, there is no research on urban function renewal based on the interdependence between functions, renewal potential, and the difficulty of urban function renewal.

2.2. Complex Network Regarding Urban Functions

The complex network regarding urban functions involves those related to urban transportation, roads, and urban industrial structure.

About urban transportation and roads, Saidi et al. analyzed the rail transit system network of six global cities and estimated the bus system using the data of the generalized passenger cost [36]. Applying the complex network to identify the pattern and characteristics of travel demand, Saberi et al. presented an interdisciplinary quantitative framework to analyze the flow feature regions in the cities [37]. Wang et al. studied the topology of urban road traffic networks using the complex network theory and proposed a new representation method for urban road networks [38]. By using the multi-center evaluation and complex network, Ma et al. analyzed the coupling development of urban public transportation and evaluated the public transportation centrality [39]. Jia et al. used the complex network method to analyze the public transportation networks and the corresponding optimization problem in Xi’an, China [40]. Lobsang et al. examined the feature of urban morphology and pattern and discussed the correlation between street morphology and economic development on an urban level [41]. Based on the flow data of urban residents, Lobsang et al. studied the urban spatial structure and organizational relationship by analyzing multi-scale urban spatial characteristics based on complex networks [42].

Concerning urban industrial structure, Donoso et al. analyzed the relationship between the industrial systems, investigated the process of new industries in America from 2002 to 2012 using the proximity index, and analyzed the correlation between the industrial structure and export products of each state [43]. From social network analysis, Li et al. presented an evaluation model to analyze the evolution process of industrial structure, analyzed the inherent correlation among various sectors of the industrial system, and studied the carbon emission generated from industries [44]. Guo et al. computed the industrial relevance to describe the product space of manufacturing sectors in China by using a co-occurrence method. They evaluated how industrial relevance influences the regional evolution of the industry [45]. Heo et al. explored the industrial amalgamation of different sectors according to the input–output table in South Korea. They applied the network of industrial convergence to reveal the feature of the inter-industry structure [46]. Yang et al. analyzed the spatial distribution of the sectors related to information services in Beijing, China. They tested the spatial path dependence of the industries based on the neural network [47], and Cheng et al. investigated the optimization of industry and sub-industry structures in Jiangxi Province of China based on the complex network method [48].

From the extant literature, most of the researchers apply the complex network to investigate the networks of urban roads and urban transportation, as well as industrial systems. There is no study on the correlation between urban functions according to the urban function interdependence.

3. Methodology

The complex network is the basic method used in this paper to study the urban function renewal in Shenzhen, China.

By collecting the POI of urban functions in each district of Shenzhen, the dominant urban functions can be obtained according to the location quotient. Based on conditional probability, the interdependence of urban functions is analyzed. The complex networks of the functions and function clusters are presented to discuss the relationship between the functions, the overall characteristics of the functions, and the features of the function clusters in Shenzhen, respectively. The average degree and average weighted degree of the main categories of the functions are obtained to explore the characteristics of urban function classification. The index of renewal potential of the urban functions is calculated to show the potential of the non-dominant functions renewing to dominant ones in the coming years. The index of the difficulty of the urban function renewal for each district is presented to calculate the degree of the difficulty of the original dominant urban function group renewing to a new one. Then, the direction of the urban function renewal in Shenzhen is obtained, and some policy implications are presented.

3.1. Analysis of Dominant Urban Functions

By computing the location quotient, i.e.,

$$L{Q}_{aw}=\frac{P_{aw}/P_w}{P_a/P}$$

(1)

we can analyze the dominant level of each function on the district level in Shenzhen.

The definition of parameters in Equation (1) is shown in

Table 1. The definition of parameters in Equations (1)–(3).

Parameter	Definition
$a$	An urban function
$w$	A district
$L{Q}_{aw}$	Location quotient in the district $w$
$P_{aw}$	Number of the function $a$ in the district $w$
$P_m$	Number of all functions in the district $w$
$P_a$	Number of the function $a$ in Shenzhen
$P$	Number of all functions in Shenzhen
$b$	An urban function
${\zeta }_{ab}$	The independence index of the two functions
$L{Q}_a$	The location quotient of $a$ in Shenzhen
$L{Q}_b$	The location quotient of $b$ in Shenzhen
$P(L{Q}_a>1)$	Probability that $a$ is a dominant function
$P(L{Q}_b>1)$	Probability that $b$ is a dominant function
$P(L{Q}_a>1,L{Q}_b>1)$	Probability that both $a$ and $b$ are dominant functions
$V_a$	Index of the renewal potential of non-dominant urban function $a$
$DFG$	Dominant urban function group
$\alpha$	Parameter ($\alpha =0.002$)

. When $L{Q}_{aw}>1$, the function $a$ is dominant in the district $w$. The higher value of $L{Q}_{aw}$ indicates that the function $a$ is more dominant.

3.2. Computation of the Interdependence of Urban Functions

To investigate the correlation between urban functions, the index of interdependence of the functions is presented based on the dominant functions in each district of Shenzhen. This index can show the probability of urban functions appearing as dominant in a district. The interdependence index of urban functions can be computed as [49]

$${\zeta }_{ab}=\frac{P(L{Q}_a>1,L{Q}_b>1)}{P(L{Q}_a>1)P(L{Q}_b>1)}-1$$

(2)

The definition of parameters in Equation (2) is shown in Table 1. When ${\zeta }_{ab}>0$, it means that $a$ and $b$ have more probability to be dominant functions in a district. When ${\zeta }_{ab}<0$, it means that $a$ and $b$ have less probability to be dominant functions. ${\zeta }_{ab}=-1$ means urban functions $a$ and $b$ are completely distributed independently and these two functions are uncorrelated.

3.3. Construction of the Complex Networks

Complex networks are essential for understanding and modeling various complex systems in the natural and social sciences [50]. Complex network analysis is a multidisciplinary field that applies graph theory and related mathematical and computational techniques to study the structure, behavior, and evolution of complex systems represented as networks or graphs. Complex networks consist of nodes (vertices) and edges (links or connections). Nodes represent individual entities, while edges denote relationships or interactions between nodes. Complex networks can exhibit clustering, where nodes form groups or clusters with relatively dense connections within clusters and sparse connections between them. These clusters can represent communities or functional substructures within the network. Studying complex networks has provided valuable insights into these systems’ structure, behavior, and evolution.

Complex networks can be static and dynamic [51]. Static networks refer to a network with a fixed and unchanging network structure; dynamic networks refer to changes in the connectivity relationships between individuals over time. Complex networks used in this paper are static.

To present the complex network of urban functions, the interdependence values of the functions are considered to be the edges, and the quantities of different dominant functions are regarded as the nodes. Based on the edges and nodes, the complex network can be obtained using the software Gephi 0.9.2. Using the complex network, the relationship and the corresponding overall characteristics of the functions in Shenzhen are obtained more clearly. Then, the average degree and average weighted degree of each main function category are calculated to explore the characteristics of the function classification.

After that, the complex network of function clusters is established to investigate the feature of the clusters and analyze the high internal-correlation function clusters in the network. The filtering threshold is identified with the suitable edge weight, which is 1.25, to establish the complex network, because this edge weight corresponds to the most significant characteristics of the cluster. Then, the classical function clusters are analyzed. The gravity layout is adopted by adjusting the threshold based on Gephi, and the edge weight corresponding to the most significant cluster characteristics is considered to be the filtering threshold.

3.4. Renewal Potential of Non-Dominant Urban Functions

The index of renewal potential of urban functions is calculated to show the potential of non-dominant functions renewing to dominant functions in the coming years. Understanding the renewal potential of non-dominant urban functions can promote the urban renewal and development. The index of renewal potential of non-dominant urban functions is

$$V_a=1-\prod _{b\in DFG}(1-\alpha P[L{Q}_b>1|L{Q}_a>1])=1-\prod _{b\in DFG}(1-\alpha ({\zeta }_{ab}+1)P[L{Q}_a>1])$$

(3)

The definition of parameters in Equation (3) is shown in Table 1. In this paper, $\alpha =0.002$ is selected. When $V_a$ is higher, the urban function $a$ is more likely to renew to be dominant.

3.5. Difficulty of the Urban Function Renewal

The index of the difficulty of the urban function renewal for each district is presented to calculate the degree of the difficulty of the original dominant urban function group renewing to a new one. Renewal urban functions is denoted as $R$ that $R<1$ in the original dominant urban function group, while $R>1$ in the possible new dominant urban function group. Then

$$R=DF{G}_2\cap DF{G}_1^{’},$$

(4)

where $DF{G}_1$ is the original dominant urban function group, $DF{G}_2$ is the new dominant urban function group, and $DF{G}_1^{\prime }$ is the complementary group of $DF{G}_1$.

Define the difficulty index as

$$\theta ={\displaystyle \sum _{a\in R}{V}_a/N_R},$$

(5)

where $N_R$ is the number of renewal urban functions in total. The index of $\theta$ reflects the degree of difficulty of $DF{G}_1$ renewing to $DF{G}_2$.

4. Data Source

POI is the point of an urban function, and it can reflect the place of activities related to people’s daily lives in a city. The data of POI in Shenzhen in 2021 are collected for each district in the city from the Baidu Map. The software Vectordown 3.0 is used to grab the coordinates of the POI based on the selected area. POI contains information on name, category, coordinates, classification, etc.

There are nine districts in Shenzhen, including the Bao’an District, the Futian District, the Guangming District, the Longgang District, the Longhua District, the Luohu District, the Nanshan District, the Pingshan District, and the Yantian District. The POI includes 17 main categories and 129 sub-categories of urban functions. The sub-categories can illustrate the urban functions in more detail and clearly. The main categories are real estate, company, shopping, transportation, education and training, finance, hotels, beauty, scenic spots, fine food, auto services, life services, cultural media, leisure and entertainment, medical treatment, sports and fitness, and government organs.

Table 2. The main categories and sub-categories of POI in Shenzhen.

Main Category	Sub-Category
Auto service	Auto accessory; auto beauty; auto inspection; auto lease; auto repair; auto sales
Beauty	Body shop; cosmetology; hairdressing; manicure
Company	Company; horticulture; industrial park
Cultural media	Art group; art museum; culture hall; exhibition hall; news publication; radio & television
Education & training	Adult education; kindergarten; library; middle school; overseas agent; primary school; childcare education; scientific institution; science & technology museum; special education; training institution; university
Finance	ATM; bank; credit union; investment; pawnshop
Fine food	Chinese restaurant; coffee bar; cake & dessert shop; pub; snack bar; tea bar; western restaurant
Government organ	Administrative unit; central institution; foreign institution; government institution; party group; political education institution; political parties; public security organs, procuratorial organs & people’s courts; residential committee; social organization; welfare institution
Hotel	Apartment hotel; express hotel; family hotel; star hotel
Leisure & entertainment	Ballroom; bath center; cinema; cybercafé; farmyard; KTV; leisure square; playground; resort; theatre
Life service	Camera shop; communication hall; estate agency; funeral service; laundry; logistics company; lottery service; maintain shop; newsstand; pet service; post office; print shop; public toilet; public service; ticket office
Medical treatment	Centers for disease control & prevention; clinic; emergency center; hospital; medical care; medical center; medical equipment; pharmacy; sanatorium
Real estate	Residential area; dormitory; office building
Scenic spot	Aquarium; bathing place; botany garden; carnie; church; museum; park; heritage site; scenic zone; temple; zoo
Shopping	Building material; convenience store; digit appliance; emporium; market; shopping center; store; supermarket
Sports & fitness	Gymnasium; fitting center
Transportation	Airport; bridge; bus station; charging station; parking lots; gasoline station; highway entrances & exits (HEE); highway service; long-bus station; metro station; port; railway station; toll station

shows 129 sub-categories of POI in Shenzhen.

The data are processed, organized, and summarized by using the software ArcGIS 10.2. The number of each sub-category for POI in each district and all districts is calculated by using ArcGIS. The geographical position of Shenzhen in China is shown in Figure 1. The POI distribution of cultural media is shown in Figure 2, and the POI distribution of finance is shown in Figure 3.

5. Results and Discussion

5.1. Analysis of Interdependence of Urban Functions in Shenzhen

The dominant functions of sub-categories for each district in Shenzhen can be calculated based on Equation (1). The values of independence indices between the urban functions in Shenzhen are obtained from Equation (2), and the results are shown in

Table 3. The results of the interdependences between the urban functions.

${\mathit{\zeta }}_{\mathit{a}\mathit{b}}$	Quantity	Total	Proportion
${\zeta }_{ab}=-1$	1207	3662	44.36%
$-1<{\zeta }_{ab}\le -0.75$	0
$-0.75<{\zeta }_{ab}\le -0.5$	528
$-0.5<{\zeta }_{ab}\le -0.25$	1350
$-0.25<{\zeta }_{ab}\le -0.1$	0
$-0.1<{\zeta }_{ab}<0$	577
${\zeta }_{ab}=0$	132	132	1.59%
$0<{\zeta }_{ab}\le 0.1$	89	4462	54.05%
$0.1<{\zeta }_{ab}\le 0.25$	1027
$0.25<{\zeta }_{ab}\le 0.5$	1459
$0.5<{\zeta }_{ab}\le 0.75$	473
$0.75<{\zeta }_{ab}\le 3.5$	1414

. The frequencies of the values of interdependence indices of the functions are shown in Figure 4.

From Table 1, there are more urban functions with positive values of independence index ${\zeta }_{ab}$ than those with negative ones. The number of positive values is 4462, and the one of negative values is 3662. The urban functions with a positive independence index ${\zeta }_{ab}$ take up 54.05%, exceeding half of the total. For the negative interdependences, 1878 values of the indices are in the range of −0.5 to −0.75. Also, 1207 values are equal to −1. It is shown that most negative interdependence indices are relatively strong. There are 1207 values of the indices with strong negative ${\zeta }_{ab}$, meaning that it has no probability that these urban functions are changed to be the dominant ones in a district. Regarding the positive index ${\zeta }_{ab}$, the values between 2486 functions are in the range of 0.1 to 0.5. Also, the fact that over 0.75 of the values of ${\zeta }_{ab}$ between 1414 functions exceed this threshold indicates that the majority of positive interrelationships are also reasonably robust. Specifically, from Figure 4, the highest frequencies of ${\zeta }_{ab}$ are 0.125 and 0.5, which indicates that there is moderate intensity of most functions with positive ${\zeta }_{ab}$. The highest value of interdependence reaches 3.5, showing that positive interdependence is stronger than negative ones.

In summary, in Shenzhen, more urban functions are more likely to be dominant in a district, and there is a moderate intensity of the interdependence values between most functions. Most urban functions in Shenzhen show a positive correlation. The dominant functions are more than the non-dominant ones, which shows the dominant ones in Shenzhen can develop mutually, and the non-dominant ones cannot easily influence the development of dominant functions. This correlation among urban functions promotes positive and favorable development.

5.2. The Overall Features of Functions in Shenzhen

In the complex network of functions in Shenzhen, the interdependence values of functions are considered to be the edges, and the quantities of different dominant functions are regarded as the nodes. Based on the main categories of POI, the complex network can be obtained (Figure 5). To display the complex network more clearly, Figure 6 shows the complex network with edges greater than or equal to 2 in Shenzhen.

From Figure 5, we can see that when the node size is more extensive, the quantities of dominant functions of the city are more significant. When the line of the edge is more expansive, the value of the interdependence index of the urban functions is larger. Shenzhen has larger and fewer small nodes, meaning more common functions in Shenzhen are dominant. The size of the nodes for some common functions, such as transportation, education and training, and leisure and entertainment, is similar; the functions, such as scenic spots, are relatively uncommon, and there are tiny nodes for these functions. Transportation facilities are the fundamental services for residents and urban operations and are intimately tied to the well-being of individuals and their financial circumstances [52]. Education and training are the supporting facilities related to real estate. Leisure and entertainment are vital parts of the tertiary industry. On the district level, the integrated development of these functions is balanced. While for the function of scenic spots, it shows significant differences on the district level that tourism is well-developed in some districts, such as Luohu, Yantian, and Nanshan Districts.

The indices ${\zeta }_{ab}$ between relatively small nodes are vital, such as zoo and scientific institutions, airport and auto inspection, aquariums, and emporiums. There exist positive interdependence values between these urban functions. Weak interdependences exist between relatively large nodes, and these urban functions are not susceptible to changes in other functions. Common urban functions are more stable and not easily affected by other functions than uncommon ones because these functions have been developed for many years, and the development foundation is relatively stable. For the urban development strategy, common urban functions can better guarantee the sustainable development of the city. These functions can provide the needs of residents and strengthen the foundation of urban development.

The degree of positive and negative interdependence indices of the functions is calculated by using Gephi.

Table 4. Positive interdependence indices of urban functions.

${\mathit{\zeta }}_{\mathit{a}\mathit{b}}$	Urban Function with Maximum Degree	Main Category	Total Number of Maximum Degree	Average Degree
${\zeta }_{ab}>0.1$	Post office; public service	Life service	86	67.8
${\zeta }_{ab}>0.25$	Star hotel	Hotel	80	51.83
${\zeta }_{ab}>0.5$	Zoo	Scenic spot	67	29.02
${\zeta }_{ab}>0.75$	Zoo	Scenic spot	67	21.92

and

Table 5. Negative interdependence values of urban functions.

${\mathit{\zeta }}_{\mathit{a}\mathit{b}}$	Urban Function with Maximum Degree	Main Category	Total Number of Maximum Degree	Average Degree
${\zeta }_{ab}<-0.1$	Store	Shopping	75	47.83
${\zeta }_{ab}<-0.25$	Snack bar; store	Fine food; shopping	70	40.67
${\zeta }_{ab}<-0.5$	Zoo	Scenic spot	57	26.68
${\zeta }_{ab}<-0.75$	Zoo	Scenic spot	57	18.71

show the interdependence indices of the urban functions with positive and negative values. The degree indicates the cumulative number of edges linked to each node.

From Table 4, the dominance of these functions is conducive to mutual development. When ${\zeta }_{ab}>0.1$, there is the highest degree of positive interdependence between the post office or public services and the other 86 functions. The probability that the post office or public services and other 86 functions dominate in the same district is more than 10%. When ${\zeta }_{ab}>0.25$, the probability that the star hotel and other 80 functions dominate in the same district exceeds 25%. When ${\zeta }_{ab}>0.75$, the probability that the zoo and other 67 functions dominate in the same district exceeds 75%.

From Table 5, the dominance of these urban functions impedes the development of each other. When ${\zeta }_{ab}<-0.1$, there is the highest degree of negative interdependence between the store and the other 75 functions. The probability that the store and other 75 functions dominate in the same district is lower than 10%. When ${\zeta }_{ab}<-0.25$, the probability that the snack bar or store and other 70 functions dominate in the same district is lower than 25%. When ${\zeta }_{ab}<-0.75$, the probability that the zoo and other 57 functions dominate in the same district is lower than 75%.

From the discussion, life services and hotels are essential for urban development in Shenzhen, and these have a high probability of being advantageous with other functions. Life services and hotels, as service and supporting facilities, can benefit the development of other functions, such as real estate, commerce, and tourism. The scenic spot, such as the zoo, has double-sided effects on other dominant urban functions, which follow the results in Section 5.2.

5.3. The Characteristics of Urban Function Classification in Shenzhen

The average degree and average weighted degree are used to investigate the characteristics of the urban function classification in Shenzhen. The weighted degree is a measure of the cumulative interdependences between each function and the remaining 128 functions, offering the most direct reflection of the overall mixed degree among urban functions. Figure 7 and Figure 8 show the average degree and the average weighted degree of the main categories of the functions. From Figure 7, life services and companies have the most interdependences with other urban functions, because the average degree of those is 127.33 and 127, respectively. It is shown that the functions of life services and companies correlate positively with other main categories of the functions, and the functions of leisure and entertainment have the least interdependences with other functions. From Figure 8, the functions with the highest average weighted degree are hotel and fine food, showing that the spatial agglomeration distribution trend of these two categories of urban functions is the most obvious; finance, cultural media, government organs, and scenic spots take second place; and the agglomeration trend of sports and fitness and shopping is weak.

The functions of employment places and public services are correlated most positively with other functions. The employment place is possibly associated with urban functions, such as transportation, fine food, government organs, leisure and entertainment, life services, real estate, and shopping. Meanwhile, employment places can support innovation and entrepreneurship and attract high-tech and creative industries to the city. Public service is possibly correlated with functions of government organs, finance, education and training, hotels, medical treatment, and real estate. These functions are mutually needed and developed. The highest degree of spatial agglomeration distribution in Shenzhen is observed within the consumption service sector. For example, hotels and fine food are gathered in the center of business districts for commercial developments. Fine food can be agglomerated in the commercial area or shopping facilities. Hotels and catering facilities are gathered around the scenic spot. The consumption service is more likely to be agglomeration distribution in Shenzhen.

5.4. The Features of Urban Function Clusters in Shenzhen

The complex network of function clusters is established to investigate the characteristics of the clusters and analyze the high internal correlation function clusters. The filtering threshold is identified with the suitable edge weight, which is 1.25, to establish the complex network, because this edge weight corresponds to the most significant characteristics of the cluster. Then, the classical function clusters are analyzed. The gravity layout is adopted by adjusting the threshold based on Gephi. The classical clusters of the functions are presented, as shown in Figure 9.

In Figure 9, Shenzhen has four classical clusters of urban functions. The first cluster includes the functions of scenic zones, heritage sites, pet services, and HEE. The second one contains the functions of the public service, theatre, store, Chinese restaurant, bathing place, and post office. The third one consists of the functions of the clinic, medical center, childcare education, family hotel, and foreign institution. The fourth one contains the functions of communication hall, investment, market, office building, middle school, auto repair, and hairdressing. Thus, the functions of life services, scenic spots and transportation are concentrated and have significant correlations with each other; the ones of leisure and entertainment, life services, shopping, and fine food are well-gathered; the ones of medical treatment, education and training, and government organs are closet; and the ones of finance, life services, shopping, real estate, auto services, education and training, and beauty are highly clustered in Shenzhen.

Specifically, scenic spots, transportation, and life services are highly clustered, mainly because scenic spots and life services need a transportation system to support them. Tourism and residences are associated with transportation facilities [53]. Especially, scenic spots need more convenient and complete transportation services to attract more visitors. Leisure and entertainment, life services, shopping, and fine food are gathered to form a commercial area or commercial-based comprehensive cluster, which can improve the construction of a combination of residence and commerce and promote the economic development of the city. Medical treatment, education and training, and government organs are closet, and these can develop public utilities and services, such as education, science and technology, and health, and government agencies to ensure the public’s participation in socio-economic, political, and scientific activities and promote Shenzhen to be an international science and technology center, industry innovation center, and comprehensive national science center. Finance, life services, shopping, real estate, auto services, education and training, and beauty are highly clustered, which can create the employment center and reduce the unemployment rate, as well as enhance the consumption services and educational services around the employment center.

5.5. Renewal Potential of Non-Dominant Urban Functions

From Equation (3), the results of the renewal potential of non-dominant urban functions are obtained. The top and last three urban functions with the highest and lowest renewal potential for each district in Shenzhen are shown in

Table 6. The results of the renewal potential of non-dominant urban functions.

District	Top 3 Urban Functions		Last 3 Urban Functions
	Urban Function	$\mathit{V}$	Urban Function	$\mathit{V}$
Luohu	Gasoline station	0.10496	Zoo	0.02111
	Building material	0.10165	Emporium	0.0392
	Auto accessory	0.09814	Digit appliance	0.03959
Futian	Building material	0.09818	Zoo	0.0216
	Auto accessory	0.09342	Emporium	0.0382
	Bus station	0.09088	Funeral service	0.03825
Nanshan	Building material	0.09652	Funeral service	0.03354
	Ballroom	0.08723	Airport	0.03668
	Hairdressing	0.08494	Emporium	0.03727
Bao’an	Library	0.06012	Zoo	0.01368
	Carnie	0.05884	Farmyard	0.01983
	Theatre	0.05881	Aquarium	0.02361
Longgang	Dormitory	0.06706	Laundry	0.01075
	Apartment hotel	0.063	Zoo	0.0149
	Gasoline station	0.06271	Airport	0.01928
Yantian	Pet service	0.05916	Zoo	0.01335
	Residential committee	0.05862	Airport	0.01782
	Building material	0.05639	Funeral service	0.01929
Longhua	Gasoline station	0.07427	Zoo	0.01469
	Temple	0.0672	Funeral service	0.02204
	Ticket office	0.06644	Airport	0.02513
Pingshan	Dormitory	0.05719	Zoo	0.01121
	Social organization	0.0525	Airport	0.01372
	Party group	0.05189	Funeral service	0.01453
Guangming	Dormitory	0.06169	Zoo	0.0121
	Theatre	0.06068	Aquarium	0.01777
	Temple	0.05784	Airport	0.01819

.

From Table 6, the three urban functions with the highest renewal potential are more likely to be developed in the future. For example, in the Luohu District, it is more likely to build gasoline stations, building materials, and auto accessories; and it is less possible to develop zoos, emporiums, and digit appliances. In the Futian District, it is more likely to create building materials, auto accessories, and bus stations; and it is less possible to develop zoos, emporiums, and funeral services. In the Nanshan District, it has more probability to create building materials, ballrooms, and hairdressing; and it is less likely to develop funeral services, airports, and emporiums.

The detailed direction of the urban function renewal of Shenzhen can be obtained. The Luohu District can develop transportation, shopping, and auto services. The Futian District can develop shopping, auto services, and transportation. The Nanshan District can create shopping, leisure and entertainment, and beauty. The Bao’an District can improve education and training, scenic spots, and leisure and entertainment. The Longgang District can develop real estate, hotels, and transportation. Yantian District can improve life services, government organs, and shopping. The Longhua District can promote transportation, scenic spots, and life services. Pingshan District can develop real estate and government organs. The Guangming District can improve real estate, leisure and entertainment, and scenic spots.

For center districts, such as Nanshan, Luohu, Futian, and Yantian Districts, it is necessary to optimize non-dominant shopping services to stabilize and upgrade the service sector. For urban peripheral districts, including Bao’an, Longhua, and Longgang Districts, it is favorable to improve transportation to have a complete transportation network and alleviate land tension and travel congestion caused by urban expansion. Dayun and Pinghu hub stations will be established in the Longgang District. Also, it is essential to enhance scenic spots for tourism development, especially for the Longgang District, to correspond to the planning of the global marine center city centralized carrying area and a world-class coastal eco-tourism resort in 2025. For suburban districts such as Guangming and Pingshan, enlarging real estate constructions is essential to attract employment, expand the population and jobs, and alleviate housing issues.

With the development of a city, urban functions change gradually, and then some functions will be unnecessary and eliminated. If non-dominant functions cannot transform into dominant ones, they will be eliminated in the future. The index of renewal potential for urban functions is essential for the local government and the companies related to the functions to identify the potential of non-dominant urban functions so that they can transform and develop the functions with high potential and eliminate the functions with low potential. For the governments, the index of the potential of non-dominant urban functions renewing to dominant ones can help them to optimize and improve the urban functions, and they can develop the functions with high potential to make the urban functions more diverse and more coordinated development. It is helpful for upgrading the industrial structure and achieving sustainable urban development.

The renewal potential of urban functions studied in this paper aims to serve as a reference for the formulation of government policies. Whether the government decides to strengthen and improve these functions depends on future government policy formulation.

5.6. Difficulty of the Urban Function Renewal

From Equation (5), the results of the difficulty of the urban function renewal for each district in Shenzhen are obtained, as shown in

Table 7. The results of the difficulty of the urban function renewal for each district in Shenzhen.

District	Difficulty of the Urban Function Renewal	GDP (Hundred Million CNY)	Resident Population (Ten Thousand)	Per Capita GDP (CNY)
Bao’an	0.0412	3853.5847	334.25	11.53
Futian	0.0701	4546.4993	166.29	27.34
Guangming	0.0386	1020.9216	65.8	15.52
Longgang	0.0425	1020.9216	250.86	4.07
Longhua	0.047	2510.7724	170.63	14.71
Luohu	0.0706	2390.2556	105.66	22.62
Nanshan	0.065	6103.6866	154.58	39.49
Pingshan	0.0346	760.87	46.3	16.43
Yantian	0.0445	656.4795	24.36	26.95

. To investigate the correlation between the economic level and the difficulty of the urban function renewal on the district level, the GDP and resident population of nine districts in Shenzhen in 2019 are collected from the Shenzhen Statistical Yearbook. The GDP is used to measure the economic level at the district level. Figure 10 shows the correlation between the difficulty of the urban function renewal and the GDP of each district.

In Table 7 and Figure 10, Luohu District has the highest value of the difficulty of the urban function renewal, while there is the lowest value of that in Pingshan District. It is shown that Luohu is easier to renew its urban functions, and Pingshan is more challenging to renew urban functions. The districts with higher GDP have greater values of the difficulty of the urban function renewal. For example, Nanshan District has the highest GDP of 6103.6866 hundred million CNY, and its value of the difficulty of the function renewal is 0.065, which is relatively high among all the districts. Pingshan has the lowest GDP of 760.87 hundred million CNY, and its value of the difficulty of the urban function renewal is 0.0346, which is the weakest among all the districts. Thus, the district with a better economic level can easily renew its urban functions.

In summary, Futian and Luohu Districts can focus on developing the functions of the finance, business, and service centers in the future based on the functions of the administrative and cultural centers of the city. Bao’an and Nanshan Districts can combine the advantages of dense large-scale transportation infrastructure, such as ports, airports, and highways, to develop the functions of modern logistics, build high-end manufacturing parks, and develop manufacturing industries, such as the information and communication industries. Also, they can strengthen cooperation with Hong Kong and create a modern service industry. Guangming and Longhua Districts can form a cluster of high-tech industries based on an excellent ecological environment and build the passenger railway hub to expand the urban area. Yantian and Longgang Districts can develop into a service center radiating from Shenzhen to northeast Guangdong by constructing regional transportation facilities, such as the eastern coastal railway, intercity rail, and expressway. They can also build vocational training and higher education bases to develop into new industries. Furthermore, they can expand sea-rail intermodal transportation and develop an international port logistics industry with commerce and storage based on the advantages of Yantian port.

Compared with other similar studies, the functions of hotels and life services are essential in the planning and development of Shenzhen. The functions of employment place and public service are correlated most positively with other functions. These findings follow the results of Zhen et al. [54] that the distribution of producer services positively impacts the development of urban networks.

The functions related to consumption services, such as hotels and fine food, and function of education and training is relatively scattered in Shenzhen, show the most significant spatial agglomeration distribution, which is in agreement with the results of Myint [8] and Gao et al. [22] that food restaurants are spatially clustered, while schools tend to be exclusionary.

Scenic spots, transportation, and life services are highly clustered, mainly because scenic spots and life services need a transportation system to support them. This is identical to the results of Yu et al. [53] that tourism and residences are associated with transportation facilities.

It is favorable for urban peripheral districts to improve transportation to have a complete transportation network and alleviate land tension and travel congestion caused by urban expansion, which aligns with the findings of Wu et al. [55]. To enhance suburban residents’ accessibility in suburban areas, it is essential to establish a resilient and diverse multimodal public transportation network.

6. Conclusions

The urban function renewal in Shenzhen, China, is studied based on the complex network method. Firstly, the dominant functions on the district level in Shenzhen, China are analyzed based on the location quotient. Secondly, by establishing the complex networks of functions and the corresponding clusters, the overall features of the functions and the related classification and clusters are discussed, and the average degree and average weighted degree of the main categories of the functions are analyzed. Thirdly, the indexes of renewal potential of the functions and the difficulty of the function renewal are proposed to show the potential of non-dominant urban functions renewing to dominant ones in the coming years and the degree of the difficulty of the original dominant urban function group renewing to a new one. Finally, the direction of the urban function renewal in Shenzhen is obtained.

The conclusions can be summarized as follows.

(1)

In Shenzhen, more dominant urban functions have a great probability of being dominant ones in a district, and there is a moderate intensity of the interdependence values between most functions;

(2)

There are strong interdependences between uncommon functions and weak interdependences between common ones. The common functions are not easy to be influenced by the changes in other ones.

(3)

The functions of hotels and life services are essential in the planning and development in Shenzhen. The functions of employment place and public service are most correlated positively with other ones. The function of consumption services exhibits the most pronounced spatial agglomeration distribution.

(4)

The districts with better economic levels have greater values of the difficulty of the urban function renewal.

Some policy implications are presented according to the conclusions.

Firstly, the government can develop uncommon urban functions with positive interdependences to improve the positive correlation among the functions and make urban functions more diverse. Promoting diverse economic activities and reducing the city’s dependence on a single industry is helpful. Shopping services, scenic spots, and hotel services, etc., can be developed to support the development of common functions and coordinate the classification of urban functions.

Secondly, the urban functions of public service and consumption service are advanced in Shenzhen; thus, the government can enhance the functions to have a positive correlation with other functions, such as shopping and sports and fitness, to increase the connection between the functions. In addition, the educational, scientific, or cultural services promote the integrated and balanced development of the city.

Thirdly, the government can develop the non-dominant urban functions with high renewal potential in each district, and maximize the characteristics and advantages of each district, to promote the renewal of urban functions. For center districts, it is necessary to optimize non-dominant shopping services to stabilize and upgrade the service sector. For urban peripheral districts, it is favorable to improve transportation to have a more complete transportation network and alleviate land tension and travel congestion caused by urban expansion. Also, it is essential to enhance scenic spots for tourism development. For suburban districts, enlarging real estate constructions is important to attract employment, expand the population and jobs, and alleviate housing issues.

Finally, other cities and countries worldwide may face the same problems in urban function renewal during the planning and development of the cities. This study’s methodologies and implications can be applied and offer references to the urban function renewal and urban planning for these cities and countries. The dominant and non-dominant urban functions can be identified to make up for the weakness of urban development. The characteristics of dominant urban functions can be analyzed to promote the mutual development of these functions. The renewal potential of non-dominant urban functions and the difficulty of the urban function renewal can obtain the optimization and improvement direction of non-dominant urban functions of a certain district.