Introduction

The rapid pace of global urbanization, particularly in developing countries, has led to the rise of urban villages as a prominent feature of urban spatial structures and social dynamics. In China, decades of urban expansion have driven significant migration to city centers, resulting in dense urban areas and rapid growth in surrounding towns and cities1.An “urban village” in China refers a transitional rural-urban settlement within municipal boundaries, distinguished by collective land tenure, compact informal habitats, a migrant-dominant populace, mixed land-use patterns, and intricate infrastructural and governance challenges2. While urban villages provide housing for both local residents and migrants, they face numerous challenges, including disorganized land use, poor living conditions, inadequate infrastructure, and complex social and governance issues3,4,5,6. Approaches to urban village transformation vary across countries. In Europe and the United States, urban planning research frequently utilizes geographic information systems(GIS) and accessibility analysis to examine population dynamics and ensure the equitable distribution of public services. This integration of urban morphology with functionality aims to refine spatial configurations, thereby enhancing social functionality and improving residents’ quality of life7,8. This approach underscores the significance of fostering inclusive and livable urban environments that cater to the needs and aspirations of diverse communities. In China and India, the issue of urban villages poses a multifaceted challenge, with research primarily concentrating on economic revitalization, social cohesion, and sustainable land use9,10. Chinese scholars often delve into intricate issues pertaining to land ownership, social relations, and governance within urban villages11,12. Their work emphasizes not only the economic upgrading of these areas but also the enhancement of public facilities, the improvement of residents’ quality of life, and the maintenance of social stability in dense and complex urban environments13,14. Previous research indicates that public space is a crucial area for socializing and daily activities, with residents’ needs primarily focused on functional spaces15. However, insufficient attention has been paid to the failure of urban villages to fully stimulate regional vitality, despite their unique spatial dynamics.Unlike typical residential areas, urban villages often lack comprehensive planning, resulting in streets and alleys serving as de facto public spaces. While these organically evolved spaces offer diverse paths for residents, they face systemic challenges—including public health risks, safety hazards, and traffic inefficiencies—that degrade spatial quality and functional performance16,17. Existing studies on urban village vitality predominantly focus on temporal-spatial pattern evolution18, built environment impacts19, or nighttime activity intensity20, yet few address how to optimize vitality through spatial restructuring. This research gap persists partly due to methodological limitations: although complex network theory has proven effective in analyzing interconnected urban systems21,22, its application to urban villages remains underexplored. The theory’s capacity to model scattered spatial nodes and nonlinear interactions aligns precisely with the fragmented distribution characteristics of public spaces in urban villages, suggesting its potential as a transformative analytical tool for vitality enhancement.

This study examines three representative urban villages in Guiyang, China, using complex network analysis to construct morphological and vitality networks of public spaces. The morphology network focuses on spatial structure, connectivity, and organization, while the vitality network highlights activity patterns, social interactions, and functional utilization. By analyzing network structure and node attributes, the study explores the roles of individual nodes and how public spaces can be improved through both individual and collective transformations. The coupled analysis also investigates how to better integrate urban villages into the surrounding urban environment, offering theoretical and practical insights for optimizing public spaces in urban planning and management.

Research methods

Overview of the study area

Figure 1 reveals that the study area is located in the Yunyan District of Guiyang City, Guizhou Province, China(106°44’13"E, 26°36’30"N), one of the city’s two primary historical urban areas. To ensure the representativeness and comprehensiveness of the study object, we selected three urban villages with well-developed public space systems and large areas, In this study, the “urban village public space” refers collectively to the outdoor areas within urban villages that are left after excluding the buliding entities designated for residential use, these spaces serve as venues for the daily lives and social activities of the resident. This study verified the online data by checking the website of the government’s urban planning department online and by conducting field surveys offline. In addition to the public spaces recorded in the online data, the field survey recorded the outdoor venues in the urban villages with people’s activities and certain service facilities as “public space”. After online data and field surveys, it was found that there are 62 public spaces in Chayuan Village, 108 public spaces in Meikuang Village, and 48 public spaces in Shahe Village.

Fig. 1
figure 1

Overview map of the study area. (Note: The geographical location of the study area. (a) Is from the Ministry of Natural Resources of China, and the review number is GS (2019) 1686. (b–c) are based on (a); (c):①Chayuan Village ②Shahe Village ③Meikuang Village; the authors used ArcGIS software ).

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Construction of public space morphology network in urban villages

Complex network analysis, originating from measurement sociology, explores interrelationships among actors in social contexts23,24. In recent years, this method has also been used in the field of urban planning25. The basic principle is to take the actors as “points” and the relationship between them as “edges”, and build a “network” of actors after forming a binarized matrix based on whether the conditions are met or not. This paper takes the public space in urban villages as the “point”, and the road between the public space as the “edges” to construct “the public space morphology network of urban villages”(later abbreviated as“morphology network”) based on the topological relationship between the public space and the road. Indicators were selected for analysis at the overall level and at the individual level, and it is annotated in Table 1.

Table 1 Meaning and calculation formula of public space network indicators for urban villages.
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Construction of evaluation index system for vitality of public space in urban villages

Spatial vitality refers to the frequency, duration, diversity and intensity of interaction of various types of activities in a space, and is a key indicator for assessing the functional completeness, attractiveness and vitality of a space. It emerges from the interaction between space and people, so the characteristics of crowd activities serve as a direct reflection of the vibrancy of a space. and environmental characteristics significantly influencing crowd activities and behaviors26. Therefore, this paper constructs the evaluation system of public space vitality indicators for urban villages from the level of residents’ vitality and the level of environmental characteristics of public space. Measuring the level of residents’ vitality by the degree of vitality fluctuation and crowd aggregation27,28,29,30,31, and measuring the environmental characteristics of public space in urban villages by the level of service functionality19,32. The meaning of the indicators and how they were calculated are shown in Table 2.

Table 2 Interpretation and calculation method of public space vitality evaluation indicators for urban villages.
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In empirical research, variations in indicator weights can significantly influence evaluation outcomes. The entropy weighting method provides an objective approach to determine the relative importance of each indicator within a multi-criteria evaluation system, as it derives weights based on the inherent data variability rather than subjective judgments33, this paper selects the objective entropy weight method to carry out the calculation of the weight of each indicator, and its calculation steps are as follows:

First, standardized initial values are calculated for positive and negative indicators, respectively based on the following formulas.

$$\:{\text{Z}}_{\text{i}\text{j}{\prime\:}}=\frac{{\text{a}}_{\text{i}\text{j}}-{\text{a}}_{\text{i}\text{j}\text{m}\text{i}\text{n}}}{{\text{a}}_{\text{i}\text{j}\text{m}\text{a}\text{x}}-{\text{a}}_{\text{i}\text{j}\text{m}\text{i}\text{n}}}$$
$$\:{\text{Z}}_{\text{i}\text{j}{\prime\:}{\prime\:}}=\frac{{\text{a}}_{\text{i}\text{j}\text{m}\text{a}\text{x}}-{\text{a}}_{\text{i}\text{j}}}{{\text{a}}_{\text{i}\text{j}\text{m}\text{a}\text{x}}-{\text{a}}_{\text{i}\text{j}\text{m}\text{i}\text{n}}}$$

\(\:{\text{Z}}_{\text{i}\text{j}}\)Represents the standardized value of the indicator, \(\:{\text{Z}}_{\text{i}\text{j}{\prime\:}}\)and\(\:\:{\text{Z}}_{\text{i}\text{j}{\prime\:}{\prime\:}}\)are formulas for normalizing positive and negative indicators respectively. is the original data value of the jth indicator of the ith sample, \(\:{\text{a}}_{\text{i}\text{j}\text{m}\text{a}\text{x}}\)and \(\:{\text{a}}_{\text{i}\text{j}\text{m}\text{i}\text{n}}\)are the maximum and minimum values in the original data value respectively.

\(\:{\text{P}}_{\text{i}\text{j}}\) is the proportion of the jth indicator of the ith sample to its indicator value, and its expression formula is:

$$\:{\text{P}}_{\text{i}\text{j}}={\text{Z}}_{\text{i}\text{j}}{\left(\sum\:_{\text{i}=1}^{\text{m}}{\text{Z}}_{\text{i}\text{j}}\right)}^{-1}$$

Secondly, is the information entropy value of the jth indicator and is the information utility value of the jth indicator, and the expression formula of the two is as follows:

$$\:{\text{e}}_{\text{j}}=-\text{k}\sum\:_{\text{i}=1}^{\text{m}}{\text{P}}_{\text{i}\text{j}}\text{ln}{\text{P}}_{\text{i}\text{j}}$$
$$\:{\text{d}}_{\text{j}}=1-{\text{e}}_{\text{j}}$$

Finally, is the weight of the jth indicator, which is calculated by the formula:

$$\:{\text{P}}_{\text{j}}={\text{d}}_{\text{j}}{\left(\sum\:_{\text{i}=1}^{\text{m}}{\text{d}}_{\text{j}}\right)}^{-1}$$

M denotes the comprehensive vitality value of the ith sample, which is obtained by weighting and summing the standardized values of all m indicators (j = 1,2,…,m) with their weights \(\:{\text{P}}_{\text{j}}\), the range of the comprehensive vitality value M is [0, 1], which is calculated as follows:

$$\:\text{M}={\sum\:_{\text{i}=1}^{\text{m}}{\text{P}}_{\text{j}}\text{*}\text{Z}}_{\text{i}\text{j}}$$

The nature and weights of the indicators are shown in Table 3.

Table 3 Assessing the nature and weighting of indicators of public space vitality in urban villages.
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Construction of public space vitality network in urban villages

Gravitational strength is a mathematical model derived from Newton’s classical mechanics, specifically from the gravitational formula and the principle of distance attenuation. In recent years, this model has been predominantly utilized to gauge the intensity of spatial interactions among various entities such as cities, villages, towns, and parks34,35. In this paper, we use the comprehensive evaluation index for public space vitality and refine the gravitational strength model by incorporating the walking distances between each public space. This approach aims to more accurately reflect the interaction strength between these public spaces. The calculation formula is:

$$\:{G}_{ab}={K}_{ab}\frac{{M}_{a}{M}_{b}}{{R}_{ab}^{2}}$$
$$\:{K}_{ab}=\frac{{M}_{a}}{{M}_{a}+{M}_{b}}$$

\(\:{G}_{ab}\) is the gravitational strength value between public space a and b; is the medium constant in public space a and b, and are the comprehensive vitality value of public space a and b respectively; \(\:{R}_{ab\:}\)is the walking distance between public space a and b.

The construction of public space vitality network in urban villages requires two steps. In the first step, the gravitational strength value of each public space in the urban village is calculated according to the gravitational strength model constructed above; in the second step, the value matrix is divided into binary value matrix by choosing a suitable threshold. A high threshold value helps to reflect the core and key points of the network, but is not conducive to the inclusion of secondary nodes, and cannot reflect the structural characteristics of the network more comprehensively. while setting the average value of the gravitational strength of each public space as a threshold value better reflects the structural characteristics of the vitality network36.

Exploration of the relationship between morphology network and vitality network

The coupling coordination degree model serves as a scientific approach to assess the synergistic impact and coordinated development level among two or more elements. It elucidates the interconnections between various subsystems and facilitates a comprehensive evaluation and analysis of the overall system’s relationships37. The degree centrality in the morphology network shows the importance of public space in terms of geographical location, and the degree centrality in the vitality network shows the importance of public space in terms of spatial vitality. Selecting the centrality of these two networks for coupling and coordination analysis can reveal the intrinsic connection between the morphology network and the vitality network, and the understanding of this intrinsic connection can help to formulate a more scientific development plan for public space, and by evaluating the degree of coordinated development of the different elements of the network, we can determine which public spaces are the key bottlenecks in the development of the urban villages, so that we can target to increase the input of resources. The coupling coordination degree model is calculated as follows:

$$\:\text{C}=2\times\:{\left[\frac{({\text{U}}_{1}+{\text{U}}_{2})}{{({\text{U}}_{1}+{\text{U}}_{2})}^{2}}\right]}^{\frac{1}{2}}$$
$$\:\text{T}={\upalpha}\:{\text{U}}_{1}+\:{\upbeta}{\text{U}}_{2}\:,\:{\upalpha}+{\upbeta}=1$$
$$\:\text{D}=\sqrt{\text{C}\text{*}\text{T}}$$

The coupling degree C quantifies the extent of interconnection between two systems; a higher value of C signifies a reduced degree of dispersion and a stronger coupling, while a lower value indicates the opposite. and denote the values of the degree centrality indexes of the morphology network and the vitality network respectively,. T is the comprehensive coordination index, which reflects the effectiveness of the two coupled subsystems. α and β are the weighting coefficients, and since the degree centrality indexes of the public space form network and the public space vitality network are equally important, the weighting coefficients of the two networks take the value of 0.5. The coordination degree D measures the level of coordinated development between the systems, ranging from 0 to 1. A value closer to 1 indicates higher coordination and a more optimal spatial structure, whereas a lower value suggests suboptimal coordination, highlighting the need for spatial structure optimization. The degree of coordinated development is classified into several levels based on the following Table 4.

Table 4 Classification of coupling harmonization.
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Data processing

Both morphology and vigor networks are constructed based on two different data matrices relation. The data matrix of morphology network is to use Arc GIS 10.8 to draw the intersection of road, public space, and road-public space in the remote sensing map of each urban village to get the topological relationship, and if there is a topological relationship between the road and the public space, then it will be recorded as “1”, otherwise as “0”. The data matrix of the vitality network is the average value of the gravitational strength of each public space calculated based on the gravitational model, and if the value of the gravitational strength between a public space is greater than the average value, it is recorded as “1”, otherwise as “0”. The two binarized matrix data need to be processed in the UCINET software to obtain the values of the analyzed indicators in Table 138.

Morphological and vitality networks alike consider public spaces in urban villages as “points”. The distinction lies in that the morphology network views the connecting roads between these public spaces as “edges”, whereas the vitality network considers the comprehensive vitality value based on the gravity model as “edges”. Both networks are constructed for the same research subject in different research levels. Consequently, the metrics in Table 1 are applicable to both the morphology network and the vitality network.

Results and analysis

Analysis of public space morphology network in urban villages

Analysis of the overall level of public space morphology network in urban villages

(1) Analysis of the completeness and balance of the public space morphology network in urban villages.

Table 5 shows that the densities of the public spatial morphology networks in the three urban villages are generally low, with MeiKuang Village having the lowest density at 0.084. This suggests a sparse connection ratio among nodes and indicates a lack of structural cohesion within the networks. MeiKuang Village also has the highest agglomeration coefficient, while ShaHe and ChaYuan Villages exhibit lower coefficients, implying that the nodes in MeiKuang Village are more likely to morphology tightly-knit clusters. The degree centrality potentials for ChaYuan, ShaHe, and MeiKuang Villages are 8.62%, 7.31%, and 10.34% respectively, reflecting a weak tendency for aggregation of public spaces. The Betweenness Potential for ChaYuan, ShaHe, and MeiKuang Villages are 22.03%, 27.91%, and 23.83%, all of which are well below the 100% potential of a star structure. This suggests that public spaces in these villages play a limited intermediary role within the network and have not achieved a “core” status.

(2) Stability Analysis of Public Space morphology networks in Urban Villages.

Table 6 illustrates that the public space morphology networks of the three urban villages each morphology cohesive subgroups with varying scales of K core. Notably, MeiKuang Village’s public space network exhibits the highest K value among the three, with 11 core contributing to 12.7% of the total. In contrast, ChaYuan Village’s network has a maximum K value of 7, with its 7 core representing 14.5%. Shaha Village’s network, with a maximum K value of 5, features 5 core that constitute 41.7% of its structure. Given its larger size, MeiKuang Village demonstrates a more stable public space network structure compared to the other two urban villages.

Table 5 Analysis of indicators of completeness and balance of public space morphology network in urban villages.
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Table 6 Analysis of the stability indicators of the public space morphology network in urban villages.
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Individual-level analysis of public space morphology networks in urban villages

Figure 2 illustrates that at the network node level, the influence of each node within the three urban village public space networks is evenly distributed. The central trend of the nodes reveals a pattern of two network center circles, yet the intermediary capacity of each node differs significantly. The networks of the three urban village public spaces possess nodes with high intermediary centrality rather than nodes with high degree centrality. This suggests that while certain nodes in the urban village public space networks may not be in a pivotal position, they are indeed crucial hubs characterized by their strong intermediary capacity.

Fig. 2
figure 2

Individual network structure of public morphology network in urban villages. ((a), (b), (c) are the degree centrality of Chayuan Village, Shahe Village, and Meikuang Village, respectively; (e), (f), and (g) are the inter-degree centrality of Chayuan Village, Shahe Village, and Meikuang Village, respectively, and the color shades of the nodes in the graph indicate the magnitude of the above values.)

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Analysis of public space vitality in urban villages

Figure 3 shows that the comprehensive vitality value of public space in the three urban villages and towns ranges from 0.089 to 0.715, in which the three urban villages account for a lower percentage of public space with a high comprehensive vitality value and a higher percentage of public space with a low comprehensive vitality value, which indicates that the vitality of the three urban villages and towns’ public space is low, and illustrates the necessity of optimizing and improving the vitality of urban and rural public space. The high-vitality public spaces located at the edges of the three urban villages, because the edges of the urban villages are adjacent to the city’s main roads, with convenient transportation and dense pedestrian flow, which promotes social activities and commercial interactions. In addition, there are also public spaces with high vitality located in the inner part of urban villages, which are mostly located near the intersections of urban villages, with better accessibility and carrying the travel needs of residents. In summary, the overall low vitality of public space in urban villages is mainly due to the closed internal space and the dispersed layout of existing public space, which makes it difficult for residents to find centralized places for socializing and activities in their daily lives. In addition, the facilities and environment of internal public spaces are often inadequate, affecting people’s willingness to use them and the frequency of interaction.

Fig. 3
figure 3

Comprehensive vitality value of public space shape in urban villages.

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Analysis of public space vitality network in urban villages

Overall analysis of the vitality network of public space in urban villages

(1) Analysis of the completeness and balance of the vitality network of public space in urban villages.

Table 7 reveals a low density of public space vitality networks across all three urban villages, indicating sparse connections between points and a fragmented network structure. Compared to the morphology network of public space, the vitality connections between nodes show slightly higher closeness, suggesting that certain public spaces, despite their geographical distance, foster more dynamic interactions. This is likely due to the limited daily needs of residents and the constrained movement patterns resulting from the dispersed layout of public spaces, shaped by intensive land use. The centroid potentials of the public space vitality networks in the urban villages are higher than those in the morphology networks, while intermediary centroid potentials are lower. This suggests that although key nodes in the vitality networks attract significant activity, they do not effectively bridge connections between other nodes. This pattern underscores the centrality of these spaces in drawing users, yet highlights the limited facilitation of inter-node interaction.

(2)Stability Analysis of Public Space Vitality Networks in Urban Villages.

Table 7 Analysis of the completeness and balance indicators of public space formation network in urban villages.
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Table 8 illustrates that all three urban villages’ public space networks exhibit cohesive K-core subgroups at varying scales. MeiKuang Village has the largest K-core in its vitality network, with 15 core, comprising 20.4% of the total. ChaYuan Village follows with a K-core of 11, representing 27.4% of its core, while Shaha Village’s largest K-core consists of 7 core, accounting for 58.3%. In all cases, the public space vitality network structure is more stable than the morphology network structure.

Table 8 Analysis of stability indicators of public space vitality network in urban villages.
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Individual-level analysis of public space vitality networks in urban villages

Figure 4 demonstrates that in the vitality networks of the three urban villages, a significant proportion of nodes with high degree centrality concurrently exhibit high betweenness centrality, which suggests a structural consistency in nodal influence and intermediation capacity within the vitality network. This indicates that nodes with higher influence in the vitality network not only experience greater usage and traffic flow but also play a crucial role in facilitating interactions and connections across different public spaces. This pattern is linked to the spatial layout of public spaces in urban villages, where high-impact spaces are typically located near major transportation routes, positioning them as hubs that connect other key locations. The connectivity of these nodes fosters increased activities and social interactions, reinforcing their role as high-impact nodes.

Fig. 4
figure 4

Individual network structure of public space vitality network in urban villages. ((a), (b), (c) are the degree centrality of Chayuan Village, Shahe Village, and Meikuang Village, respectively; (e), (f), and (g) are the inter-degree centrality of Chayuan Village, Shahe Village, and Meikuang Village, respectively, and the color shades of the nodes in the graph indicate the magnitude of the above values.)

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Characterization of the coupled coordination of the public space morphology network and public space vitality network in urban villages

Figure 5 shows that the coupling index (C) for the three urban villages ranges from 0.241 to 0.845. The majority of public spaces fall into the low-level coupling phase (57.8%) or the antagonistic coupling phase (35.78%). The coupling coordination index (D) ranges from 0.168 to 0.914, with 19.27% of nodes classified as dysfunctional and declining, 55.50% in a transitional phase, and 25.23% in coordinated development. These results suggest limited interaction between the public space network and its vitality network. Notably, MeiKuang Village exhibits the highest proportion of dysfunctional and declining nodes and the lowest proportion of coordinated development nodes. This indicates that the spatial layout in MeiKuang Village fails to stimulate spatial vitality and urgently requires optimization and improvement measures to enhance its vitality further.

Fig. 5
figure 5

Characteristics of coupled coordination of public space morphology network and public space vitality network.

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Correlation analysis of public space network and public space node vitality in urban villages

The asterisk (*) marked in the thermal map in Fig. 6 indicates the statistical significance of the correlation between various factors. If p ≤ 0.05, it indicates that there is a significant monotonic correlation between the two variables. If p ≤ 0.01, the monotone correlation is highly significant. Figure 6 demonstrates a correlation among K-core, Degree Centrality, Betweenness Centrality, and the comprehensive vitality value of public space, suggesting a profound internal relationship between the vitality of public spaces in urban villages and both the overall and individual levels of the morphology network. Specifically, public spaces with higher K-cores tend to exhibit higher comprehensive vitality value, and similarly, those with higher Degree Centrality and Betweenness Centrality also tend to have higher comprehensive vitality value. The overall level of the network can be seen as an environmental variable that moderates the relationships among individual network nodes, thereby indirectly regulating the vitality of these nodes. Therefore, in the subsequent section, we propose a targeted improvement strategy based on complex network analysis, addressing both the overall and individual levels of the network. This strategy aims to optimize the centrality of each node within the morphology network and, consequently, enhance the vitality of public spaces in urban villages .

Fig. 6
figure 6

Correlation between urban village public space form network indicators and comprehensive vitality value.

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Construction of public space layout optimization and control system in urban villages

Principles and models of optimizing and regulating public space layout in urban villages

This paper presents a systematic approach to evaluating and optimizing the functionality of public spaces within urban villages. Using a combination of research methods—including the spatial gravity model, complex network analysis, and the entropy power method—the study develops an optimization framework for the spatial configuration of public spaces. This framework enables a macro-level understanding of both the morphological and vitality networks of urban village public spaces, as well as their interrelationships.The specific optimization steps are shown in Fig. 7.

Fig. 7
figure 7

optimization and control model of public space layout in urban villages.

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The first step evaluates the status quo of each public space node, establishes an evaluation system of public space vitality indicators for urban villages at three levels: stability of public space vitality, public space crowd aggregation, and public space service functionality, and calculates the comprehensive vitality value of each public space. The second step is to identify the public space problems, based on the comprehensive vitality value obtained in the current situation evaluation step, and with the help of the overall network index and individual network index in the complex network analysis, we can recognize the public space morphology network and the structure of the public space vitality network. The third step is to classify the nodes into three types of nodes based on the coupling results of the morphology network and vitality network: dysfunctional decline, transitional development and coordinated development, and the areas of different types of nodes are classified as dysfunctional decline areas, transitional development areas and coordinated development areas. Finally, a development blueprint to guide the optimization of the public space structure of urban villages is proposed based on the results of the above analysis.

The construction of public space layout regulation methods in urban villages - taking meiKuang village as an example

Based on the morphology network characteristics of public spaces in urban villages, key public spaces are identified within MeiKuang Village. As illustrated in Fig. 8, nodes with a higher K-core, which serve as an indicator of the stability of the morphology network, are designated as critical public space nodes. Furthermore, the results of the analysis of the coupling coordination model between the morphology network and the vitality network of public spaces in urban villages allow for the classification of these spaces into three distinct zones: dysfunctional decline area, transitional development area, and coordinated development area. Building on the results of the regionalization analysis, this study proposes targeted transformation measures and strategies for the three distinct types of regions identified. These strategies are applicable at both the network level and the individual node level. For regions characterized by incomplete functions and developmental lag, the study emphasizes the need to strengthen infrastructure and promote functional integration.

Fig. 8
figure 8

Optimization and regulation model of public space layout in MeiKuang Village.

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  1. 1.

    Transformation Strategy for Dysfunctional Decline Area

The regions experiencing functional decline are typically characterized by poor coordination between the morphological and vitality networks, accompanied by spatial differentiation and functional imbalances. A notable feature of these areas is the lack of social interactions within public spaces, leading to a significant deficiency in spatial vitality. At the node level, particular attention should be paid to those nodes exhibiting weak internal connectivity. Strategies should focus on improving road connectivity and regional spatial accessibility, as well as optimizing the layout of infrastructure, to promote the physical integration of space. For nodes where spatial activities are relatively homogeneous, the functional diversity of public spaces should be enhanced. The introduction of diversified public facilities will attract greater social interaction and economic activity, thereby enhancing the overall vitality of the area.

  1. 2.

    Transformation Strategy for Transitional Development Area

Transitional development zones represent areas in a state of flux between the morphological and vitality networks. These zones, while possessing latent potential, have yet to fully capitalize on this potential and require strategic transformation to enhance their functionality. At the network level, the overall accessibility and mobility of these zones should be improved by strengthening road connectivity and transportation hubs within the area. Optimizing the layout of existing public spaces and strategically allocating public facilities will facilitate the coordinated development of diverse functions, gradually transitioning the area toward a more efficient and vibrant network state. At the node level, nodes with significant potential for development can be revitalized by introducing commercial, educational, and cultural facilities, further improving their attractiveness and vitality. Additionally, the spatial configuration of these nodes can be optimized to accommodate a greater range of social interactions and cultural activities, thereby fostering a more dynamic environment.

  1. 3.

    Transformation Strategy for Coordinated Development Area

Coordinated development areas are distinguished by a high degree of alignment between the morphological and vitality networks, more complete spatial functions, and a higher degree of public space vitality. These areas tend to be more mature and stable. At the network level, the primary objective for such areas is to maintain and optimize the stability and vitality of the existing networks. This can be achieved by focusing on enhancing the environmental quality, landscape design, and green spaces of key nodes, thereby improving the comfort and aesthetics of the public space. This, in turn, contributes to the long-term sustainability and vitality of the area. For nodes that already exhibit high levels of vitality, the strategy should focus on enriching their service functions to further increase the functionality and interactivity of the public spaces. Moreover, fostering a greater diversity of social interactions and economic activities can be achieved by enhancing spatial accessibility and diversifying available functions.

Discussion

The public spatial morphology networks of three urban villages—Meikuang Village, ShaHe Village, and ChaYuan Village—are analyzed in this study, revealing distinct characteristics: The morphology network of Meikuang village has the lowest network density, but the Clustering Factor is higher, which indicates that the morphology network structure of Meikuang village is more decentralized but having a high Clustering Factor implies that the nodes in the local area have a better flow of information and integration of resources. The morphology network structure of Shahe village is more compact and connected, but the nodes in the network do not tend to form small groups; Chayuan village is in between of the two, showing a medium level of compactness. Previous studies have shown that well-planned urban neighborhoods, with regular layouts and shorter average street distances, tend to have more robust networks with higher connectivity and stability39,40,41. In contrast, traditional villages, fragmented by rapid urbanization, often have lower connectivity and cohesion among nodes42,43, this is the same conclusion obtained in this study. The average distance between public spaces in the three urban villages is similar, requiring residents to pass through at least four spaces to reach their target locations, indicating low access efficiency. Overall, the centrality of the public space network in the three urban villages is low, with nodes scattered across the constrained environment of high-rise buildings and limited land use, resulting in a decentralized distribution. Retaining the original village form and influenced by incomplete urbanization44,45, the public space network is vulnerable to disruptions, leading to an imbalanced distribution and reduced resource integration and information transfer efficiency.

This study reveals that the overall vitality of public spaces in urban villages remains relatively low. High-vitality-value public spaces and key nodes in the vitality network are predominantly clustered around peripheral intersections and entry points of urban villages. This spatial pattern stems from the urban villages’ internal spatial constraints: narrow thoroughfares and simplistic spatial configurations significantly impede inter-area accessibility, thereby suppressing vitality potential. The observed concentration of key vitality nodes at edge intersections and gateways correlates with their superior connectivity. These peripheral public spaces demonstrate heightened centrality in both spatial configuration and vitality networks, indicating enhanced accessibility and intensified utilization frequency. In contrast, internal intersections within urban villages present an intriguing paradox - while maintaining high vitality network centrality, they exhibit relatively low morphology network centrality. This discrepancy primarily originates from the organic development patterns of most urban villages: the absence of comprehensive urban planning coupled with spatial configurations shaped by residents’ spontaneous daily practices has engendered a structural dissonance between physical morphology and vitality distribution at internal intersections. Therefore, this paper proposes a vitality optimization improvement strategy based on the results of this analysis: while preserving existing functional attributes, emphasis should be placed on holistic spatial optimization and infrastructure upgrading. Priority interventions should encompass human-centric design principles, expansion of public amenities, multimodal transportation network optimization, and strategic public space reconfiguration to cultivate enhanced urban village livability.

This study applies complex network theory to construct morphological and vitality networks for urban villages, revealing the relationship between the overall public space network and individual vitality levels. By analyzing the centrality coupling coordination between these networks and adjusting the coordination outcomes through zoning, the study offers a novel approach to optimizing public space layout in urban villages. The morphology network reflects the geographic layout of public spaces, including roads, public areas, and their interconnectivity. The centrality index of this network highlights the significance of key nodes within the spatial structure. In contrast, the vitality network captures dynamic resident behavior, influenced by factors such as population density, services, and environmental attributes. Its centrality quantifies the functional importance of each area, directly correlating with the vitality of public spaces. The innovation of this research lies in integrating complex network theory into urban village public space optimization. Unlike traditional spatial planning and renovation methods, this approach provides a more systematic framework for analysis at both the macro and micro levels. It identifies critical nodes for targeted interventions, allowing for customized improvements tailored to the specific characteristics of different urban villages.

Conclusion

This study employs complex network analysis to construct the morphology and vitality networks of public spaces in urban villages. The coupled coordination model is then applied to investigate the relationship between these two networks. The main conclusions are as follows:

  1. (1)

    At the overall level, the morphology network of public space in urban villages presents the composite characteristics of low-density loosening and local agglomeration (network density is around 0.1, while the clustering coefficient is higher), the distribution of each nodes is fragmented (the degree centrality potentials are all smaller than the betweenness potentials), showing limited connectivity (the betweenness potentials are all lower than the 100% potentials characteristic of stellar structures)、lower stability of network structure (lower K-core value and percentage). At the individual node level, the influence among nodes is balanced, but there exists no consistency between nodes’ influence capacity and their intermediary capacity.

  2. (2)

    At the overall level, the vitality network of public space in urban villages also exhibits the composite characteristics of low-density dispersion and local agglomeration, the distribution of each node is concentrated (the degree centrality potentials are larger than the betweenness potentials), and the structural stability is higher than that of the morphology network (the K-core are larger in size and percentage than morphology networks); at the individual node level, there is a large difference in influence between nodes, and there is consistency in the influence and intermediary capacity of nodes.

  3. (3)

    The coupling between the morphological and vitality networks is weak, with Meikuang Village exhibiting the greatest discrepancy.

  4. (4)

    There is a correlation between the index representing the overall level of morphology network, the index representing the individual level of morphology network, and the comprehensive vitality value of public space, which suggests that the overall network functions as an environmental variable, indirectly influencing individual nodes and guiding the optimization of public space layouts in urban villages.