Identification, Evaluation and Optimization of Urban Park System Network Structure

Abstract

A well-structured urban park system (UPS) is crucial for optimizing urban spatial layout and improving the quality of the human living environment. In response to the tendency of current planning to prioritize quantitative indicators while overlooking the relational structure arising from the collective spatial configuration of parks, this study introduces Social Network Analysis (SNA) to evaluate the spatial structure of Shanghai’s park system by constructing a service-coverage overlap network. The findings reveal the following: (1) Parks with high degree centrality are concentrated in high-density urban core areas due to service overlap, whereas large suburban parks with high betweenness centrality function as critical bridging hubs, reflecting a polycentric structure. (2) There is a discernible discrepancy between these emergent network tiers and the statutory park hierarchy, highlighting a tension between bottom-up spatial patterns and top-down planning frameworks. (3) Stability simulations indicate a dual character of the system, where the network topology is vulnerable to attacks yet functionally resilient to failures due to spatial redundancy, suggesting that a decline in service quality may precede the loss of basic accessibility. This study demonstrates the value of SNA in diagnosing park system structure, identifying key nodes, and assessing system resilience. The insights advocate for planning approaches that transcend rigid hierarchical frameworks, integrate the actual functional roles of parks, and protect structural hubs, thereby enhancing systemic resilience and promoting equitable service provision.

1. Introduction

The Urban Park System (UPS) is an indispensable component of urban green infrastructure, playing a crucial role in enhancing environmental quality and providing recreational opportunities for residents [1,2,3]. It is typically conceptualized as a hierarchical network comprising various types of parks, designed to support ecosystem functions and meet diverse public needs [4,5,6]. However, in rapidly urbanizing regions such as China, the development of the UPS has often emphasized achieving quantitative targets and complying with formal standards. While this has led to growth in the number and area of parks, it may also shift the focus toward the attributes of individual parks at the expense of the relational performance of the system as a whole [7,8]. Consequently, a disconnect may emerge between the planned, attribute-based park hierarchy and their de facto functional roles within the urban spatial network.

Common analytical methods for studying the UPS, including fractal theory [9,10], GIS-based network analysis [11,12,13], and space syntax, have proven effective in examining the morphological patterns and physical accessibility of parks [14,15]. However, these approaches often treat parks as independent entities within predefined spatial units, offering limited insight into the structural relationships that arise from their coordinated functioning—such as how parks collectively serve populations through overlapping service areas. Understanding these relational patterns is valuable for assessing systemic efficiency, integration, and resilience.

Social Network Analysis (SNA) provides a complementary framework by shifting the analytical focus from node attributes to the patterns of connections between them [16,17]. When applied to the UPS, SNA allows parks to be modeled as nodes within a network, with links representing relational ties such as shared service populations. This perspective facilitates the examination of a system’s structural configuration, the identification of functionally critical nodes, and the assessment of its cohesive properties. Previous applications of SNA in park-related research have explored themes such as accessibility and governance [18,19,20,21], yet they often treat parks as undifferentiated nodes and seldom address the stability of the UPS as a functional network under different disturbance scenarios.

To address these considerations, this study employs SNA to evaluate the network structure of Shanghai’s urban park system through the lens of service-coverage overlap. Specifically, it aims to answer the following questions: (1) What characterizes the relational structure of Shanghai’s UPS based on service-coverage overlap, and which parks occupy structurally important positions? (2) To what extent does the functional importance of parks within this network diverge from their statutory planning hierarchy? (3) How does this network respond, in terms of both topological integrity and service continuity, when subjected to different disruption scenarios?

To this end, we construct a service-coverage overlap network for Shanghai, where the connections between parks are weighted by the number of residential blocks they jointly serve. This approach models the supply-side relational structure shaped by park locations and service ranges, using residential areas as a spatial proxy for demand. Our analysis evaluates node centrality, examines tiered structures, and assesses network stability under various disruption scenarios, combining topological metrics with an evaluation of service coverage loss.

This study seeks to contribute in the following ways: (a) by demonstrating the application of SNA to model a UPS as a coverage-based relational network, linking supply configuration to spatial proxies of demand; (b) by diagnosing systemic mismatches between emergent network roles and formal planning categories; and (c) by introducing a dual-perspective stability analysis to explore the resilience of a park system, thereby providing a more nuanced understanding of its vulnerabilities. The findings may inform a shift from purely hierarchical planning toward a more relational and resilience-sensitive approach to the planning and management of urban park systems.

2. Materials and Methods

2.1. Construction of the Urban Park Service-Coverage Overlap Network

A social network is defined by a set of nodes and the relationships (links) between them [22]. In this study, the nodes represent urban parks, and the links are derived from their spatial service relationships. The construction of the park network involved two key steps. First, a service relationship was established between a park (P) and a residential area (R) if the residential area fell within the park’s service radius. This created a bipartite (two-mode) network connecting the set of parks to the set of residential areas (Figure 1a,b). Second, this two-mode network was projected onto the set of parks to create a one-mode network where parks are directly linked to each other. A link between two parks is formed if they serve at least one common residential area. The strength of this link—the edge weight—is defined as the number of residential blocks jointly covered by both parks. For example, if parks P1 and P2 jointly serve two residential areas (R2 and R3), the link weight between them is 2. This weighted, undirected one-mode network is termed the service-coverage overlap network (Figure 1c). It does not measure functional synergy or user flow, but quantifies the extent of spatial redundancy or potential substitutability in service provision between parks.

The network was constructed using UCINET software (v6.773) [23]. The two-mode adjacency matrix was converted to a one-mode park matrix using the Affiliations function with the Sums of Cross-Products (Overlaps) method, which directly calculates the co-coverage counts. No threshold filtering was applied, and self-loops were excluded by default. This resulted in a weighted adjacency matrix for all parks, which was used for all subsequent network analyses.

Figure 1. Network relationship between urban park (P) and residential area (R). (a) Relationship between urban park and residential area; (b) ‘Two-mode’ service network; (c) ‘One-mode’ service-coverage network (Adapted from Ref. [24]).

Figure 1. Network relationship between urban park (P) and residential area (R). (a) Relationship between urban park and residential area; (b) ‘Two-mode’ service network; (c) ‘One-mode’ service-coverage network (Adapted from Ref. [24]).

2.2. Study Area and Data Sources

Shanghai is located at the estuary of the Yangtze River, covering an area of 6340 km² with a built-up area of 1237.85 km², lying between longitudes 120°52′ E and 122°12′ E and latitudes 30°40′ N and 31°53′ N (Figure 2).

A total of 304 parks (Figure 3) were used in this study, which were divided into four types: comprehensive parks (41), theme parks (18), community parks (221), and small-scale urban parks (24) (

Table 1. Functions and size of different parks in Shanghai.

Types of Parks	Features of Function	Number	Park Area (ha)	Service Radius (km)	Area Range (ha)
Comprehensive parks	Municipal and regional parks suitable for conducting various outdoor activities, are equipped with comprehensive recreational facilities and provide multiple services.	41	≥50	5	3.55~140.3
			10~<50	3
			<10	2
Theme parks	Parks with specific themes and corresponding service facilities, including zoos, botanical parks, historical parks, and heritage park etc.	18	≥50	6	1.6~207
			<50	3.5
Community parks	Parks equipped with basic recreational facilities, primarily serving residents within a certain community for nearby daily leisure activities.	221	≥5	1	0.35~51.7
			<5 ha	0.5
Small-scale urban parks	Parks that are independently sited, relatively small in scale or varied in shape, conveniently accessible to nearby residents, and offer certain recreational functions.	24	——	0.3	0.07~7.47

). The park service radiuses for parks in this study were determined based on the Urban Green Space Planning Standard (GB/T51346-2019) [25] and the Shanghai Ecological Space Master Plan (2021–2035) [26]. Service radii for comprehensive parks, community parks, and small-scale urban parks were assigned based on park scale. For theme parks, which lack a unified standard in the guidelines, a radius of 3.5 to 6 km was adopted by comparing the actual service radius [27,28,29]. The distribution of urban parks in Shanghai was obtained from the Shanghai Landscape and City Appearance Administrative Bureau (https://lhsr.sh.gov.cn/).

Figure 2. Location of Shanghai and its Districts, China. District abbreviations: BS (BaoShan); YP (YangPu); HK (HongKou); JA (JingAn); PT (PuTuo); JD (JiaDing); CN (ChangNing); MH (MinHang); XH (XuHui); HP (HuangPu); PD (PuDong); JS (JinShan); CM (ChongMing); QP (QingPu); FX (FengXian); SJ (SongJiang) (Reprinted from Ref. [30]).

Figure 2. Location of Shanghai and its Districts, China. District abbreviations: BS (BaoShan); YP (YangPu); HK (HongKou); JA (JingAn); PT (PuTuo); JD (JiaDing); CN (ChangNing); MH (MinHang); XH (XuHui); HP (HuangPu); PD (PuDong); JS (JinShan); CM (ChongMing); QP (QingPu); FX (FengXian); SJ (SongJiang) (Reprinted from Ref. [30]).

Figure 3. Distribution of urban parks in Shanghai City (Reprinted from Ref. [30]).

Figure 3. Distribution of urban parks in Shanghai City (Reprinted from Ref. [30]).

According to the definition of ‘5-min living circle’ in the Urban Residential Area Planning and Design Standard (GB50180-2018) [31], centralized and contiguous residential plots with an area of >4 ha can be used as residential nodes in the network structure (Figure 4). Data on parks and residential areas were derived from Landsat 8 OLI/TIRS imagery (obtained from the USGS Data Center, https://glovis.usgs.gov/) and concurrent Sentinel-2 imagery (obtained from the Copernicus Open Access Hub, https://dataspace.copernicus.eu/) acquired in September 2019. A 10-m resolution dataset was generated through image fusion techniques. Supervised classification was performed using the Random Forest algorithm, with training samples and validation samples independently obtained via visual interpretation. The overall accuracy of the classification result was 85%, with a Kappa coefficient of 0.82, which was fused to generate a 10 m resolution dataset. Supervised classification was performed using a Random Forest classifier trained on visually interpreted samples, achieving an overall accuracy exceeding 80%. The classification results were post-processed through clustering and filtering, and patches were screened according to area and continuity criteria. Finally, the result was spatially calibrated and validated against Shanghai Land Use Change Survey data. The boundaries of Shanghai and its districts were obtained from the National Platform for Common GeoSpatial Information Services (https://www.tianditu.gov.cn/).

2.3. Network Structure Evaluation for Urban Park System

Urban park networks are holistic structures consisting of nodes and their relationships. Therefore, the network structure of a park system can be evaluated at two levels: the nodes themselves and the overall network structure [32]. Regarding network nodes, attention must be paid to their individual characteristics and the survival ability of the nodes within the network [33]. The importance of each node must be analyzed from an individual perspective. Regarding the overall network structure, the status of different parks when functioning as an integrated system must be considered; that is, the stability of the network structure must be analyzed from a global perspective. This enhances the structural optimization and functional stability of the system by promoting internal connections within the urban park system, ultimately achieving perfection in the park network.

2.3.1. Analysis of Node Importance

The purpose of analyzing the importance of individuals within a network is to allocate more resources to important nodes and promote connections between nodes within an urban park system. This improves the tier structure, functional stability, and service efficiency of the system. This study selected the centrality indicators (Degree Centrality and Betweenness Centrality) that best reflect the importance and connectivity of urban parks for evaluation.

(1) Degree centrality measures the total strength of a park’s direct connections within the service coverage network, quantified as the sum of weights from all its incident links [34]. In this context, the link weight represents the extent of service overlap (i.e., the number of residential blocks jointly covered by two parks). A higher degree centrality indicates a greater aggregate service coverage through direct partnerships and a stronger local influence within the park system. The formula for degree centrality is as follows:

$$C_D\left(n_i\right)=\sum _{j=1}^g{W}_{ij}\left(i\ne j\right)$$

(1)

where $C_D\left(n_i\right)$ is the weighted degree centrality of node i, g is the total number of nodes in the network, and $W_{ij}$ denotes the weight of the undirected link between node i to node j (i.e., the number of residential blocks amount they jointly cover). The sum is taken over all other nodes j (i ≠ j), excluding self-connections.

(2) Betweenness centrality measures the frequency with which a park lies on the shortest paths between other parks in the binary, unweighted service-overlap network, reflecting its potential role as a bridge or broker in the overall connectivity [35]. This indicates a park’s position as a structural bridge within the pattern of service coverage overlaps, not necessarily a geographical bridge. A park with high betweenness centrality thus occupies a critical position in maintaining the global connectivity of the service-overlap network. The formula is as follows:

$$C_B\left(n_i\right)=\sum _{j<k}{\displaystyle \frac{g_{jk}\left(n_i\right)}{g_{jk}}}$$

(2)

where $C_B\left(n_i\right)$ is the absolute betweenness centrality of node i, $g_{jk}$ denotes the total number of shortest paths between nodes j and k, and $g_{jk}\left(n_i\right)$ is the number of those shortest paths that pass-through node i.

(3) The results of each centrality index were normalized to a comparable scale. The comprehensive importance index for each node was then calculated as the arithmetic mean of its normalized degree centrality $C_D\left(n_i\right)$ and betweenness centrality $C_B\left(n_i\right)$. The detailed calculation results are provided in

Table A1. Results of node importance in the social network of urban parks in Shanghai.

Number	Park Name	Degree Centrality	Betweenness Centrality	Comprehensive Importance	Number	Park Name	Degree Centrality	Betweenness Centrality	Comprehensive Importance
1	Shanghai Zoo	0.623	0.527	0.575	153	Shuisheng Garden	0.096	0.051	0.074
2	Guyi Garden	0.263	0.631	0.447	154	Li’an Park	0.298	0.394	0.346
3	Shanghai Binjiang Forest Park	0.237	0.012	0.125	155	Xinzhuang Mei Garden	0.254	0.126	0.190
4	Shanghai Botanical Garden	0.614	0.389	0.501	156	Huaxiang Green Space	0.263	0.133	0.198
5	Shanghai Chenshan Botanical Garden	0.158	0.435	0.296	157	Xincheng Central Park	0.237	0.668	0.453
6	Shanghai Gongqing Forest Park	0.465	0.087	0.276	158	Jiwang Park	0.018	0.000	0.009
7	Yu Garden	0.895	0.216	0.556	159	Chuzhai Park	0.053	0.000	0.026
8	Huangpu Park	0.421	0.006	0.214	160	Tian Park	0.088	0.005	0.046
9	People’s Park	0.825	0.090	0.457	161	Chenxing Park	0.026	0.000	0.013
10	Penglai Park	0.368	0.003	0.186	162	Maqiao Park	0.061	0.000	0.031
11	Gucheng Park	0.377	0.003	0.190	163	Meilong Leisure Park	0.175	0.001	0.088
12	Plaza Park (Huangpu Section)	0.825	0.093	0.459	164	Pingyang Shuangyong Park	0.149	0.000	0.075
13	Jiuzi Park	0.474	0.004	0.239	165	Xiyang Garden	0.096	0.051	0.074
14	Fuxing Park	0.781	0.066	0.424	166	Meilong Park	0.167	0.001	0.084
15	Shaoxing Park	0.482	0.005	0.244	167	Mei Xin Long Yun	0.114	0.011	0.063
16	South Park	0.649	0.055	0.352	168	Jinbo Garden	0.035	0.000	0.018
17	Huaihai Park	0.456	0.005	0.230	169	Xinhua Garden	0.079	0.002	0.041
18	Liyuan Park	0.430	0.004	0.217	170	Jiangwei Green Space	0.026	0.000	0.013
19	Yanfu Park	0.404	0.002	0.203	171	Jinta Park	0.096	0.511	0.304
20	Daguanyuan Green Space	0.430	0.003	0.216	172	Zhuanqiao paper-cut Park	0.096	0.043	0.070
21	Xiaotaoyuan Green Space	0.412	0.003	0.208	173	Pukang Recreation Park	0.132	0.520	0.326
22	Hengshan Park	0.421	0.002	0.212	174	Yindu Green Space	0.088	0.005	0.046
23	Xiangyang Park	0.491	0.004	0.247	175	Jinhongqiao Park	0.219	0.003	0.111
24	Longhua Martyrs Cemetery	0.772	0.444	0.608	176	Zhuanlian Leisure Park	0.114	0.498	0.306
25	Kangjian Garden	0.544	0.075	0.310	177	Pujiang First Bay Park	0.123	0.422	0.273
26	Guilin Park	0.535	0.073	0.304	178	Minhang Cultural Park	0.360	0.223	0.291
27	Caoxi Park	0.307	0.006	0.156	179	Huilongtan Park	0.158	0.088	0.123
28	GuangqiPark	0.404	0.007	0.205	180	Qiuxia Garden	0.175	0.112	0.144
29	Dong’an Park	0.351	0.001	0.176	181	Jiading District Youth Activity Centre	0.140	0.001	0.071
30	Caohejing High-tech Park	0.509	0.063	0.286	182	Anting Park	0.035	0.006	0.021
31	Xujiahui Park	0.807	0.177	0.492	183	Shanghai Auto Expo Park	0.044	0.008	0.026
32	Huang Daopo Memorial Park	0.140	0.007	0.074	184	Jiading Wisteria Garden	0.132	0.000	0.066
33	Paodao Park	0.588	0.197	0.392	185	Chenjiashan Lotus Park	0.132	0.000	0.066
34	Donghu Green Space	0.474	0.003	0.238	186	Fuhua Park	0.132	0.000	0.066
35	Wuzhong Green Space	0.482	0.004	0.243	187	South Wall Park	0.132	0.000	0.066
36	Xikang Park	0.482	0.003	0.243	188	Jinhe Park	0.263	0.379	0.321
37	Jing’an Park	0.825	0.072	0.448	189	Wisteria Park	0.132	0.000	0.066
38	Jing’an Sculpture Park	1.000	0.253	0.627	190	Xiaohekou Gingko Garden	0.123	0.000	0.061
39	Zhabei Park	0.860	0.219	0.539	191	South Park	0.123	0.000	0.061
40	Jiaotong Park	0.465	0.004	0.234	192	Shanghai Millenium Ginkgo Garden	0.070	0.017	0.043
41	Pengpu Park	0.342	0.006	0.174	193	Shin Shing Park	0.132	0.000	0.066
42	Lingnan Park	0.289	0.004	0.147	194	Jinsha Park	0.500	0.156	0.328
43	Sanquan Park	0.263	0.003	0.133	195	Malu Park	0.079	0.003	0.041
44	Daning Park	0.956	0.348	0.652	196	Huangdu Park	0.026	0.000	0.013
45	Buyecheng Green Space	0.868	0.136	0.502	197	Nanshuiguan Park	0.132	0.000	0.066
46	Hudiewan Garden	0.500	0.004	0.252	198	Pantuozi Park	0.132	0.000	0.066
47	Plaza Park (Jing’an section)	0.465	0.004	0.235	199	Ziqidonglai Park (Phase 1)	0.184	0.299	0.242
48	Zhongxing Green Space	0.404	0.003	0.203	200	Tanyuan Park	0.079	0.020	0.049
49	Dongjiaojing Park	0.246	0.002	0.124	201	Century Green	0.105	0.000	0.053
50	Jing’an Central Park	0.693	0.110	0.401	202	Haibo Park	0.158	0.005	0.081
51	99 Guangzhong Green Space	0.368	0.005	0.187	203	Yuanxiang Lake Park	0.184	0.368	0.276
52	Pengpu New Village Park	0.465	0.061	0.263	204	Guzhong Garden	0.009	0.000	0.004
53	Yonghe Park	0.360	0.010	0.185	205	Shanghai Wildlife Park	0.018	0.069	0.043
54	Zhongshan Park	0.842	0.130	0.486	206	Chuansha Park	0.070	0.088	0.079
55	Huashan Children’s Park	0.447	0.004	0.226	207	Changqing Park	0.158	0.000	0.079
56	Tianshan Park	0.789	0.113	0.451	208	Meiyuan Park	0.325	0.004	0.164
57	Tianyuan Park	0.333	0.004	0.169	209	Manqu Park	0.193	0.000	0.097
58	Hongqiao Park	0.421	0.008	0.215	210	Jingdong Park	0.211	0.001	0.106
59	Shuixia Park	0.360	0.006	0.183	211	Gaoqiao Park	0.158	0.006	0.082
60	Xinhongqiao Central Garden	0.719	0.126	0.423	212	Linyi Park	0.263	0.002	0.133
61	Huashan Green Space	0.465	0.005	0.235	213	Jiyang Park	0.246	0.003	0.124
62	Haisu Green Space	0.807	0.120	0.464	214	Shangnan Park	0.465	0.054	0.259
63	Xinjing Park	0.254	0.003	0.129	215	Nanpu Square Park	0.298	0.005	0.151
64	Yanhong Green Space	0.368	0.005	0.187	216	Century Park	0.614	0.537	0.576
65	Hongqiao Riverside Park	0.404	0.008	0.206	217	Jinqiao Park	0.289	0.073	0.181
66	Hami Park	0.325	0.007	0.166	218	Tangqiao Park	0.298	0.006	0.152
67	Linkong Skate Park	0.588	0.323	0.455	219	Jingnan Park	0.211	0.015	0.113
68	Zhongxinjing Park	0.272	0.006	0.139	220	Lujiazui central Green Space	0.728	0.108	0.418
69	Putuo Park	0.421	0.004	0.212	221	Riverside Promenade	0.851	0.181	0.516
70	Caoyang Park	0.430	0.005	0.217	222	Mingren Yuan Park	0.404	0.160	0.282
71	Changfeng Park	0.798	0.264	0.531	223	Expo Park	0.667	0.182	0.424
72	Lanxi Youth Park	0.395	0.004	0.199	224	Douxiang Yuen	0.263	0.004	0.134
73	Yichuan Park	0.447	0.007	0.227	225	Huaxia Park	0.123	0.146	0.134
74	Hutai Park	0.404	0.005	0.204	226	Gaodong Park	0.088	0.002	0.045
75	Guannong Park	0.430	0.006	0.218	227	Jiangzhen Citizen Square Park	0.018	0.000	0.009
76	Ganquan Park	0.421	0.012	0.216	228	Riverside Cultural Park	0.009	0.000	0.004
77	Haitang Park	0.368	0.008	0.188	229	Haumu Park	0.149	0.005	0.077
78	Zhenguang Park	0.298	0.009	0.154	230	Zhangheng Park	0.132	0.093	0.112
79	Meichuan Park	0.368	0.003	0.186	231	Bailianjing Park	0.640	0.055	0.348
80	Weilaidao Park	0.263	0.010	0.137	232	Houtan Park	0.684	0.239	0.462
81	Changshou Park	0.851	0.108	0.479	233	Ziwei Park	0.079	0.000	0.040
82	Mengqing Garden	0.895	0.208	0.551	234	Jinfeng Park	0.044	0.031	0.037
83	Qingjian Park	0.263	0.006	0.134	235	Heyuan Park	0.035	0.019	0.027
84	Xianghe Park	0.325	0.012	0.169	236	Heqing Park	0.018	0.000	0.009
85	Wuning Park	0.842	0.255	0.549	237	Zhoupu Park	0.044	0.024	0.034
86	Taopu Park	0.289	0.013	0.151	238	Dezhou Leisure Green Space	0.167	0.006	0.087
87	Zhenru Park	0.342	0.003	0.173	239	Shuguang Green Space	0.228	0.125	0.177
88	Danba Park	0.333	0.006	0.170	240	Youcheng Park	0.509	0.148	0.329
89	Zaoyang Garden	0.412	0.005	0.208	241	Xingyuan Park	0.079	0.179	0.129
90	Changfeng No. 2 Green Space	0.754	0.216	0.485	242	Gangcheng Park	0.140	0.001	0.071
91	Kunshan Park	0.325	0.002	0.163	243	Mianqing Park	0.096	0.049	0.073
92	Luxun Park	0.781	0.112	0.446	244	Pufa Park	0.228	0.211	0.220
93	Huoshan Park	0.298	0.002	0.150	245	Xiangmei Park	0.237	0.004	0.121
94	Aisi Children’s Park	0.956	0.277	0.616	246	Zhangjiang theme Park	0.096	0.000	0.048
95	Heping Park	0.772	0.128	0.450	247	Luchaogang Park	0.009	0.000	0.004
96	Liangcheng Park	0.333	0.003	0.168	248	Jinkui Green Space	0.088	0.031	0.059
97	Jiangwan Park	0.325	0.002	0.163	249	Guanglan Park	0.088	0.000	0.044
98	Quyang Park	0.640	0.175	0.408	250	Zhangyan Park	0.000	0.000	0.000
99	Sichuan North Road Park	0.833	0.142	0.487	251	Jinshan Park	0.009	0.000	0.004
100	Caohongwan Park	0.289	0.001	0.145	252	Gusong Garden	0.009	0.000	0.004
101	Guangdong Sports Park	0.377	0.005	0.191	253	Binhai Park	0.018	0.000	0.009
102	Fuxingdao Park	0.342	0.023	0.182	254	Huicui Garden	0.018	0.000	0.009
103	Boyang Park	0.237	0.001	0.119	255	Tinglin Park	0.009	0.000	0.004
104	Yangpu Park	0.482	0.057	0.270	256	Fengxi Park	0.000	0.000	0.000
105	Pingliang Park	0.246	0.001	0.123	257	Chejing Park	0.000	0.000	0.000
106	Huimin Park	0.325	0.004	0.164	258	Jinshan New Town Park	0.018	0.000	0.009
107	Neijiang Park	0.219	0.003	0.111	259	Zuibaichi Park	0.105	0.000	0.053
108	Songhe Park	0.289	0.003	0.146	260	Fangta Park	0.105	0.000	0.053
109	Yanchun Park	0.263	0.005	0.134	261	Sijing Park	0.114	1.000	0.557
110	Gongnong Park	0.149	0.001	0.075	262	Sixian Park	0.105	0.000	0.053
111	Minxing Park	0.175	0.002	0.089	263	Xinqiao Park	0.018	0.000	0.009
112	Haungxing Park	0.553	0.080	0.316	264	Maogang Park	0.009	0.000	0.004
113	Siping Science and Technology Park	0.632	0.082	0.357	265	Shihudangtahui Park	0.000	0.000	0.000
114	Jiangpu Park	0.298	0.003	0.151	266	Qichang Park	0.105	0.000	0.053
115	Xinjaingwancheng Park	0.386	0.044	0.215	267	Songjiang People’s Square	0.105	0.000	0.053
116	Dalian Road Green Space	0.325	0.003	0.164	268	Silu Garden	0.096	0.000	0.048
117	Xinjiangwancheng Ecological Corridor (Phase I)	0.404	0.051	0.227	269	Central Green Space (Phase III)	0.105	0.000	0.053
118	Xinjiangwancheng Ecological Corridor (Phase II)	0.482	0.067	0.275	270	Central Green Space (Phase 4)	0.105	0.000	0.053
119	Baoshan Martyrs’ Cemetery	0.184	0.013	0.099	271	Wulonghu Park (Phase I)	0.096	0.000	0.048
120	Shanghai Songhu anti-japanese War Memorial Park	0.167	0.003	0.085	272	Central Park (Phase 1)	0.105	0.000	0.053
121	Wusong Paotaiwan Wetland	0.158	0.002	0.080	273	Central Park (Phase II)	0.105	0.000	0.053
122	Yuepu Park	0.175	0.078	0.127	274	Wulonghu Park (Phase II)	0.123	0.349	0.236
123	Luoxi Park	0.035	0.000	0.018	275	Chedun Health Park	0.018	0.000	0.009
124	Youyi Park	0.149	0.004	0.077	276	Qushui Park	0.070	0.110	0.090
125	Sitang Park	0.412	0.079	0.245	277	Daguan Garden	0.000	0.000	0.000
126	Yongqing Park	0.114	0.000	0.057	278	Zhuxi Garden	0.018	0.000	0.009
127	Songnan Park	0.412	0.078	0.245	279	Beijing Garden	0.044	0.000	0.022
128	Dahuaxingzhi Park	0.693	0.187	0.440	280	Huaxin People’s Park	0.044	0.108	0.076
129	Gonghe Park	0.465	0.108	0.286	281	Nanjing Garden	0.053	0.002	0.027
130	Luojing Park	0.000	0.000	0.000	282	Xujing Square	0.096	0.487	0.292
131	Gucun Park	0.360	0.579	0.469	283	Zhaoxiang Park	0.079	0.474	0.276
132	Baoshan Waterfront Park	0.114	0.000	0.057	284	Minhui Plaza Park	0.009	0.000	0.004
133	Zhili Park	0.386	0.061	0.223	285	Zhujiajiao Residents Park	0.026	0.000	0.013
134	Yijing Palace	0.193	0.012	0.103	286	Xiayanghu Park	0.053	0.002	0.027
135	Miaoxing Park	0.456	0.094	0.275	287	Qinyuanhu Park	0.061	0.098	0.080
136	Meilanhu Park	0.105	0.019	0.062	288	Zhaoxiang Sports Park	0.044	0.020	0.032
137	Nobel Park	0.070	0.007	0.039	289	Guhua Park	0.088	0.058	0.073
138	Shengqiao Park	0.009	0.000	0.004	290	Siji Ecological Garden	0.096	0.107	0.102
139	Qilian Park	0.237	0.042	0.139	291	Wangchun Garden	0.070	0.000	0.035
140	Jusheng Park	0.167	0.018	0.093	292	Xidu Park	0.053	0.000	0.026
141	Zoumatang Garden	0.140	0.001	0.071	293	People’s Park	0.088	0.034	0.061
142	Hulin Park	0.368	0.049	0.209	294	Fengcheng Park	0.000	0.000	0.000
143	Yangquan Garden	0.263	0.005	0.134	295	Zhuangxing Park	0.070	0.000	0.035
144	Nanda Park	0.316	0.211	0.264	296	Xinghuo Park	0.026	0.000	0.013
145	Hong Garden	0.114	0.203	0.158	297	Youth Art Park	0.088	0.034	0.061
146	Minhang Park	0.105	0.103	0.104	298	Sculpture Art Park	0.088	0.034	0.061
147	Xinzhuang Park	0.202	0.165	0.184	299	Zhengyang Central Park	0.070	0.000	0.035
148	Wujing Park	0.061	0.278	0.170	300	Punan Canal North Bank Park	0.079	0.011	0.045
149	Guteng Garden	0.061	0.000	0.031	301	Yingzhou Park	0.018	0.000	0.009
150	Huacao Park	0.132	0.010	0.071	302	Xincheng Park	0.018	0.000	0.009
151	Hanghua Park	0.333	0.207	0.270	303	Baozhen Citizen Park	0.000	0.000	0.000
152	Minhang Sports Park	0.404	0.303	0.353	304	Nanmen Green Space	0.000	0.000	0.000

. Finally, the nodes were classified into three tiers (high, medium, and low) using the natural breaks (Jenks) method.

2.3.2. Analysis of Network Stability

To comprehensively assess the stability of urban park systems in response to disturbances, this study simulates the system’s performance under different failure scenarios from two dimensions: the topological structure and its service function. During operation, urban parks are inevitably exposed to various disruptions, such as natural disasters (typhoons, floods) or human-induced damage (fires, overcrowding), which may impair their service capacity and alter the structure of the service network [36,37]. Therefore, evaluating the system’s ability to maintain services, withstand damage, and restore its original service level after disturbances is critical. This study assesses stability by simulating network changes after park node failures, employing two classic disturbance scenarios for analysis: targeted attacks and random failures [38].

(1) Network disturbance scenarios: Attacks and Failures

Attacks refer to the targeted removal of nodes from a network according to a specific rule [39]. In this study, we employ a non-adaptive attack strategy, where the importance order of park nodes (based on degree, betweenness, or comprehensive importance) is calculated from the initial intact network. Nodes are then removed in a fixed order of descending importance. Each removal simulates a planned human-induced disruption (e.g., park closure, functional change). This scenario models long-term, value-driven planning pressures, such as the potential repurposing or redevelopment of highly central parks due to their locational advantage or high visitation, allowing us to assess the network’s vulnerability when critical nodes are systematically compromised.

Failures refer to the completely random failure of nodes within the network, simulating damage caused by natural disasters or other sudden, unforeseen events (e.g., local flooding, equipment failures). To accurately evaluate the network’s inherent resistance to such random disturbances and ensure statistical robustness, this study adopts a Monte Carlo simulation approach: the random failure process is repeated for 1000 independent experimental runs. In each run, nodes fail in a random sequence, and the final results are averaged across all runs.

(2) Network Stability

When the urban park network is disrupted, it may fragment into multiple subnetworks of varying sizes. The largest of these, containing the most interconnected park nodes, is termed the Largest Connected Component (LCC) [40]. To quantify network stability, this study employs the maximum connectivity (S), defined as the ratio of the number of nodes in the LCC after disruption to the total number of nodes in the initial network. The metric S primarily reflects the topological integrity and structural redundancy of the park synergy network. A high S value indicates that the network remains largely connected as a graph, which is a foundational aspect of structural stability. The calculation formula is:

$$s={\displaystyle \frac{N_{max}}{N}}$$

(3)

where N_max is the number of nodes in the LCC after disruption; and N is the total number of nodes in the initial network.

(3) Service Stability Analysis

The topological stability (S) assesses the structural connectivity of the park service-overlap network but does not directly measure the resulting impact on service provision for residents. To bridge this gap and link network disruptions explicitly to service accessibility, we introduce a complementary metric of service coverage loss. In each step of the attack and failure simulations, following the removal of a set of parks, we identify all residential areas that are no longer covered by the service area of any remaining park. The service impact is quantified by the Residential Coverage Loss Rate (RCLR), calculated as:

$$RCLR={\displaystyle \frac{N_{uncovered}}{N_{total}}}\times 100\%$$

(4)

where $N_{uncovered}$ is the number of residential areas that have lost all park coverage, and $N_{total}$ is the total number of residential areas in the study.

2.4. Mapping the Networks of Urban Park System

Constructing a network model of Shanghai’s urban parks using UCINET software reveals that the network consists of one large cluster, several smaller clusters, and a few isolated nodes. The overall network was highly interconnected and concentrated (Figure 5a). Subsequently, adding the geographical location information of the parks in ArcGIS software (v 10.7) obtained the network relationships of urban parks in Shanghai (Figure 5b).

3. Results

3.1. Importance Results of Network Nodes

3.1.1. Spatial Distribution of Important Network Nodes

Analysis of the network revealed that 39 parks exhibited high degree centrality within the service-overlap network (Figure 6), with an average area of 24.62 ha. Most of these parks are located in the densely populated central urban area west of the Huangpu River, such as Renmin Park, Jing’an Park, and Luxun Park. The high connectivity of these parks in the network primarily results from the dense residential development and high population density in this area, which leads to extensive overlap in their service coverage with many other parks.

Within the service-overlap network, 20 parks were identified with high betweenness centrality (Figure 7). These parks are predominantly large in scale (average area 48.28 ha), such as Gucun Park, Century Park, and Shanghai Zoo, and are mainly located in outer-ring and suburban areas. Their high betweenness centrality indicates that they serve as structural bridges within the overlap pattern—their service areas extensively intersect with those of multiple other parks that are not directly connected to each other. This position makes them critical for maintaining the overall connectivity of the service-overlap network.

The comprehensive importance of each park node was derived by integrating its degree centrality and betweenness centrality in the service-overlap network (Figure 8,

Table 2. Statistics of node importance of urban parks in Shanghai City.

Indicators	Class	Numbers of Parks	Average Park Size/ha	Mean Value
Degree Centrality	High	39	18.61	0.482
	Medium	111	9.34	0.212
	Low	154	10.19	0.073
Betweenness Centrality	High	20	48.28	0.405
	Medium	54	11.68	0.346
	Low	230	7.55	0.116
Comprehensive Importance	High	40	24.62	0.490
	Medium	111	9.54	0.225
	Low	153	7.14	0.058

). Spatially, nodes were classified into three tiers: 39 parks were of high importance, primarily clustered in the densely populated central city west of the Huangpu River and near the Outer Ring Road; 111 parks were of medium importance, mainly distributed in the central city and in western and southern suburban districts such as Qingpu, Songjiang, and Minhang; and 154 parks were of low importance, distributed primarily outside the central urban area.

A Pearson correlation analysis indicated a statistically significant but weak positive relationship between a park’s comprehensive importance and its area (r = 0.203, n = 304, p < 0.01). The average park area decreased across importance tiers: high-importance parks averaged 24.62 ha, medium-importance 9.54 ha, and low-importance 7.14 ha. Overall, parks with higher structural importance within the service-overlap network tended to have larger areas.

3.1.2. Tier Structure of Urban Park Networks Based on Node Importance

The comprehensive importance of nodes was classified into three tiers using the Natural Breaks method, delineating a three-tiered structure within the urban park service-overlap network (

Table 3. The tier structure of node importance of urban parks in Shanghai City.

Tier Structure	Number of Parks	Percentage	Average Park Size (ha)	Composition		Tier Structure Chart
				Types of Parks	Amount
Tier-1 network	40	13.16%	24.62	Comprehensive parks	21
				Theme parks	8
				Community parks	11
				Small-scale urban parks	0
Tier-2 network	111	36.51%	9.54	Comprehensive parks	9
				Theme parks	3
				Community parks	85
				Small-scale urban parks	14
Tier-3 network	153	50.33%	7.14	Comprehensive parks	10
				Theme parks	8
				Community parks	125
				Small-scale urban parks	10

). Tier-1 comprises 40 parks characterized by the highest combined connectivity (degree centrality) and bridging function (betweenness centrality) within the network. These parks, averaging 24.62 ha in size, include 21 comprehensive parks, 8 theme parks, and 11 community parks and are predominantly located in the high-density central urban area. Tier-2 consists of 111 parks where community parks constitute the dominant type (76.58%), indicating a layer with substantial local service redundancy. This tier also includes 9 comprehensive parks, 3 theme parks, and 14 small-scale urban parks, with an average area of 9.54 ha. Tier-3 forms the extensive base layer of the network, containing 153 parks with the lowest structural importance and the smallest average area (7.14 ha). Community parks are the main component (81.70%), and these parks are primarily distributed outside the central urban area, providing widespread foundational coverage.

3.2. Stability Results of Network Structure

3.2.1. Network Stability Under Attacks

Under attacks on the park service overlap network, both the topological structure and service function of the network exhibit differentiated and phased failure characteristics (Figure 9).

In terms of topological connectivity, the size of the LCC (S) continuously decreases as the number of attacked nodes increases, indicating a gradual decline in structural stability (Figure 9a). Attack efficiency varies significantly depending on the node attribute used for targeting. Specifically, when attacks follow the order of betweenness centrality, the network shows the highest initial vulnerability: removing only 9 nodes (3.0%) causes S to drop sharply from 0.97 to 0.79. This suggests that a few park nodes (e.g., 176, Zhuanlian Leisure Park), which act as structural bridges in the service overlap pattern, play a critical role in maintaining the overall connectivity of the network. In contrast, attacks based on degree centrality result in the most gradual decline in stability; a significant drop in S (from 0.47 to 0.31) only occurs after approximately 147 nodes (48.5%) are removed. This reflects the network’s strong redundancy against attacks based on local connectivity. Taking severe structural disruption (S = 0.5) as the threshold [41,42], attacks based on the comprehensive importance measure require the removal of 90 nodes (29.7%). This efficiency is similar to that of betweenness-based attacks (requiring 89 nodes, 29.4%) and significantly higher than that of degree-based attacks (requiring 133 nodes, 43.9%).

From the perspective of service function, its decline occurs earlier and is more severe than that of topological connectivity (Figure 9b). When attacks are conducted in the order of node comprehensive importance, the loss of service coverage exhibits a clear phased pattern. Removing the top 67 park nodes (22.1%) results in a 50% reduction in the average park coverage per residential area across the city, marking a halving of the service choices and redundant space available to residents. When the scope of failure expands to the top 116 nodes (38.3%), 10.1% of residential areas completely lose park services. As the number of removed nodes increases to 150 (49.5%), this proportion rapidly rises to 25.8%, indicating the onset of regional service collapse.

3.2.2. Network Stability Under Failures

Under failure scenarios, the urban park network in Shanghai exhibits strong robustness in both topological structure and service function (Figure 10). In terms of topological connectivity, based on 1000 independent Monte Carlo simulations, the size of S shows a steady, slow, and approximately linear decline as the number of failed nodes increases (Figure 10a). On average, 132.4 nodes (43.6%) need to fail to reduce S to 0.5, and 152.8 nodes (50.3%) are required to lower it to 0.3. This indicates that the network can maintain over half of its structural connectivity even when nearly half of its nodes fail randomly. The 95% confidence interval is relatively narrow in the early stages of failure, suggesting consistent network behavior under small-scale failures. As the failure scale expands, the interval gradually widens, reflecting increased uncertainty in the collapse pathway as the network approaches its load-bearing limit. The failure curve is significantly flatter than all targeted attack curves (Figure 9a). The number of node failures required to maintain 50% connectivity under random failure is much higher than under targeted attacks based on comprehensive importance (132.4 compared to 90), highlighting the network’s structural redundancy against random disturbances.

From the perspective of service function, its loss also exhibits a gradual, high-threshold characteristic (Figure 10b). The proportion of residential areas completely losing service coverage increases slowly: it requires failure of up to 90.4% (274) of park nodes to cause 50% of residential areas to lose all park services; even with 50.8% (154) of nodes failing, only about 10.1% of residential areas are affected. Meanwhile, the indicator reflecting the overall service redundancy of the system—the average number of parks covering residential areas—decreases by 50.3% when 50.5% (153) of nodes fail randomly. Contrary to the ‘service collapse precedes topological failure’ characteristic observed under attacks, under failures, topological stability and service functionality stability demonstrate highly consistent and strong resilience. Both require the failure of nearly half or more nodes for their core indicators (S = 0.5 and 50% of residential areas losing all coverage) to drop to the threshold, jointly confirming that the system’s spatial redundancy effectively buffers random, localized impacts.

4. Discussion

4.1. Spatial Patterns and Influencing Factors of Key Park Nodes

In densely populated residential areas, the demand for park services is pronounced, which elevates the structural importance of parks located there. Consequently, parks within historic, high-density central urban areas—such as those in the Puxi old town—frequently emerge as key nodes in the network [8], exhibiting high degree centrality due to extensive overlap in service coverage with neighboring parks. As urban expansion continues, parks in suburban areas have developed rapidly, often leveraging their proximity to the central city [43,44]. Compared to the central core, these areas generally possess more available land and superior environmental conditions [45,46], attracting visitors from across the municipality [47]. Notably, our analysis reveals that many larger suburban parks (e.g., Gucun Park, Century Park) attain high betweenness centrality. They act as critical bridging hubs within the service-overlap network, connecting otherwise disparate park clusters. This pattern aligns with the polycentric spatial structure of Shanghai, where large suburban parks serve as regional destinations that integrate broader sectors of the urban park system.

Although important parks are concentrated in central areas, a park’s network importance is not determined solely by its location. Central Shanghai also contains parks of lower importance (e.g., Penglai Park), while some suburban parks hold pivotal structural roles. This indicates that importance is mediated by additional factors: (1) Park attractiveness and functional capacity. High quality park environments are known to significantly enhance usage rates [48,49]. Parks with greater aesthetic, recreational, or cultural appeal can attract users from beyond their nominal service radius, extending their influence and network relevance. (2) Spatial connectivity and service extent. The spatial relationship between parks and residential areas is fundamental. A larger service radius, often associated with park scale, increases the potential for co-coverage with other parks [50,51]. This enhances a park’s role in creating redundancy and connectivity within the network, making it less replaceable in structural terms.

It is also important to consider that in highly saturated urban areas, extensive service-coverage overlap, while beneficial for network resilience, may entail a trade-off [52]. The clustering of numerous parks with similar service radii and functions can lead to a certain degree of service homogenization, potentially diluting the distinctiveness and appeal of individual parks. Under such conditions, the marginal utility of additional spatial redundancy—in terms of enhancing residents’ recreational experience or choice quality—may diminish. Therefore, planning practice should not only leverage overlap for structural stability but also strategically promote functional complementarity and distinctive differentiation among spatially proximate parks. This approach can mitigate homogenization and elevate overall service efficacy and experiential diversity beyond the provision of basic structural redundancy.

4.2. Discrepancy Between Emergent Network Tiers and Statutory Park Hierarchies

China’s Urban Green Space Classification Standard (CJJ/T85-2017) [53] defines a hierarchical park system (e.g., comprehensive, community, theme parks, etc.) based primarily on scale and facility provisions, reflecting a conventional, top-down planning approach [54,55]. Our SNA, however, reveals a discernible discrepancy between these statutory hierarchies and the emergent functional tiers identified within the service-coverage overlap network (

Table 4. Different types between network tiers and statutory hierarchies.

Types	Contents	Examples of Parks
Aligned tier and hierarchy	Comprehensive parks and Theme parks in the Tier-1 network	Comprehensive parks: Century Park, Lu Xun Park, etc. Theme parks: Shanghai Botanical Garden, Guyiyuan Garden, etc.
	Theme parks and Community parks in the Tier-2 network	Theme parks: Shanghai Gongqing Forest Park, Shanghai Chenshan Botanical Garden, etc. Community parks: Huashan Green Space, Xiangyang Park, etc.
	Theme parks and Small-scale parks in the Tier-3 network	Theme parks: Baoshan Martyrs’ Cemetery, Shanghai Auto Expo Park, etc. Small-scale parks: Kunshan Park, Xinhua Garden, etc.
High network tier but low statutory hierarchy	Community parks in the Tier-1 network	Sichuan North Road Park, Mengqing Park, Haisu Greenland, etc.
	Small-scale parks in the Tier-2 network	Shaoxing Park, Xikang Park, Wuzhong Greenland, etc.
Low network tier but high statutory hierarchy	Comprehensive parks in the Tier-2 network	Shenzhuang Park, Guilin Park, Youcheng Park, etc.
	Comprehensive parks and Community parks in the Tier-3 network	Comprehensive parks: Guhua Park, Fangta Park, etc. Community parks: Mianqing Park, Meilan Lake Park, etc.

). For instance, several community parks (e.g., Sichuan North Road Park, etc.) were positioned in the top network tier (Tier-1). This outcome appears to stem from highly concentrated and overlapping service radii in dense urban cores, representing a case of high network tier but low statutory hierarchy. Conversely, some comprehensive parks (e.g., Shenzhuang Park, Fangta Park, etc.) were identified in lower network tiers (Tier-2/3), illustrating low network tier but high statutory hierarchy.

This observed discrepancy may be attributed to several interacting factors: (1) Spatial adaptation to land constraints: In high-density central areas, the proximity of numerous small parks leads to extensive service overlap, which can elevate their structural importance in the network beyond their nominal statutory grade. (2) Structural influence from co-coverage: The overlap network captures relationships based on shared service populations—a form of spatial redundancy or potential substitutability that is not accounted for in static, attribute-based classifications. (3) Institutional pacing of statutory planning: The established classification system may evolve more slowly than dynamic urban spatial patterns and de facto service coverage.

These findings prompt a pertinent planning reflection: Should statutory hierarchies be adjusted to better reflect the emergent spatial patterns of service overlap and usage? Alternatively, should spatial configurations be actively steered to align with predefined hierarchical categories? This consideration underscores a tension between the bottom-up, spatially self-organized network structure and the top-down, attribute-based planning framework, while also indicating a limitation of current planning approaches that tend to emphasize individual park attributes over the relational structure of the park system as a whole.

Building on this analysis, we propose a network-informed optimization strategy that tailors interventions to the specific functional-spatial role of parks, rather than applying uniform standards based solely on statutory grade.

For parks with high network importance (e.g., Tier-1) but lower statutory grades (e.g., central community parks): The planning priority should be to augment their service capacity and manage localized demand. This involves: (1) Targeted investments to upgrade facilities, landscape quality, and management intensity to sustainably support the high demand within their overlapping service zones; (2) In surrounding high-density areas where land is scarce, actively incorporating pocket parks, vertical greening, and recreational gardens into urban renewal projects to increase local park density [56,57], disperse usage pressure, and enrich the network’s fine-grained redundancy.

For parks with high statutory grades but lower network importance (e.g., some comprehensive parks in Tier-2/3): The focus should shift to activating their potential and enhancing systemic integration. Key strategies include: (1) Prioritizing ecological protection and functional resilience as their primary role, while reserving service capacity for future surrounding development [58,59]; (2) Strengthening their network connectivity by improving multi-modal accessibility (e.g., via greenway development [60]) from broader residential areas and cultivating distinctive functional themes to attract users and solidify their role as regional destinations.

For parks where network tier and statutory hierarchy are aligned: The emphasis should be on the protection and steady maintenance of their existing service functions to ensure they continue to serve as reliable backbone elements of the system.

Looking ahead, the planning of urban park systems could be viewed not merely as an application of static hierarchies, but as a dynamic and integrative process—one that seeks to both accommodate the functional network patterns emerging from actual use (adapting from the bottom up) and to guide the development of more balanced and resilient networks through strategic investment and design (steering from the top down).

4.3. The Duality of Network Stability: Topological Structure, Service Function, and Planning Implications

This study evaluated the stability of Shanghai’s urban park system by simulating two disturbance scenarios—targeted attacks and random failures—from two dimensions: topological structure (size of the Largest Connected Component, S) and service function (Residential Coverage Loss Rate, RCLR). The results reveal a notable duality in system stability: topological integrity and service continuity respond asynchronously, and at times inversely, to different disturbances, presenting deeper requirements for resilience-oriented planning.

Under targeted attacks, service function proves more vulnerable than topological structure. When parks were removed in descending order of comprehensive importance, the decline in service function occurred significantly earlier than the breakdown of the topological network. Data analysis indicates that removing only 22.1% of key nodes led to a 50% reduction in the average park coverage options for residents, while the topological network remained largely intact (S ≈ 0.85). More notably, regional service interruption (over 25% of residential blocks losing all coverage) occurred before the network topology reached a severe damage threshold (S = 0.5). This highlights an important contrast: traditional topological connectivity analysis may overestimate the system’s capacity to maintain actual service provision. The decline in service quality and choice experienced by residents represents a more sensitive and pressing risk signal than the abstract rupture of network connections. Therefore, “service coverage stability” should be considered a core resilience metric that more closely aligns with public needs.

Under random failures, the system demonstrates general robustness based on spatial redundancy. Both topological connectivity and service coverage showed considerable resistance to random node failures, requiring the failure of nearly half the nodes to cause severe degradation in connectivity or coverage. This robustness stems from structural redundancy created by the extensive overlap of park service radii in the high-density urban form, allowing the system to effectively buffer common random disturbances such as temporary maintenance or minor disasters, thereby ensuring the reliability of the basic service network.

The comparison between the two scenarios underscores the heterogeneity of system resilience and its deep dependence on key nodes. The high stability under random failures (high redundancy) contrasts sharply with the marked vulnerability under targeted attacks (high dependency). This insight reveals that the overall redundant efficacy of the system heavily relies on the connective skeleton and service coverage maintained by a few key nodes. Should these structural hubs be strategically removed, the service efficacy of the seemingly redundant network could decline rapidly.

In summary, this study provides a tiered framework for resilience management in park system planning. First, the inherent resilience to random failures validates the effectiveness of the current polycentric, high-overlap spatial layout, which should be maintained as a foundational structure. Second, the research clearly indicates that planning and management must pay heightened attention to the system’s acute sensitivity to the failure of key nodes, rather than being satisfied with average redundancy. Therefore, the core strategy lies in implementing differentiated management and a segmented protection scheme based on node importance.

As the attack simulations confirmed that network stability hinges on a small number of critical parks, we propose ranking all park nodes by their comprehensive importance and segmenting them into three protection tiers (e.g., top 10%, next 20%, and remaining 70%) [61]. Corresponding protection measures—ranging from core to priority to basic—should be applied accordingly (specific measures are detailed in

Table 5. The segmented protection measures of park nodes.

Category	Key Measures
Core protection (Top 10% by comprehensive importance)	• Function-Oriented Planning Safeguards: Incorporate the impact on the service function and population coverage of key node parks as a specialized assessment component in urban renewal and development approvals. Prioritize the protection of their service areas from being compressed and their accessibility from being compromised through land use adjustments and design guidelines. • Intelligent Monitoring and Dynamic Carrying Capacity Management: Establish a real-time monitoring and early-warning system for service population and usage intensity based on IoT and mobile signaling data. Implement dynamic visitor guidance or reservation management during peak periods according to recreational carrying capacity models to optimize visitor experience and prevent overuse. • Service Function and Network Resilience Enhancement: Target investments to upgrade their composite recreational, ecological, and cultural functions, ensuring their service capacity matches their structural role of high network centrality. Develop specialized contingency plans to guarantee prioritized recovery and sustained core services following disturbances.
Priority protection (Next 20% by comprehensive importance)	• Preventive Maintenance and Adaptive Management: Conduct high-frequency inspections of facilities and the ecological environment, establishing a preventive maintenance protocol. Implement adaptive service management during predictable peak periods to balance usage demand with infrastructure sustainability. • Connectivity Optimization and Service Maintenance: Optimize pedestrian and cycling connections to surrounding neighborhoods and public transit stops, reinforcing their accessibility as local service hubs. Maintain and appropriately enhance existing landscapes and facilities to ensure stable service delivery.
Basic protection (Remaining nodes)	• Routine Maintenance and Basic Safeguards: Execute standardized, periodic inspection and maintenance routines to ensure facility safety and general environmental upkeep. • Ecological Base Conservation and Redundancy Maintenance: Perform sustainable green space management, focusing on preserving their role as fundamental redundant units within the service coverage network, thereby supporting the overall resilience of the system.

). This protocol should be dynamically updated if network structure shifts due to disturbances or planning interventions.

Through this approach, priority is given to ensuring the integrity and service capacity of the critical functional nodes that underpin extensive service coverage, while still safeguarding the network’s overall redundancy. This dual focus helps prevent systemic service crises and supports the stable and equitable operation of the urban park network in uncertain environments.

4.4. Limitations and Future Directions

This study has certain limitations in terms of methodology and data, while also pointing the way for future research. First, the model is constructed based on the static spatial overlay of park service radii and residential areas, which essentially represents a “geographic dependency” assumption regarding potential service relationships. Although this approach can effectively depict the coverage pattern of service provision and the network structure, it fails to incorporate dynamic factors such as residents’ actual travel behavior, time preferences, and destination choices. For instance, residents may choose parks beyond their immediate “service circles” due to park quality, social needs, or accessibility—a complex decision-making process that the current static model cannot capture. Second, the key parameters on which the model relies, such as the area threshold for residential nodes (>4 hectares) and the assigned park service radii (based on planning standards and referenced empirical studies), though reasonably simplified, still influence the identification of network structure and key nodes. Therefore, future research should conduct systematic sensitivity analysis to examine the impact of relevant parameters (e.g., different residential area thresholds, service radius values) on the robustness of the conclusions. Additionally, the use of single time-slice data in this study makes it difficult to reflect the spatiotemporal dynamics of park use (such as differences between weekdays and weekends, seasonal variations) and the long-term evolution of supply and demand driven by urban development.

To address these limitations, future research could advance in the following three directions: (1) Integrate multi-source dynamic behavioral data: Combine datasets such as mobile phone signaling, social media check-ins, and shared bicycle trajectories to construct park usage networks based on “actual human flow connections” rather than “theoretical service coverage”, thereby more authentically revealing the system structure driven by resident behavior. (2) Conduct longitudinal temporal analysis: Introduce a temporal dimension to trace the evolution process and mechanisms of park network structure alongside urban renewal, demographic changes, and spatial development. (3) Incorporate user perceptions and social semantics: Use questionnaires, interviews, and other methods to explore the micro-level socio-demographic factors and subjective preferences influencing park choice, infusing the network model with richer social semantics to enhance its explanatory power.

Through advancements in these directions, the application of SNA in urban park system research is expected to become more precise, dynamic, and multidimensional, thereby providing more insightful decision support for scientific planning and refined management.

5. Conclusions

This study applied SNA to evaluate the spatial structure of Shanghai’s urban park system and the key conclusions are as follows:

• Park importance is spatially clustered and influenced by both location and intrinsic attributes. High-degree parks concentrate in dense central areas due to service overlap, while high-betweenness parks in outer areas act as bridging hubs, reflecting the polycentric urban structure.
• A clear discrepancy exists between the emergent functional tiers of the network and the statutory park hierarchy. This stems from spatial adaptation, relational effects of co-coverage, and institutional inertia, highlighting a tension between bottom-up network patterns and top-down planning frameworks.
• The system shows dual stability: topologically vulnerable to targeted attacks yet functionally resilient due to spatial redundancy. This implies service quality may degrade before basic access is lost, requiring planning to address both network integrity and equitable coverage.
• Social network analysis offers a relational framework for optimizing park systems. It enables the identification of key nodes, diagnosis of mismatches, and stability simulation, supporting targeted, tiered interventions for more resilient and effective green space planning.

In summary, a network-oriented perspective can help align park resources with actual use patterns, contributing to more resilient green spaces in high-density cities.