Introduction

The Grand Canal is a major waterway in eastern China, connecting five major river systems: the Haihe, Yellow, Huaihe, Yangtze, and Qiantang Rivers, spanning approximately 1,794 km. Its navigational function relies heavily on a complex and precise system of water engineering facilities. These facilities are the core of the canal’s engineering, ensuing smooth navigation while also serving multiple purposes such as flood control, drainage, and agricultural irrigation, showcasing the remarkable achievements and ingenuity of ancient Chinese hydraulic engineering. The Ming and Qing dynasties marked the peak period of grain transport on the Grand Canal. However, the Huitong River section experienced siltation in parts of its channels due to prolonged lack of maintenance. In 1411, during the 9 th year of the Yongle reign of the Ming dynasty, the government undertook large-scale renovations of the Huitong River section, building numerous new dams and ship locks to restore and enhance the canal’s transportation efficiency, significantly improving its navigability. The Qing dynasty (1644–1912) continued the reconstruction of the river channels and water engineering facilities, further boosting economic exchange and material transport between northern and southern China, providing a solid foundation for the canal’s long-term stable operation1.

The water engineering facility heritage along the Grand Canal remains a crucial component of water resource management today. Therefore, the proper preservation of these heritage sites holds significant importance. However, given the limited financial, human, and material resources, implementing a uniform preservation strategy for all water engineering heritage sites is unrealistic. The central task of current research is to accurately identify the key water engineering facilities within the water transport network, enabling priority protection of the most significant sites during resource allocation to achieve optimized and efficient resource utilization.

Currently, academic research in the field of water engineering facilities is showing a trend toward diversification. On one hand, some scholars focus on the function and structure of individual hydraulic engineering projects, exploring their value within the broader water management system2,3,4,5,6; On the other hand, some scholars have examined water engineering facilities from a broader perspective, considering the interactions between these facilities and surrounding natural resources, socio-economic conditions, and engineering management7,8,9,10,11,12,13. Their primary focus has been on developing an evaluation system for the efficient operation of water engineering facilities. These research findings provide a solid theoretical foundation and practical guidance for advancing studies on key water engineering facilities.

Currently, academic research on Water engineering facilities along canals has achieved remarkable results. However, there is still a relative lack of studies that deeply explore the interaction mechanism between facilities from a relational perspective. The Beijing-Hangzhou Grand Canal, as a huge and precise water conservancy engineering system, is not composed of a simple stack of Water engineering facilities, but is based on the interconnectedness of the facilities, which together constitute an organic whole. Only by analyzing the complex and subtle interconnections between these facilities from a holistic point of view can the key facilities in the water transportation network be accurately identified.

In academic research, the “relational perspective” refers to a research entry point that focuses on the interaction between research objects, the mechanism of mutual interaction and the mode of dependence. Through this perspective, it is possible to break through the limitations of studying individual objects in isolation, and instead understand things from the level of the overall network structure. Social network analysis, as a common tool for studying the internal connections of a system, can reveal the relationships between entities and the differences in their influence”14. For example, Song et al.15, Zhang et al.16, and Guo et al.17 used social network analysis to construct different rail transit networks, revealing the differences in the overall influence and transportation capacity of each station. In addition, on the basis of using the social network analysis method, there are scholars who combine the TOPSIS method and factor analysis method to determine the importance ranking of the nodes based on the contribution of each indicator. For example, after Phong Nha et al. used the social network analysis method to construct the port network system, the study further used the TOPSIS method to comprehensively evaluate the major ports in order to filter out the ports with high influence. Based on the wide application of TOPSIS method in network research, this paper innovatively introduces the social network analysis method into the heritage study of Water engineering facilities in water transportation network and applies the TOPSIS method to provide a comprehensive score for each Water engineering facility.

Meanwhile, in order to enhance the visualization of the influence distribution of nodes in the network, the kernel density analysis method is introduced in this study. This method is usually used for the identification of hotspot areas and the visualization of spatial patterns. For example, Xie et al. used the kernel density method to effectively estimate the density of hotspots in traffic accidents18, and Okabe et al. used the kernel density estimation method to estimate the density of points on the network, and implemented the method in the GIS environment for the study of finding “hotspots” in the network19. In this paper, the values of node indexes are taken as weighting parameters, and the kernel density analysis method is used to realize the visual presentation of the distribution of node influence, which provides an important technical support and theoretical basis for the in-depth analysis of the structure of the water transport network, excavation of key facilities and optimization of the network layout.

In summary, this study adopts the social network analysis method and integrates the kernel density analysis and TOPSIS method to construct a comprehensive evaluation model, taking the water engineering facilities in the Huitong River section of the Beijing-Hangzhou Grand Canal as the object of study, and based on the multiple dimensions of whole-local-individual, the overall spatial structure change of Water engineering facility system of the Ming and Qing Dynasties is elaborated in depth; the study aims to reveal the interaction mechanism and contact between major regions; assess the importance of each Water engineering facility and identify the key nodes. At the same time, through the comparative analysis of the Ming and Qing dynasties, the study explores the changes in the center of gravity of water conservancy under different natural and social conditions. This study not only enriches the study of the complex water transport network of the ancient Chinese Huitong River section, but also has important research significance for the priority protection of canal heritage, and provides a novel perspective and idea for the discussion of the relationship between global linear cultural heritage, transportation network and various associated heritages.

Materials and methods

Research area and subjects

This study focuses on the Huitong River section of the central part of the Grand Canal, specifically examining the water engineering facilities along this segment. The Huitong River section stretches approximately 480 km from Linqing City in Shandong Province to Tai’erzhuang District in Zaozhuang City, Shandong Province (Fig. 1). This section is the highest in elevation and has the greatest topographical variation in the Grand Canal, characterized by a central high point with lower elevations on both sides. The highest point is located at Nanwang Town in Jining, Shandong Province, where the canal bifurcates into northern and southern branches20.

Fig. 1
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Geographical distribution of the huitong river section.

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Due to its unique topography and elevation, the Huitong River section has become the stretch of the Grand Canal with the highest density of ship locks and the most significant achievements in hydraulic engineering21. It also has the largest number of water engineering facilities. These facilities are constructed by the government to manage water flow, utilizing gates, ship locks, and other equipment to regulate water levels and control flow. During the Ming dynasty (1368–1644), there were 229 water engineering facilities in operation along the Huitong River section, while in the Qing dynasty, this number increased to 367 (Figs. 2 and 3). Historically, the Huitong River has faced numerous risks of siltation and flooding. These water engineering facilities have played a crucial role in flood control, silt management, water resource regulation, and ensuring smooth navigation.

Fig. 2
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Distribution of water engineering facilities in the huitong river section during the ming dynasty.

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Fig. 3
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Distribution of water engineering facilities in the huitong river section during the qing dynasty.

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Data sources

This study extensively explored hydraulic monographs and ancient maps, such as the Shandong Gazetteer and Overview of River Defense, to accurately obtain detailed information on the water engineering facilities along the Huitong River section, including their names, corresponding river sections, and geographic locations. For data processing, the research team used the internationally recognized WGS84 coordinate system to accurately extract data, ensuring its precision and reliability. Additionally, to further verify the exact locations of the water engineering facilities, the team employed field survey methods. Through on-site inspections and comparisons, they confirmed the precise geographic coordinates of the facilities along the Huitong River. The team also conducted comprehensive field research on the heritage water engineering facilities and successfully used drone technology to capture the entire site, collecting high-quality 3D point cloud model data. Subsequently, the team utilized advanced drone modeling software, Context Capture Master, to precisely integrate the collected point cloud data, producing detailed models, as shown in Figs. 2 and 3.

The research team considered multiple factors, including the geographic coordinates of the water engineering facilities, the topography of the Huitong River section, and the flow direction of the river network. Based on this, they compiled edge lists for the water engineering facilities during the Ming and Qing dynasties, providing a data foundation for model construction in UCINET. Detailed steps for constructing the model are outlined in the model construction section. When building the river network data system, the team relied on relevant information from the Historical Atlas of China and integrated it with modern DEM data (http://www.geodata.cn), accurately extracting hydrological maps that closely resemble the water systems of the Huitong River during the Ming and Qing periods. This provided a robust data foundation for the study. Additionally, the research team referenced the administrative divisions in Ming and Qing dynasty maps, using the prefecture-level administrative regions through which the Huitong River flows as the base map area. The base maps were sourced from a reputable institution, the WorldMap Harvard Community (https://worldmap.maps.arcgis.com/home/index.html), ensuring the accuracy and authority of the data results.

Research framework

In this study, GIS, UCINET, SPSS and other software are comprehensively used to systematically investigate the characteristics of the relationship network of Water engineering facilities in the Huitong section of the Beijing-Hangzhou Grand Canal during the Ming and Qing Dynasties.

Step 1: Based on the topography and terrain, the water flow direction of the Beijing-Hangzhou Grand Canal and the geographic location of Water engineering facilities, we constructed the edge list of Water engineering facilities in the Huitong River section of the Beijing-Hangzhou Grand Canal.

Step 2: The directed network diagrams of Water engineering facilities in the Huitong section of the Beijing-Hangzhou Grand Canal in the Ming and Qing Dynasties were drawn separately using Netdraw software.

Step 3: The relational networks of the Ming and Qing Dynasties were analyzed using UCINET software to obtain the overall network indexes as well as the network indexes of each node, respectively.

Step 4: In the overall network structure characterization, the overall network indicators in the network, such as network density, network diameter, average path length, clustering coefficient and other indicators, are selected to assess the connectivity and tightness of the whole network; in the local network characterization, the degree, Betweenness Centrality of each Water engineering facility in the network are extracted, Closeness Centrality of each water engineering facility in the network, after normalization, combined with the kernel density analysis method, to explore its regional spatial distribution characteristics; in the node characterization, using the TOPSIS integrated analysis method in SPSS software, the three major network indicators after normalization, with 1:1:1 weight assignment, and finally obtain the ranking of the importance of the Water engineering facilities in the Ming and Qing Dynasties, to identify the key nodes of the network. key nodes. As shown in Table 1 and Fig. 4.

Table 1 Practical significance of network indicators.
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Fig. 4
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Technical approach.

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Research methods

Social network analysis method

Social Network Analysis (SNA) originated in the 1960 s within Western anthropology and sociology. It is a method for studying social structures that reveals patterns and laws of social organization by analyzing the relationships (edges) between individuals (nodes)22,23,24. Particularly in studies of spatial structures—such as transport nodes and shipping—SNA helps researchers identify and understand key nodes and connection patterns within these networks, enabling a deeper exploration of the network’s structural characteristics and dynamic changes.

Degree

The degree of a node refers to the number of other nodes directly connected to it. A higher degree indicates greater centrality of an individual node within its local vicinity. In the relational network of water engineering facilities along the Grand Canal, a larger degree value for a facility signifies stronger connectivity within a certain range25.

(1)

Where i is the focal node, j represents all other nodes, N is the total number of nodes, CD(i) is the degree of node i, which calculates the number of direct connections between node i and other nodes j (i ≠ j, excluding self-links), and X is the edge list that represents the connection relationship between Water engineering facilities in the network.

Betweenness centrality

Betweenness centrality measures the frequency with which a node appears on the shortest paths between other nodes in the network. Nodes with high betweenness centrality can serve as“bridges”in the flow of information or the transfer of resources within the network. In the relational network of water engineering facilities along the Grand Canal, a higher betweenness centrality value for a facility indicates a greater capacity to function as a transportation hub26.

(2)

In this equation, CB(i) is the value of the node’s betweenness Centrality. bjk represents the minimum number of paths between nodes j and k, and bjk(ni) denotes the number of shortest paths between all nodes in the network (including node ni).

Closeness centrality

Closeness centrality is defined as the reciprocal of the average shortest path length from a node to all other nodes it is connected to. Nodes with high closeness centrality can access other nodes in the network more quickly. In the relational network of water engineering facilities along the Grand Canal, a higher closeness centrality value for a facility indicates a faster transfer speed to other water engineering facilities27.

(3)

In the formula, CC(i) represents the closeness centrality of node i. N is the total number of nodes in the graph. d(i,j) denotes the shortest distance between node i and node j, where j represents any other node in the network and (i ≠ j).

Kernel density analysis

Kernel density analysis is a method used to estimate the density distribution of spatial data points. This method aids in identifying spatial clustering trends in the data, such as areas of high concentration or sparse regions28,29. In this study, the network indicator values of water engineering facilities are assigned as weights in the kernel density analysis, allowing for a more accurate simulation of the actual influence and distribution patterns of facility points in the network space. The formula is as follows30:

(4)

In the formula, f(x,y) represents the estimated density at the location (x,y). n is the number of input points. xi,yi are the coordinates of the i-th point, K is the kernel function (a quartic kernel is used in ArcGIS 10.8), and h is the bandwidth.

TOPSIS method

The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) comprehensive evaluation method originated in 1981, first proposed by C.L.Hwang and K.Yoon31. The TOPSIS method is a multi-criteria decision analysis tool used for comprehensive evaluation of multiple objects or alternatives based on various indicators. Its fundamental principle is to rank the alternatives by assessing the distances between the evaluated object and the ideal and anti-ideal solutions. An alternative is considered the optimal solution if it is closest to the ideal solution while being farthest from the anti-ideal solution32. This method effectively utilizes the information contained in the original data to accurately reflect the differences between various evaluation alternatives33,34. However, it is crucial to carefully consider the objective selection of weights during its application, as improper weighting can introduce a degree of subjectivity into the results.

This study analyzes the significance of each water engineering facility, requiring a comprehensive evaluation and ranking of multiple indicators for each facility. In this research, the method takes into account various indicators and their weights to calculate a composite score for each water engineering facility, allowing for effective ranking. Furthermore, the TOPSIS method requires all attribute values to be converted into numerical forms, making it particularly suitable for the indicators that have already been quantified in this study35,36. The evaluation results are intuitive, easy to understand and interpret, and assist decision-makers in quickly grasping key information. Therefore, the choice to use the TOPSIS method for the comprehensive assessment of water engineering facilities in this study is both appropriate and rational.

Assuming there are m nodes in the network that need to be evaluated, each node has n evaluation indicator values, and an indicator system composed of n indicators is used to assess the importance ranking of the m nodes37.

Data preprocessing
(5)
(6)

For positive coordinates:

(7)

For negative coordinates:

(8)
Optimal and anti-optimal solutions

Optimal solution:

(9)

AntiOptimal solution:

(10)
Calculate the distances between each evaluation alternative and the optimal and anti-optimal solutions
(11)
(12)

Where wj is the weight of the j-th attribute.

The proximity of the evaluation object to the optimal solution is indicated by the Ci value; a larger Ci value signifies a more favorable evaluation object
(13)

Model construction

Based on the topography and water flow direction of the Huitong River section of the Beijing-Hangzhou Grand Canal, the research team combed the water flow connectivity between two neighboring Water engineering facilities to generate the edge list of water engineering facilities in the Huitong River section of the Ming and Qing Dynasties. In the edge list, the starting node is the Water engineering facility where the river flows out, and the ending node is the Water engineering facility where the river flows in. The direction of pointing between two nodes, i.e., the direction of water flow, is represented by an edge in the network diagram (if the river passes through point A to reach point B, the diagram is expressed as A → B). In addition, given that this paper is concerned with the correlation between nodes or the connectivity of nodes, and does not consider the transmission of specific water flow, the weight of the edges between nodes is uniformly set to 1, which only indicates that there is a linkage relationship between nodes. This not only simplifies the model, but also helps to highlight the basic structural characteristics of the network, making the analysis more concise and clear, and facilitating the understanding and grasping of the overall architecture of the network.

Subsequently, the Network tool in UCINET software was used to analyze the data and format conversion, and then the “Netdraw” tool was used to visualize the data. Finally, the team successfully constructed the corresponding relational network model of Water engineering facilities. Specifically, the Water engineering facility network of the Ming Dynasty contains 229 nodes and 245 edges, while the Water engineering facility network of the Qing Dynasty contains 367 nodes and 376 edges. Visual representations of these networks can be seen in Figs. 5 and 6.

Fig. 5
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Relationship network model of water engineering facilities in the huitong river section in the ming dynasty.

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Fig. 6
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Relationship network model of water engineering facilities in the huitong river section in the qing dynasty.

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Results

Evolution of the overall network structure of the huitong river section during the ming and qing dynasties

To investigate the changes in the Water Engineering Facilities network during the Ming and Qing dynasties, this study constructed a network model representing the connections between these facilities and extracted network metrics such as average path length, network density, and clustering coefficient. This analysis facilitates a comparative examination of the overall network characteristics of the two dynasties (Table 2).

Table 2 Characteristics of the huitong river section relationship network metrics.
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From the Ming Dynasty to the Qing Dynasty, the scale of the water engineering facilities network along the Huitong section of the Grand Canal significantly expanded. Specifically, the number of nodes increased from 229 in the Ming Dynasty to 367 in the Qing Dynasty, representing a growth of 60%. Meanwhile, the number of connecting edges also rose from 245 to 376, reflecting an increase in network complexity. However, despite the significant expansion of network scale, the overall network density showed a decreasing trend. This phenomenon indicates that the expansion of network scale did not directly enhance the spatial connections among water engineering facilities; rather, it likely allowed these facilities to cover a broader geographic area, while the density of connections may have relatively decreased due to this expanded geographic distribution.

As shown in Table 1, the network diameter increased from 48 in the Ming Dynasty to 79 in the Qing Dynasty, indicating a significant increase in the maximum distance between nodes, which typically implies an increase in the number of inter-regional connections. At the same time, the average path length increased from 15.6 to 23.5, indicating that the connectivity within the network has decreased or that the network structure has become more complex. Furthermore, the decline in the average clustering coefficient, from 0.007 to 0.001, indicates a weakening of the network’s local cohesion and stability, with a reduction in direct connections between nodes, reflecting a decrease in the local aggregation of the network.

From the Ming Dynasty to the Qing Dynasty, both the Out-Degree and In-Degree of water engineering facilities declined, indicating that as the network expanded, the importance of individual facilities within the network diminished. This may suggest a more decentralized distribution of power and functions, with a reduced reliance on individual nodes for the consolidation of goods. Meanwhile, the slight increase in betweenness Centrality indicates that, despite the network’s decentralization, more nodes began to assume the role of transit hubs, thereby maintaining overall network connectivity.

Analysis of the structural evolution of regional differences in the network of the huitong river section from the ming to the qing dynasty

To visually present the characteristics of spatial aggregation, the research team used ArcGIS 10.8 software to conduct spatial kernel density analyses of the water engineering facilities in the Huitong River section during the Ming and Qing Dynasties. The results of the study are shown in Figs. 7,8,9,10,11,12.

Fig. 7
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In-degree of water engineering facilities in the huitong river section in the ming dynasty.

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Fig. 8
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In-degree of water engineering facilities in the huitong river section in the qing dynasty.

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Fig. 9
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Out-degree of water engineering facilities in the huitong river section in the ming dynasty.

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Fig. 10
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Out-degree of water engineering facilities in the huitong river section in the qing dynasty.

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Fig. 11
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Distribution map of in-degree of water engineering facilities during the qing dynasty.

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Fig. 12
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Distribution map of out-degree of water engineering facilities during the qing dynasty.

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During the Ming and Qing Dynasties, the water engineering facilities in the Huitong River section, characterized by high degree, exhibited a"single-core belt-shaped"distribution centered around the Nanwang Water Diversion Hub. The Nanwang Water Diversion Hub, which includes the Nanwang Diversion Weir, Changming Dourmen, Liulin Gate (Nanwang Upper Gate), Shili Gate, and Yongtai Dourmen, constitutes one of the most technologically advanced projects along the Grand Canal and is often referred to as the“Northern Dujiangyan”38. This area was historically home to the Matahu Lake, Nanwang Lake, Shushan Lake, and Machang Lake, which were part of the"Northern Five Lakes."The existence of these lakes not only provided vast water bodies for the water engineering facilities but also facilitated closer and more diverse connections among them. According to the analysis results presented in Figs. 7,8,9,10, the red areas indicate a strong connectivity within the network, serving as important“connection stations”for shipping traffic in the Huitong River section during the Ming and Qing Dynasties.

The relationship network of water engineering facilities in the Qing Dynasty showed stronger overall connectivity compared to that in the Ming Dynasty. For instance, In the figure, the elliptically selected area shows that there were gaps in connectivity during the Ming Dynasty, whereas improvements made in the Qing Dynasty significantly enhanced connectivity in this area, ensuring the continuity of the waterways. This indicates that the newly added water engineering facilities in the Qing Dynasty played a crucial role in enhancing the overall accessibility and connectivity of the network. They not only addressed the shortcomings in water transport regulation from the Ming Dynasty but also effectively prevented issues such as river segment siltation or inability to regulate excessive water flow due to sparse water engineering facilities.

The study examines the degree of water engineering facilities to identify and protect key nodes. For instance, for water engineering facilities with high In-Degree, it is important to strengthen the water retention function on the inflow side to prevent damage from water flow to the facilities themselves; For facilities with high Out-Degree, the stability of the dam on the outflow side should be enhanced, employing energy dissipation methods such as stilling basins, anti-scour channels, and hydraulic jumps to manage water flow and protect downstream areas and river vessels from erosion caused by water currents. Additionally, regular dredging at river bifurcation points should be conducted to maintain unobstructed water flow and prevent sediment accumulation that could lead to channel blockages. Specific data can be found in Figs. 11 and 12, For the corresponding numbers of water engineering facilities, see Appendices A and B.

During the Ming and Qing dynasties, water engineering facilities with high betweenness centrality exhibited a“striped”distribution centered around Nanyang Lake (Fig. 13,14). Building on the foundations laid in the Ming dynasty, the Qing dynasty further strengthened the hub function of water engineering facilities in these areas. Nanyang Lake is located in the northern part of Weishan County, Shandong Province, where important water engineering facilities such as Yong’an Gate, Nanwang North Gate, Nanwang South Gate, and Shijiazhuang Gate are distributed. Additionally, the performance of water engineering facilities in the northern part of Xuzhou Prefecture during the Qing dynasty was enhanced based on improvements made in the Ming dynasty, including the Sankong Bridge, Zhaoyang Lake Gate, Luba Three-Hole Bridge Stilling Basin, Hekou New Gate, and Xu Family Lower Gate. These improvements transformed the area into an important hub center.

Fig. 13
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Betweenness centrality of water engineering facilities in the huitong river section in the ming dynasty.

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Fig. 14
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Betweenness centrality of water engineering facilities in the huitong river section in the qing dynasty.

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The Nanyang Lake area, with its abundant rainfall and well-developed water systems, including multiple tributaries such as the Guangfu River and the Si River, provides ideal natural conditions for the development of water engineering facilities39. At the same time, repeated breaches of the Yellow River at locations such as Tongwaxiang have disrupted the canal. These natural disasters, combined with society’s urgent demand for water engineering facilities, have jointly driven the region to become a key“transit station”in the Huitong River segment.

High betweenness Centrality of Water engineering facilities in the network in a key connection position, can play an important role in the transmission and deployment of water flow control. However, these areas are often prone to frequent natural disasters. Therefore, the maintenance and protection of these water engineering facilities are particularly critical. Once damaged, they can have a significant impact on the entire system. To enhance monitoring and management efficiency, relevant departments can employ remote sensing technologies for regular inspections and maintenance to ensure the normal operation of the facilities.

During the Ming and Qing dynasties, water engineering facilities with high closeness centrality exhibited a"multi-core"dispersed distribution pattern (Fig. 15,16,17,18). As the number of water engineering facilities increased in the Qing dynasty, the spatial distribution of core areas became more balanced. These transfer center areas are mainly located along the secondary channels of the Grand Canal, near facilities such as the Manjia Single Gate, Wangjia Single Gate, Pengkou Gate, and the Zhuji Zhuang Water Reduction Gate. This also indicates that the natural regulation of rivers in these areas is weak, necessitating human intervention through the installation of facilities. In future water flow regulation efforts, it is essential to strengthen facility construction in areas with weak natural regulation capabilities to ensure the long-term sustainable use of rivers.

Fig. 15
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In-closeness centrality of water engineering facilities in the huitong river section in the ming dynasty.

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Fig. 16
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In-closeness centrality of water engineering facilities in the huitong river section in the qing dynasty.

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Fig. 17
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Out-closeness centrality of water engineering facilities in the huitong river section in the ming dynasty.

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Fig. 18
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Out-closeness centrality of water engineering facilities in the huitong river section in the qing dynasty.

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The new water engineering facilities added during the Qing dynasty, building upon those of the Ming dynasty, became emerging transfer stations in the network, as illustrated in the Fig. 18. Their geographic locations lie between the transfer centers of the main river channel and those of significant tributaries, enhancing the operational efficiency of goods between the main channel and the tributaries. Water engineering facilities with high transfer capacity have a direct impact on surrounding villages, promoting local economic development, providing irrigation water sources, supporting agricultural activities, and potentially creating opportunities for tourism and fisheries.

In summary, the water engineering facilities located along the main river channels in the Beiwuhu and Nanyang Lake regions are closely interconnected, creating a high degree of interdependence. This layout reflects the vertical connectivity among the various gates, showcasing the overall coordination and efficiency of the water engineering system. For instance, the ancient gate group in the Yanggu section of the Huitong River exemplifies this connectivity, as the spatial relationships among the gates and the curvature of the river bend provide tangible evidence of vertical interaction within the ancient canal system40. Moreover, the water engineering facilities along the secondary channels possess significant transshipment capabilities and a high degree of independence. Each facility plays a unique role in its specific location, collectively maintaining the normal operation of the complex water engineering system of the Grand Canal. These facilities not only represent outstanding examples of ancient hydraulic engineering but also serve as powerful evidence of the well-developed and efficient management system of the Grand Canal.

Comprehensive evaluation of the importance of water engineering facilities in the huitong river section during the ming and qing dynasties

This study provides a comprehensive evaluation of the network from multiple dimensions, utilizing key indicators such as average path length, network density, and clustering coefficient to analyze the trends in network structure. At the node level, the research focuses on three core indicators closely related to the functions of water engineering facilities: degree, betweenness centrality, and closeness centrality. The aim is to accurately characterize the connectivity, hub role, and transfer efficiency of water engineering facilities within the water transport network.

To ensure the objectivity and comparability of the analysis results, the study first normalized the network data and employed an equal-weight calculation method to establish a positively oriented indicator system, where higher indicator values directly reflect better performance of the water engineering facilities. Subsequently, the study utilized the TOPSIS comprehensive analysis method to systematically compute the aforementioned three indicators41, resulting in a ranking of the importance of each node within the Ming and Qing water engineering facility network. For a comprehensive list of rankings, refer to Appendices A and B. Given the large number of network nodes, this study only presents a selection of the water engineering facilities with the highest importance rankings, with detailed rankings available in Tables 3 and 4.

Table 3 Comprehensive evaluation of the importance of water engineering facilities in the ming dynasty along the grand canal section.
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Table 4 Comprehensive evaluation of the importance of water engineering facilities in the qing dynasty along the grand canal section.
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The research results indicate that during the Ming Dynasty, 19 water engineering facilities had a closeness centrality of 0.4 or higher, while this number increased to 31 in the Qing Dynasty. Notably, some core facilities from the Ming period continued to play crucial roles in the Qing period. This phenomenon is closely related to the geographical locations of these facilities, which are primarily concentrated around Nanyang Lake in the Southern Four Lakes area and the Ancient Northern Five Lakes region. The extensive water bodies in these lakes facilitated a richer network of connections among the water engineering facilities. Consequently, the water engineering facilities in this region are regarded as key projects within the Grand Canal section, underscoring their vital role as an essential artery for water transport. In the context of heritage conservation and restoration, these facilities should be prioritized for protection and given significant attention. Additionally, relevant authorities can utilize the calculation results to scientifically and rationally categorize the importance of the water engineering facilities, allowing for the implementation of more targeted protection measures.

Discussion

This study adopts social network analysis, kernel density analysis method and TOPSIS comprehensive evaluation tool to construct a systematic and data-driven basic framework for identifying and evaluating the importance of Water engineering facilities in the Huitong section of the Beijing-Hangzhou Grand Canal and their changing patterns with historical changes.

Evolution of the overall structure of the relationship network

The evolution of the relationship network of Water engineering facilities in the Huitong River section during the Ming and Qing Dynasties reflects the profound impact of the era’s development on the water transportation system. At the level of network scale, compared with the Ming Dynasty, the network of Water engineering facilities in the Qing Dynasty expanded significantly and became more massive and complex. This change reflects the Qing Dynasty on the development and utilization of the Huitong River increased, added a number of Water engineering facilities to meet the growing demand for water transportation, such as regulating the amount of water to build additional locks and dams, for ships docking wharf, etc.

In terms of network structure, the Qing Dynasty showed a more balanced and decentralized layout. While the Ming Dynasty may have been dominated by some facilities, the Qing Dynasty, through the addition of facilities and the optimization of the layout, resulted in a narrowing of the differences in the status of the nodes and a more balanced distribution of resources. Although the tightness and local connectivity of the network were weakened in the Qing Dynasty, i.e., there were fewer direct links between facilities in some areas, the overall connectivity and stability of the network was consolidated. This means that by constructing a wider range of connections and redundant paths, the Qing Dynasty enhances the ability of the entire water transportation network to cope with local failures or changes, so that even if some nodes have problems, the network can still remain basically uninterrupted to ensure the continuous operation of water transportation.

Characteristics of the evolution of network regional differences in structure

During the Ming and Qing Dynasties, the Water engineering facilities in the Huitong River section had distinctive features in spatial distribution. In the area centered on Nanwang Diversion Hub, the connectivity of Water engineering facilities is relatively strong, and there are a large number of water engineering facilities with high connectivity degree, forming the spatial distribution of “mono-core belt”. As a key hydraulic project of Huitong River, Nanwang Diversion Hub plays a central role in regulating water volume and guaranteeing smooth water transportation, and the surrounding facilities are arranged around it to realize efficient collaboration and ensure smooth operation of water transportation. Water engineering facilities with high betweenness Centrality show a clear “band” pattern around Lake Nanyang. Betweenness Centrality is a measure of the ability of Water engineering facilities in a network to serve as transportation hubs. Nanyang Lake gathers a number of important water transportation routes, and the Water engineering facilities distributed around it, with high betweenness Centrality, are able to effectively regulate and manage the transfer of materials and the movement of people between different water transportation routes, and thus play an important role in maintaining spatial connections in the regional transportation system.

In the spatial layout, Water engineering facilities with high Closeness Centrality show a “multi-core” discrete distribution pattern. Closeness Centrality is used to measure the convenience of a node in the network to reach other nodes. The “multi-core” distribution pattern in the Huitong River section indicates the existence of multiple regional transit hubs, each of which radiates to the surrounding areas with itself as the center, synergistically enhancing the transport efficiency of the entire water transport network and expanding its coverage.

Comprehensive assessment of the importance of water engineering facilities and the significance of heritage conservation

Through the comprehensive assessment of the importance of Water engineering facilities in the Ming and Qing Huitong River section, key nodes in the water transportation network were successfully identified. These key nodes, such as pivotal locks and dams, assumed a central function in the water transportation network during the historical period, and were key to the transportation role of the Huitong River. Prioritizing the protection of these key nodes can maximize the retention of the historical function and cultural value of the Huitong River, allowing the world to see the wisdom and brilliance of the ancient water transport project, and continue its historical memory as an important channel for ancient water transport.

From a practical point of view, these key nodes often have high potential for tourism development and cultural dissemination value. Priority protection can, on the one hand, rely on its unique historical and cultural connotations, develop cultural tourism projects, attract tourists, and promote regional economic development; on the other hand, through the display and publicity of the key nodes, it can enhance the public’s awareness of the heritage of the Ming and Qing Huitong River, promote the inheritance and dissemination of culture, and realize the benign interaction between the protection of cultural heritage and the development of the regional economy, so as to revitalize the historical and cultural heritage in the modern society. It can realize the positive interaction between cultural heritage protection and regional economic development, so that the historical cultural heritage can be revitalized in the modern society.

This study puts forward suggestions for the protection and development of Water engineering facility heritage from the perspective of sustainable development:

  1. 1.

    Establishment of a hierarchical and dynamic conservation strategy: The framework and assessment methodology constructed in the study provide a scientific basis for the hierarchical conservation of Water engineering facilities in the Huitong River section of the Beijing-Hangzhou Grand Canal. Policy makers can prioritize resources for repairing important facilities according to the assessment results, establish a dynamic assessment mechanism to avoid resource mismatch, and provide references for heritage protection in other regions according to its theories and methods.

  2. 2.

    Innovative mechanisms for joint conservation of historical heritage: Based on the relational perspective, it is possible to clarify the intrinsic links between different hydraulic heritage sites. Policy makers can promote the establishment of a joint protection mechanism for historical heritage, integrate resources of all parties to create a coherent historical and cultural line, enhance the systematic nature of heritage protection, and promote regional cultural exchanges.

  3. 3.

    Developing a new path for global water heritage management: The study provides a new perspective on the protection and rational utilization of global water engineering and historical heritage by approaching it from a relational perspective. The broad applicability of the research methodology makes it generalizable to global water conservancy project management. Policy makers can make use of this research system to formulate management policies based on the unique network structure and functional characteristics of water projects such as the Panama Canal and the Suez Canal, so as to optimize water resources allocation and enhance the efficiency of transportation. Meanwhile, for heritage projects such as ancient irrigation systems, policies can be formulated based on the historical role and modern significance revealed by the study, taking into account both conservation and rational utilization, so as to achieve a balance between cultural heritage and engineering benefits.

Comparison of studies and limitations

The research on the Beijing-Hangzhou Grand Canal has attracted more and more scholars’ attention. In the past, studies usually focused on the function and structure of individual Water engineering facilities7, or focused on evaluating the effectiveness of these facilities at the level of operation and management8, as well as exploring the heritage value of these facilities as a tourism resource42. In recent years, the research perspective has been expanded, and some scholars have begun to try to systematically study the spatial distribution of Water engineering facilities43,44, which has brought a new direction to the research in this field. This paper takes the water transportation network of the Huitong section of the Beijing-Hangzhou Grand Canal as an organic whole as the research basis, and focuses on the network association and interaction mechanism among Water engineering facilities from the perspective of relationship, breaking through the limitations of traditional research perspectives, and analyzing the inherent law of water conservancy project operation in a more comprehensive and systematic way.

However, this study also has certain limitations. When analyzing the changes in the importance of Water engineering facilities, the study mainly focuses on internal factors such as the network structure and the function of the facilities themselves. Although external factors such as climate change, river diversion, and national policies were explored in the analysis of the results, the depth of the study was insufficient due to the lack of systematic information on hydrology and climate in ancient times. In the future, the study will take external factors as a breakthrough, explore the relationship between them and key nodes, integrate multidisciplinary resources such as historical geography, environmental archaeology, etc., and make up for the insufficiency of the documentary records by means of on-site archaeological surveys and ancient environmental reconstruction, so as to obtain richer first-hand information and build a more complete assessment system of the significance of Water engineering facilities, which will provide scientific references for the protection of water conservancy heritage and the planning of modern water conservancy projects. scientific reference for the protection of water conservancy heritage and planning of modern water conservancy projects.

Conclusions

This study takes the water engineering facilities of the Grand Canal’s Huitong River section as a case study, focusing on these facilities as the primary research subjects. First, the research employs UCINET to construct the water engineering facility networks for both the Ming and Qing dynasties, extracting relevant network metrics related to the functions of these facilities for analysis. Next, a kernel density estimation method is used to analyze the regional network. Finally, the TOPSIS method is applied for a comprehensive ranking of the importance of each water engineering facility.

The results indicate that: (1) From an overall network perspective, the evolution of the network structure from the Ming to Qing dynasties shows a general trend of scale expansion and network decentralization. The Qing dynasty’s network is more complex and extensive than that of the Ming dynasty, covering a larger area; however, the network density and local connectivity have decreased. (2) From a regional perspective, water engineering facilities with strong connectivity during the Ming and Qing dynasties were primarily located near the Nanwang water diversion hub in the Gubei Five Lakes area. Facilities that served as important transportation hubs were distributed around the Nanyang Lake area and the Nanwang water diversion hub. Meanwhile, facilities that facilitated transfer functions were concentrated in the tributaries surrounding the main channel of the Grand Canal. (3) During the Qing dynasty, water engineering facilities exhibited stronger transfer capabilities compared to the Ming dynasty, and the distribution of facilities serving as transfer centers became more balanced. These developments contributed to a more systematic and scientific water transport network in the Qing dynasty, facilitating navigation. In contrast to the Ming dynasty, the state’s reliance on the water transport network gradually deepened during the Qing dynasty. (4) In terms of overall strength, there were 19 key water engineering facilities in the Huaihe River section during the Ming dynasty and 31 during the Qing dynasty, primarily located in the Nanyang Lake and the ancient Northern Five Lakes, which serve as the core hub areas of the Huaihe River section.