Research on Risk Evolution Mechanism of Urban River Ecological Governance Project Based on Social Network Analysis

Abstract

The evolution and transfer of risk elements of urban river ecological management projects are primarily responsible for the difficulty of risk management in these projects. In this paper, we identify 63 risk elements of urban river ecological management projects using in-depth literature reviews and brainstorming. The association among all the risk elements is constructed using an expert survey method, and the risk elements are utilized as network nodes. The relationships between these nodes are then used as network edges (i.e., paths) to construct a complex network model. By using the network visualization and analysis tool anaconda3, we analyze the overall and local characteristic parameters of the risk network. The risk transmission characteristics of the urban river ecological management project are analyzed according to the parameter characteristics to reveal the inner relationships of risk transmission inherent in the complex network. We use the Jinghe ecological management project in Jinghe New City to verify the effectiveness of the proposed model. The study demonstrates that the starting node risk needs to be controlled, and the conduction node that indirectly triggers risk propagation needs to be cut off to achieve risk prevention and control. Accordingly, the risk prevention strategy is proposed, namely, paying close attention to the starting nodes of schedule delay risk, construction cycle risk and cost overrun risk, as well as the conduction risk nodes of project complexity risk, quality assessment risk, construction accident risk and improper drawing design risk. Effective measures should be taken to control the transmission and occurrence of risks based on these two aspects. The study reveals the network evolution of risk factors, which enriches the theory of the risk factor network evolution and evaluation of urban river ecological management projects.

1. Introduction

With the continuous development of the Chinese economy, the water conservancy industry is currently in a stage of rapid development. An increasing number of single and comprehensive water conservancy projects are continuously being constructed and applied, providing an important guarantee for the social stability and sustained economic development of the country. Recent statistics indicate that the total cumulative investment in water conservancy construction reached two trillion Yuan in the “water conservancy reform and development” “Twelfth Five-Year Plan” period. During the “Thirteenth Five-Year Plan” period, the national water conservancy investment reached 3.58 trillion Yuan, which increased 57% over the previous “Twelfth Five-Year Plan” period. The number of water conservancy projects and investment funds is increasing quickly.

Compared with conventional engineering, water conservancy projects are characterized by high capital demand, high construction difficulty, long construction periods and a high impact on the surrounding ecological environment [1]. With the development of water conservancy project construction, the construction mode is diversified, the construction management technology is diversified, the construction management environment is more complex, and social benefits are more multi-targeted. All of these risk factors will inevitably lead to many uncertainties encountered during the construction process of water conservancy projects. These uncertainties are referred to as “risks” [2]. The above-mentioned reasons result in various risky accidents in the construction process of water conservancy projects. Increasingly more attention is paid by researchers to the evaluation of various risks involved in water conservancy projects [3,4]. Researchers around the world have applied traditional analysis methods to evaluate the risks inherent in water conservancy engineering construction projects, including the evidence-based reasoning method [5], safety checklist method [6], fuzzy comprehensive evaluation method [7], accident tree analysis method [8], cloud model evaluation method [9] and material element topological evaluation method [10]. These studies primarily focus on the level of risk evaluation research, and there is a lack of research that focuses on the influence relationship between project risk factors.

Complex network theory can be used to describe realistic systems and reveal the correlation between objective facts. Recently, researchers from various fields conducted numerous network topology and empirical statistical applications of actual complex systems based on constructions of models. For example, Xu et al. [11], Hua and Zheng [12], and Ma [13] constructed causal models of railroad accidents with complex networks; they highlighted the key factors and the correlation among them by analyzing the statistical characteristics of complex networks, such as node degree and mediators. Xiao [14] analyzed the risk evolution process of amphibious seaplane takeoff and landing safety based on the complex network construction model. Liu [15] constructed an accident causation network of highways through town sections by complex network theory and analyzed the network by using the GN algorithm of association division. Meng et al. [16] constructed an unweighted directed network for a pipeline system leakage evolution system and investigated the shortest path of accident risk transmission by analyzing node access degree and clustering coefficient. Li [17] constructed a DEMATEL-ISM explanatory structure model to study the hierarchical structure between causal risk factors and the corresponding complex network model. There are also productive results of complex networks in the natural field, social sciences, biology, engineering, etc.

Social Networks: Yao et al. [18] studied network nodes in undirected and directed graphs using proximity centrality, mesoscopic centrality, node importance and PageRank as evaluation metrics. These metrics proved effective for identifying key nodes, confirming the algorithm’s reliability. Sun et al. [19] used a network evolution game model to simulate the impact of social networks and market environment factors on advertising strategies in complex social networks. Technology Network: Yu et al. [20] used a scale-free network to model the diffusion of electric energy substitution technology. They constructed an evolutionary game model that incorporated indicators such as the penalty strength of coal-fired enterprises, government subsidies and transformation costs. The study analyzed the impact of various parameters on the diffusion of the technology. Ecological Network: Williams et al. [21] conducted an empirical study on the topology of the seven largest food chain networks in the world. They found that with a short average path length, the degree distribution of the network obeyed a smaller power–law distribution. Moreover, Montoya et al. [22] and Camacho et al. [23] also obtained similar results. Biological Networks: Jeong et al. [24] found that all the outgoing and incoming degrees obeyed the curtain–law distribution in the metabolic system of 43 living organisms. Fell et al. [25] not only obtained the curtain–law distribution but also found that the corresponding undirected network has a small-world property. Transportation Network: Yuan et al. [26] identified the vulnerable points and domains of the complex network from the risk resistance of the urban metro network system (UMNS). Liu et al. [27] calculated the complex network characteristics of a communication network based on the topological characteristics and investigated the node protection strategies to reduce the occurrence of accidents using centrality analysis.

In the past years, scholars have already studied the problem of risk contagion in engineering projects and obtained rich results. However, there are difficulties in obtaining data, uncertainty in determining network structure, the potential impact on model reliability and prediction accuracy due to assumptions and simplifications, and limitations in the real-time application for engineering risk management and decision-making. From the perspective of the research paradigm, there is a lack of excavation on the mechanism of risk contagion generation and evolution, as well as a lack of providing corresponding interpretation on the mechanism of project risk contagion generation, accumulation and contagion process. Moreover, from the perspective of the research object, most of the current research focus on project combinations such as computer, technology research and development or supply chain. To the best of our knowledge, there are few applications of complex networks in the field of engineering projects, especially in the urban river ecological management project. Based on the engineering characteristics of the urban river ecological management project, we applied the complex network to discuss the evolution of risk in the present paper.

Risk in urban river ecological management projects is the result of multiple risk factors interacting with each other. The risk factors show nonlinear change characteristics, so the complex network is beneficial for analyzing the correlation and interaction between risk factors and their risk transfer process. In order to solve the risk transmission problem of complex engineering projects, it is crucial to investigate the transmission path and process between risk nodes. Once the correlation between risk nodes in the urban river ecological management project was generated, it formed a complex network. Therefore, it is advantageous to employ complex networks to investigate the correlation between risk elements in urban river ecological management projects. In this study, in the urban river ecological management project, the risk elements are regarded as network nodes and a complex network model is constructed to study the inherent laws of risk transmission. In addition, through the use of network visualization analysis tools, the overall and local characteristics of the risk network parameters are analyzed, and strategies for controlling risk transmission are proposed. This method is relatively less commonly used in the application of urban river ecological management projects. Therefore, the novelty of this type of research lies in providing a new way and method to identify risk elements, evaluate risk transmission patterns, and formulate risk prevention strategies, which has important practical significance for risk management in urban river ecological management projects.

The remainder of this paper is organized as follows. The research design and methodology are in Section 2. The construction of the risk network is in Section 3. A case study is presented in Section 4. We present a discussion of the results in Section 5. Finally, we summarize the study in Section 6.

2. Research Design and Methodology

2.1. Study Design

Brainstorming, reviewing the literature and expert consultation are used to extract the set of risk factors for urban river ecological management projects and construct a novel risk relationship model of an urban river ecological management project based on complex network theory. Firstly, the transfer interaction of risk factors was obtained, the core nodes and starting nodes in the transfer process were identified, and then the process and mechanism of risk transfer in the urban river ecological governance project were analyzed (please see Figure 1 for the conceptual framework diagram of this study). Our results could provide a useful reference and help organizations to make better decisions to avoid major damage caused by risks and guarantee the smooth implementation of the project.

2.2. Risk Node Identification

Risk nodes, as one of the components of complex networks, are the main tools for describing the research object. Network nodes refer to the risk elements that occur in urban river ecological management projects. In this work, we searched relevant academic studies from 2011 to 2021 using the CNKI and Vipul databases as the primary data source. We made a combination of queries based on keywords such as urban rivers [28,29,30], risk evaluation [31,32,33], risk identification [34,35,36], evolutionary mechanism, risk control [37,38] and complex network. Based on the principle of project decomposition structure and the current situation of urban river ecological management projects in China, we summarized all the possible risk elements in these types of projects, counted the frequency of each risk element, and then filtered and organized them. The risk items with similar meanings were summarized and organized.

Table 1. Risk of river ecological treatment projects.

Stage	Level 1 Risk	Level 2 Risk
project plan	1 Political risks	11 Project Approval Risks
		12 Government credit risk
		13 Legal and regulatory risks
	2 Economic risks	21 Funded risk
		22 Inflation risk
		23 Interest rate change risk
		24 Financing risk
	3 Natural environment risks	31 Hydrological and geological risks
		32 Meteorological condition risk
		33 Natural force majeure risk
		34 Ecological environment risk
	4 Social risks	41 Social and cultural risks
		42 Resident negotiate land acquisition risk
		43 Social security risk
		45 Public opinion risk
		46 Land change risk
	5 Project decision risks	51 Risk of basic acceptance before implementation
		52 Decision error risk
		53 Approval of work procedure compliance risk
		54 Incomplete collection of basic data risk
Project standard Preparation stage	6 Bidding risks	61 Bidder technical and management risk
		62 Project complexity risk
		63 Competitive risk
		64 Bid evaluation risk
		65 Calibration risk
		66 Risk of information leakage
		67 Risk of bidding documents
		68 Contract perfection risk
		69 Risk of contract signing deviating from bidding content
		610 Legality risk of contract signing procedure
		611 Contract dispute risk
	7 Planning and design risks	71 Qualification risk of design unit
		72 Design progress lag risk
		73 Design has defects, errors, omissions and frequent changes
		74 Improper standard selection
		75 Survey accuracy risk
	8 Preparation before construction risks	81 Construction site layout and technical preparation risk
		82 Risk of insufficient supply of substances (materials) and materials
		83 Risk of illegal commencement
Project construction stage	9 Construction personnel risks	91 Low technical level
		92 Weak safety awareness
		93 Qualification risk of employees
		94 Risk of slowdown of construction personnel
	10 Construction technology risks	101 Risk of improper drawing design
		102 Engineering technology risk
		103 Risk of construction equipment
		104 Risk of cross operation
		105 Construction accident risk
	11 Construction management risks	111 Safety management risk
		112 Coordination risks of participants
		113 Rationality of construction organization design
		114 Plan adjustment and engineering change
		115 Contract management and execution risk
		116 The organizational structure setting is chaotic
		117 Management authority risk
	12 Risk factors of construction period	121 Certificate cycle
		122 Construction period
		123 Risk of construction delay
Project completion acceptance stage	13 Quality assessment risk	131 Risk of unqualified project acceptance and putting into use
		132 Risk of file transfer not in place
		133 Quality assessment risk
		134 Audit risk
		135 Cost overrun

shows the network nodes of the identified complex network model by selecting the risk elements with more frequent occurrences. We obtained the final list of risk elements of urban river ecological management projects (Table 1).

2.3. Network Characterization

2.3.1. Overall Network Analysis

The topology of complex networks is complex and irregular. However, it was found that the overall characteristics of complex networks also exhibit some prevalent characteristics. In this study, we analyzed the following three types of indicators for the overall characteristics of the network.

(1)

Network density

The “network density” metric in complex networks refers to the density of interconnected edges between nodes within the network. It is often applied in social networks to measure the density of social relationships and their evolutionary trends. The network density of a network with $N$ nodes and $L$ actual connected edges is:

$$d(G)=\frac{2L}{N(N-1)}$$

(1)

(2)

Average path length

The average path length, denoted by $L$, is the mean value of the shortest path between any two nodes. The average path length in a small-world network is the corresponding order of magnitude of its network size.

$$L=\frac{{\displaystyle \sum _{\mathrm{i}\ne j}{d}_{ij}}}{N(N-1)}$$

(2)

where $N$ is the total number of network nodes, and $d_{ij}$ is the shortest distance between nodes $i$ and $j$.

(3)

Clustering coefficient

The clustering coefficient is an important parameter for measuring the degree of network grouping. The clustering coefficient of node $i$ in a network represents the ratio of the number of existing edges $E_i$ to the maximum number of possible edges in the subnet formed by all nodes directly connected to node $i$, denoted as $C_i$. Assuming that node $i$ has $k_i$ nearest neighbors, then, at most, $k_i(k_i-1)/2$ edges may exist in these nearest neighbors, and the clustering coefficient of node $i$ can be expressed as:

$$C_i=\frac{2E_i}{k_i(k_i-1)}$$

(3)

2.3.2. Local Network

(1)

Degree distribution

The degree of a node in a directed network comprises the out-degree and in-degree. The out-degree of node $i$ is expressed as the number of edges of node $i$ pointing to other nodes, and the in-degree of node $i$ is expressed as the number of edges of other nodes pointing to node $i$ in the network. The degree $k_i$ of node $i$ is the sum of the in-degree $k_i^{in}$ and out-degree $k_i^{out}$ of node $i$. This is defined as:

$$k_i^{in}={\mathrm{\Sigma }}_{j=1}^n{a}_{ji}, k_i^{out}={\mathrm{\Sigma }}_{j=1}^n{a}_{ji}, k_i=k_i^{in}+k_i^{out}.$$

(4)

The degree distribution $p(k)$ denotes the probability that a node in the network is specified at random, and the degree of the node is equal to $k$. $p(k)$ is defined as the ratio of the number of nodes of degree $k$ in the network $n_k$ to the total number of nodes $N$

$$p(k)=n_k/N$$

(5)

(2)

Medio centricity

The mediator of a node indicates the role of the node within the network. If nodes $i$ and $j$, which are not adjacent to each other in a complex network, can be reached by some mediator node (i.e., if the mediator node m is more active in the network and can serve as a bridge for the relationship between node pairs), then the role of node $m$ as a mediator is more important in the network, and its importance can be expressed by the mediator number $B_m$. This is defined as

$$B_m={\displaystyle \sum _{i,j\in Ni\ne j}\frac{n_{ij(m)}}{n_{ij}}}$$

(6)

where $n_{ij}$ is the number of shortest paths between nodes $i$ and $j$, $n_{ij(m)}$ is the number of times node $m$ appears in all the shortest paths between $i$ and $j$ as a mediator role, and $N$ is the total number of network nodes.

(3)

Proximity centrality

The proximity centrality index refers to the degree of proximity between node $i$ and other nodes $j$. If the node $i$ is nearer to other nodes, the dependence of node $i$ on other nodes to disseminate information becomes less, and the restriction by other nodes becomes weaker. The proximity centrality of a node is the inverse of the sum of the shortest paths based on node $i$ to all other nodes $j$ in the network, as in the following equation

$$C(i)=\frac{1}{{\mathrm{\Sigma }}_{y}d(y,x)}$$

(7)

where $C(i)$ represents the proximity centrality of node $i$, and ${\mathrm{\Sigma }}_{y}d(y,x)$ is the sum of distances from node $i$ to all other nodes.

(4)

PR value

PageRank (PR) is a comprehensive index that measures the number of internal and external links and the quality of the links on a web page. The higher the PR value of a web page, the higher the number of pages linking to it. If a web page is linked by another with a high PR value, its PR value increases accordingly. Thus, the nodes with a higher PR value in the project risk network are more important.

$$\mathrm{PageRank}(p_i)=\frac{1-d}{N}+d{\displaystyle \sum _{pj\in m(p_i)}\frac{\mathrm{PageRank}(p_i)}{L(pj)}}$$

(8)

(5)

Eigenvector centrality

Eigenvector centrality is different from point centrality, where a node with high point centrality (i.e., with many connections) does not necessarily have high eigenvector centrality because the connections may have low eigenvector centrality. Similarly, high eigenvector centrality does not mean that it has high point centrality; it can also have high eigenvector centrality with a small number of important connectors.

Feature vector centrality considers the importance of a node based on both the number of its neighboring nodes (i.e., the degree of that node) and the importance of each neighboring node. Let x_i be the important measure of node $i$, then

$$EC(i)=x_i=c\underset{j=1}{\overset{n}{\mathrm{\Sigma }}}{a}_{ij}{x}_j$$

(9)

where $c$ is a proportional constant.

3. Construction of Risk Network

In this section, we construct the risk network. Figure 2 depicts the research method.

3.1. Risk Element Relationship Extraction

There is a close relationship between complex networks and risk networks in urban river management projects. The risk factors in these projects are often interrelated, and their relationships can be viewed as a complex network. In this complex network, there are various complex relationships between risk factors, including positive relationships, negative relationships, nonlinear relationships, etc. These relationships can be expressed by data, and different types of data are needed to represent them. By studying these relationships, the interactive relationships between risk factors in urban river management projects can be revealed, which can lead to the development of more effective risk management strategies.

The relationship of risk factors in the complex network of risk factors of urban river ecological management projects is expressed by data, and various relationships need to be represented by different types of data. Since the number of risk factors in urban river ecological management projects is large and complex, it is difficult to quantify the precise relationship with different values. Therefore, this study aimed to analyze the risk transfer mechanism of urban river ecological management projects, focusing on the causal relationship between risks. This network relationship is directional, and binary directional relationship data were utilized. The expert scoring method was used to collect their judgments on whether a correlation between risk elements exists. In this study, 11 experts were selected, and the “0, 1” method was applied. A larger number of answers were selected to maximize the risk relationship and obtain the results of the risk relationship elements.

The construction of risk network relationships for urban river ecological management projects using the expert survey method was established in the following steps.

(1)

Formation of a senior expert group

Risk assessment experts from river ecological management construction units and researchers from universities were invited to form a senior expert group.

(2)

Conducting expert consultation activities

A group of 11 experts, all with relevant expertise and experience, were invited to identify the relationships between engineering risk factors, and 2 rounds of questionnaires were conducted to obtain the desired results and avoid interference. The expert opinions were summarized to form the final risk factor relationships.

3.2. Construction of Complex Network Model

The topology of a complex network can be divided into the multi-core, single-core, no-core, star, lumped line, ring and mesh network. Network topologies such as coreless, star, and convergence lines cannot fully describe the complex interrelationships and interactions in a risk network. Coreless networks lack a clear central node, making it difficult to describe the important core components and key nodes in a risk network. Star and convergent wire networks lack stability and reversibility, which can easily lead to unstable and uneven information transmission and integration, and do not fully reflect the characteristics of risk networks. Therefore, single-core ring networks have important topological characteristics, such as a high degree of stability and reversibility. At the same time, single-core ring networks have efficient information transfer and integration capabilities and can effectively describe the relationships and interactions between risk factors. Single-core ring networks are better suited to describe the topology and complexity of risk networks than other types of networks.

In this study, according to the risk factor relationship data matrix defined in

Table 2. Risk relationship matrix of urban river ecological treatment project.

Risk Factor	A1	A2	A3	…	An
A1	0	b12	b13	…	b1n
A2	b21	0	b23	…	b2n
A3	b31	b32	0	…	b3n
︙	︙	︙	︙	0	b4n
An	bn1	bn2	bn3	bn4	0

, columns represent the emitters of the relationship (i.e., causers), while rows represent the affected parties of the relationship (i.e., effectors). The “1” indicates the existence of the relationship, while the “0” indicates the non-existence of the relationship. Let n be risk nodes in the risk element set $A$. Let $A_h=\left(R_1,R_2,\cdots ,R_h\right)$ be the row risk element set and $A_m=\left(R_1,R_2,\cdots ,R_m\right)$ be the column risk element set, respectively. We denote $b_{ij}$ as the binary relationship data with $i, j=1, 2,\cdots ,n$.

$b_{ij}=1$ means that the risk element in row $i$ affects the risk element in column $j$.

$b_{ij}=0$ means that the risk element in row $i$ does not affect the risk element in column $j$.

Since the risk factor cannot be causally related to itself, the risk factor’s impact on itself is “0”, and the value on the diagonal is “0”. The above data are expressed in the form of a matrix to derive the risk factor relationship matrix $A$. Since the relationship between two risk factors is not necessarily causal, the adjacency matrix $A$ is not necessarily symmetric. Therefore, the adjacency matrix $A$ is an asymmetric matrix.

4. Case Study: Application in Jinghe River Management

The Jing River is the mother river of Jinghe New City, and it carries the history of the community. This ecological environment comprehensive management project is an important part of the establishment of the Jinghe New City waterfront landscape belt, which enhances the cultural quality of the city, strengthens the livable urban environment and promotes the Jinghe New City developed in high-speed standards.

In Jinghe New City, the upstream of the Jinghe River flood control and ecological management project (referred to as the “Jinghe comprehensive management project”) is about 1.0 km from the Jinghe River Jiyuan Bridge (formerly Xiushi Du Bridge). The downstream of the project is down to the Jinghe River Xiantong railroad bridge. This project invests 3.8 billion Yuan and includes the Jinghe River embankment construction project, the Jinghe River beach management and ecological restoration project, and the Jinghe River outside the ecological protection project.

4.1. Mapping of Risk Network

The social network analysis software is selected to draw and analyze the risk network diagram. The risk network adjacency matrix is imported into the software to obtain a visualization of the risk network (Figure 3), where $R_i$ represents the risk element number and the one-way arrow indicates the causal relationship existing between the risk elements.

4.2. Risk Network Parameter Analysis

In this work, we employed the anaconda3 software to analyze a large amount of network parameter data of an urban river ecological management project. Based on the analysis of the data for the overall and local networks, we could obtain the overall characteristics of the network and the key risk factors in the process of project risk transmission. Firstly, we analyzed the parameters for the overall characteristics of the complex network and obtained the basic characteristics of network density, network means path and network aggregation coefficient of the risk network of urban river ecological management project with the aid of Equations (1)–(3). The parameters of the local characteristics of the network were then analyzed. By using Equations (4)–(9), we obtained the network degree and degree distribution, proximity centrality, intermediary centrality, feature vector centrality and PR value, respectively. Finally, we obtain the most critical risk initiation nodes and conduction nodes in the complex network of the project.

4.2.1. Analysis of Overall Network Parameters

(1)

Network density

Network density is a parameter used to determine the connectivity between nodes in a complex network. A higher network density indicated more connected paths among nodes and stronger network connectivity. In this study, the average network density of the complex network of urban river ecological management risk was calculated to be 0.2209 by anaconda3 software, indicating that the network is more closely connected.

(2)

Clustering coefficient

The clustering coefficient size of a complex network reflects the degree of clustering and connectivity of the network. The connectivity and clustering of the network are stronger in the region where the network clustering is larger. In this study, the average clustering coefficient of the network was computed by anaconda3 software as 0.5559. The distribution range of the clustering coefficients of nodes was 0.2408–1.0000, which shows that the overall clustering and connectivity of the network is at a low level, but the uniform distribution of the clustering coefficients of nodes from the low to the middle level indicates the existence of small association distribution within the network.

The network nodes with large clustering coefficients have a strong correlation with their neighboring factors. According to the calculation in the network, construction workers’ denial risk (95), weak safety awareness (92) and natural force majeure risk (33) clustering coefficient values were 1, 0.88 and 0.82, respectively. The clustering coefficient values were large if the neighboring risk factors also had problems, resulting in a chain effect caused by the overall project risk. Therefore, in the risk complex network, such nodes with high clustering coefficients should be controlled to block the occurrence of a chain reaction in the risk network.

(3)

Average path length

The average path length of a network is the average of the shortest path lengths among all the pairs of nodes within the network. If the average path length of the network is shorter, the risk nodes need to pass through fewer intermediate nodes, indicating that the rate of risk propagation in the network is faster. By using the anaconda3 software, the average path length of the network of the urban river ecological management project was calculated to be 1.8815. This means that any risk factor within the network needs to pass through 1.8815 edges on average to cause changes in non-neighboring other factors. Therefore, the relationship between risks is relatively “tight”.

(4)

Cohesive analysis

Conducting nodal component analysis is the most common method for cohesive subgroup analysis. A component analysis is divided into strong component analysis and weak component analysis. Strong component analysis requires a bidirectional connection between any two risk elements within the network. Moreover, weak component analysis has lower requirements; a one-way connection between any two risk elements is sufficient. Therefore, this study applies weak component analysis to analyze the small group coefficients and factional indicators of urban river ecological management project risk factors. The top five small group coefficients are shown in

Table 3. Small groups of risk factors.

Clique	Risk Name	Size	Cohesion Index
Clique74	122, 123, 135, 66, 61, 63, 64, 65	8	2.558
Clique50	122, 123, 135, 32, 31, 33, 75, 105, 114	9	2.418
Clique49	122, 123, 135, 32, 31, 33, 75, 105, 111	9	2.371
Clique4	122, 123, 135,62, 10, 101, 114, 611, 112, 113, 115	11	2.335
Clique51	122, 123, 135, 32, 31, 33, 34	7	2.333

.

The present study investigated the risk factors associated with urban river ecological management projects and analyzed the robustness of the risk factions using a K-cluster analysis. According to Table 3, the risk factors 122, 123 and 135 demonstrated an overlap in small groups with a frequency of 5, indicating their significance as important risks for such projects. Conversely, some risk factor nodes did not appear in the faction, implying their relative lack of connection to the overall risk network and their identification as non-core factors. For the K-cluster analysis, the results indicated that a K value of 2 and a group size of 2 accurately reflected the state of the cohesive subgroups in the risk network of urban river ecological quality engineering projects. The results of the K-cluster coefficient analysis identified three explicit cohesive subgroups in the risk network of the project, as shown in

Table 4. Condensed subgroup analysis of risk factors.

G-Clique	Risk Name	Size	Density
G-Clique23	72, 73, 54, 114, 115, 62, 122, 123, 101, 102, 611, 135	12	0.985
G-Clique24	72, 113, 54, 114, 115, 62, 122, 123, 101, 102, 611, 135	12	0.985
G-Clique26	112, 113, 54, 114, 115, 62, 122, 123, 101, 102, 611, 135	12	0.985

.

4.2.2. Network Local Parameter Analysis

(1)

Degree and degree distribution

Degree, one measure of the centrality of network nodes, is a simple but important concept for describing individual nodes. A higher degree value of a particular node indicated more nodes connected to it and a greater influence ability of this node in the network. For directed networks, the degree is divided into three types, namely, entry degree, exit degree and degree. The entry degree is the sum of the number of neighboring edges in a node, and a node with a higher degree of entry is more likely to be influenced by other nodes. The node out-degree is the sum of the number of neighboring edges connected outward from a node, and a node with a larger out-degree is more likely to influence other nodes. The sum of in-degree and out-degree for the node is referred to as the degree. The degree values of each node in the urban river ecological management project are obtained by the anaconda3 software. The degree value is shown in

Table 5. Risk node degree value.

Node Number	The Degree of Input	The Degree of Output	Degree	Node Number	The Degree of Input	The Degree of Output	Degree
11	12	8	20	105	27	24	51
12	7	7	14	81	12	13	25
13	17	12	29	111	26	19	45
31	14	9	23	41	7	3	10
32	12	7	19	72	12	14	26
34	9	10	19	101	24	20	44
45	9	16	25	114	18	22	40
73	18	16	34	134	10	20	30
75	14	12	26	54	20	19	39
24	5	4	9	71	20	15	35
42	9	9	18	83	9	13	22
52	5	5	10	93	10	10	20
53	11	8	19	103	9	6	15
43	7	8	15	131	4	8	12
46	5	8	13	132	5	6	11
51	10	21	31	61	14	16	30
68	20	21	41	62	29	26	55
69	23	23	46	67	11	10	21
610	6	6	12	113	14	14	28
611	13	20	33	115	17	16	33
74	14	11	25	133	27	24	51
21	5	3	8	64	14	15	29
22	4	4	8	65	9	6	15
23	4	4	8	66	5	9	14
82	9	4	13	104	11	18	29
135	47	47	94	112	16	11	27
63	10	10	20	116	9	7	16
122	47	50	97	117	7	10	17
123	46	52	98	92	6	5	11
33	10	8	18	94	4	3	7
91	12	14	26	121	2	3	5
102	21	21	42

, and the degree chart is shown in Figure 4.

In this study, the nodes with high-risk out-degree value and low-risk in-degree value are the starting nodes in the risk transmission process. The control of such nodes should be increased in the urban river ecological management project to reduce the impact of risk transmission. The top 10 nodes in this study are the risk of delay, construction cycle, cost overrun, project complexity, quality assessment, construction accident, contract deviation from the bidding content, plan adjustment and engineering changes, engineering technology and the risk of basic acceptance before implementation.

The higher entry degree value of a node risk indicated a larger influence by other nodes. In the complex engineering project risk network constructed, nodes with both risks out-degree and in-degree values are important conduction nodes in the network. Thus, several nodes with higher out-degree in the project risk network were selected for further analysis. The top −10 risk entry degree nodes in the sequence are as follows: construction cycle, cost overrun, delay risk, project complexity risk, quality assessment risk, construction accident risk, safety management risk, improper design risk, contract signing deviation from the bidding content risk and engineering technology risk.

The nodes with higher degree values in the sequence are schedule delay risk, construction cycle, cost overrun, project complexity risk, quality assessment risk, construction accident risk, design schedule lag, safety management risk, improper drawing design risk and engineering technology risk. These particular types of risks have a more dominating impact than other risk factors.

(2)

Proximity to the center

It is equal to the reciprocal sum of all the paths between the node and other nodes. The larger the value is, the smaller the sum of the paths from one node to other nodes can be (i.e., the closer the node is to the center of the network). Therefore, the proximity to the center of the project risk network is used as the basis for determining whether the node is the “center of gravity” of the overall network. According to

Table 6. Local parameters of project risk nodes.

Ranking	Risk Name	Near Centrality	Risk Name	Intermediary Centrality	Risk Name	Centrality of Eigenvector	Risk Name	Clustering Coefficient	Risk Name	Pagerank
1	135	0.81	135	698.31	122	0.29	95	1.00	135	0.05
2	122	0.81	132	600.86	132	0.29	92	0.88	122	0.05
3	132	0.79	122	557.77	135	0.28	33	0.82	132	0.05
4	62	0.63	62	146.86	105	0.22	32	0.77	105	0.03
5	105	0.62	133	115.06	62	0.22	117	0.76	62	0.03
6	111	0.62	69	82.86	111	0.21	93	0.75	111	0.03
7	133	0.61	13	77.95	101	0.20	64	0.74	133	0.03
8	101	0.61	73	73.66	102	0.18	82	0.73	101	0.02
9	69	0.60	105	67.54	133	0.18	112	0.72	102	0.02
10	71	0.59	45	63.70	69	0.17	91	0.71	69	0.02

, the top ten nodes of proximity to the center are, in order, cost overrun, construction cycle, delay risk, project complexity risk, construction accident risk, safety management risk, quality assessment risk, improper design risk, contract signing deviation from the bidding content risk and design unit qualification risk. These are closest to the center of the risk factor network and are extremely important in the risk network.

(3)

Intermediation centrality

Intermediation centrality measures the size of the transport capacity of nodes in a complex network. A higher intermediation centrality indicated more influence on the nodes. Thus, nodes with large intermediary centrality values in the project risk network have a strong risk transmission capability. As shown in Table 6, the top ten risks are cost overrun, delay risk, construction cycle, project complexity risk, quality assessment risk, contract signing deviation from the bidding content risk, laws and regulations risk, design defects errors, omissions, frequent design case changes, construction accident risk and social opinion risk.

(4)

Eigenvector centrality

Eigenvector centrality is a parameter that measures the influence of a node on the network and can be used to describe the criticality of a node. A greater eigenvector centrality of a node in the project risk network indicated that the node in the network is more critical. Similar to the degree value, the eigenvector centrality also reflects the importance of a node to a certain extent. Moreover, it takes into account the importance of the node’s neighboring nodes and the differences of the neighboring nodes, rather than treating the neighboring nodes “equally”. This enables it to reflect the actual important nodes of the risk network more objectively. According to Table 6, the top 10 risks are construction cycle, delay risk, cost overrun risk, construction accident risk, project complexity risk, safety management risk, improper design risk, engineering risk, quality assessment risk and contract deviation from the bidding content risk.

(5)

PR value

The higher PR value of a web page indicated a higher number of connected pages. Additionally, if a web page is linked by another web page with a high PR value, its PR value increases accordingly. Thus, nodes with higher PR values in the project risk network have a stronger risk transmission effect. According to Table 6, the top ten risks are as follows: cost overrun, construction cycle, delay risk, construction accident risk, project complexity risk, safety management risk, quality assessment risk, improper drawing design risk, engineering technology risk and contract signing deviation from the bidding content risk.

4.2.3. Critical Risk Determination

Four indicators are considered to determine the importance of nodes, namely, the degree value of nodes, proximity to the center, PR value and feature vector centrality. The top ten risk elements of these indicators in the project risk network are selected and listed in

Table 7. List of the top 10 risk nodes.

Serial Number	Degree	Near Centrality	Feature Vector	PageRank
1	132	135	122	135
2	122	122	132	122
3	135	132	135	132
4	62	62	105	105
5	133	105	62	62
6	105	111	111	111
7	72	133	101	133
8	111	101	102	101
9	101	69	133	102
10	102	71	69	69

. The risk elements with a frequency higher or equal to 3 are identified as key nodes in the network. The key transmission nodes are judged based on the size of the outgoing and incoming degree values, the centrality of the characteristic vector and the PR value. The results are shown in

Table 8. Key nodes of the risk network.

Node Type	Node	Risk Name	Production Stage	Judgment Basis
Initial risk node	132	Risk of construction delay	Project construction stage	Ranking first in terms of exit, third in terms of entry and first in terms of value
	122	Construction period risk	Project construction stage	The output ranked second, the entry ranked first and the value ranked second
	135	Cost overrun risk	Project completion acceptance stage	The output ranks third, the input ranks second and the value ranks third
Conduction risk node	62	Project complexity risk	Project preparation stage	The output ranks fourth, the PR value ranks top (fifth), the feature vector (fifth) and the intermediary centrality (fourth)
	133	Quality assessment risk	Project completion acceptance stage	The ranking of degree value, PR value (seventh), intermediary centrality (fifth) and proximity centrality (seventh)
	105	Construction accident risk	Project construction stage	The ranking of degree value is high (sixth), PR is high (fourth), intermediary centrality is high (ninth) and close to centrality (fifth)
	111	Safety management risk	Project construction stage	The ranking of degree value is high (eighth), the ranking of PR value is high (sixth), the ranking of intermediary centrality is high (fifth) and close to centrality (seventh))
	101	Risk of improper drawing design	Project construction stage	The degree value ranks first (ninth), the PR value ranks first (seventh), the centrality of the eigenvector ranks first (seventh) and the near centrality ranks eighth
	69	Risk of contract signing deviating from bidding content	Project preparation stage	The output value ranks high, the PR value ranks high (tenth), the intermediary centrality ranks high (sixth) and the feature vector centrality ranks high

.

5. Discussion

In contrast to similar research literature [39,40], in terms of research content, this study provides a more comprehensive analysis of the risk network of water conservancy projects, starting from the four stages of water conservancy project construction. In terms of research methodology, this study adds a cohesive analysis of risk in urban river ecological management projects based on complex networks, further elaborating the aggregation effect of risk factors in risk networks. In terms of findings, the results of this study are partially consistent with the focused risk nodes obtained from studies in the literature [39,40], justifying the results of this study.

This study constructs a complex network model and analyzes the overall and local characteristic parameters of the risk network. Moreover, we analyzed the risk transfer characteristics of the urban river ecological management project according to the parameter characteristics, and we also revealed the inner law of risk transfer of the complex network in the case of the Jinghe ecological management project in Jinghe New City. The results can improve the risk management awareness and ability of the main body of the urban river ecological management project to effectively achieve the goal of risk management. In particular, this paper is based on the case study of the risk of the Jinghe ecological management project. A detailed analysis of engineering risk management to guarantee the quality of the project and reduce the occurrence of engineering risks ensures the optimization of the ecological environment of Jinghe, promoting the high-quality development of Jinghe and improving the lives of the people.

Firstly, this study enriched the theory and practice of urban river ecological management engineering risk management research. With the rapid development of urban river ecological management engineering in recent years, it requires a higher level of engineering risk management. This paper investigates the urban river ecological management engineering risk evolution process, and it is meaningful for river management engineering, risk management theory and multi-link complex theory. Secondly, it can improve the risk management level of urban river ecological management project participants. Urban river ecological management project is extremely complex, involving many management factors and technical factors, including personnel, materials, management, environment and technical methods. Managers need sufficient safety theory and management level. By exploring the problem of dynamic engineering risk evolution, this study found the risk links in the construction process, we controlled the transformation conditions by judging the important links, and we also replaced the remedial measures after the occurrence of the risk with preventive management in advance, to improve the management’s emergency response-ability to the risk. Thirdly, this study can help the managers of urban river ecological management understand the law of accident risk evolution by preventing the occurrence of risks and improving engineering economic efficiency. These research results help managers formulate corresponding preventive measures to reduce the probability of accidents and increase the economic benefits of enterprises and society.

This study comes with several limitations. The occurrence of the risk and its causes are complex, and 63 risk points and risk factor data cannot fully reflect the law of urban river ecological management project risk evolution. Therefore, the model slightly deviates from reality. It is crucial to expand on existing data in further research and improve the complex network model to further confirm the research results. Additionally, this study only considered the static risk network. In the future, we can consider adding the state of risk nodes and other factors to construct a dynamic risk network model. Moreover, the network constructed in this study considers the relationship between nodes as directed and unweighted, but the relationship between risk elements in engineering practice is more complex, and the weight of edges should be taken into account in future studies to make the conclusions more applicable to the actual situation, and the realistic risk network of complex engineering projects is dynamic and variable, and the risk elements in it may increase, decrease or change with time, but this study only analyzes the static network structure, and the dynamic changes of risks can be included in the study afterward.

6. Conclusions

Urban river ecological management projects are typically characterized by large capital investment, many involved parties, long construction and operation cycles, and pervasive risk factors. This makes their project risks difficult to control, and the risk of any one link may lead to the risk of the overall project. Risk prevention and control need to control direct risks and cut off the transmission path of indirectly triggered risks. This study draws the following conclusions by constructing a risk factor network, analyzing the statistical characteristics of the network and comprehensively evaluating the importance of the risk factors involved.

From the perspective of the risk generation phase, key risks in the project risk network primarily appear in the second preparation phase and the third project construction phase phases of the project. They are also the most critical phases of the project, with the longest time span and the strongest interaction among the parties involved. Therefore, the number of risk elements in these two particular phases grows extremely fast, and the interaction among the nodes increases obviously. The analysis demonstrates that schedule delay risk, construction cycle risk, and project complexity risk are the most important risks in these two phases, which interact with each other. This shows that they have a key role in the risk transfer process.

The cost overrun risk in the completion and acceptance stage is also an important transmission node that cannot be ignored. The high entry value of this risk indicates that the occurrence of risks in other stages of the project leads to the occurrence of this risk, and it will also react to other risks.

The risk factor network has complex characteristics, small-world characteristics and scale-free characteristics. It reflects that the interaction among risk factors leads to the occurrence of risk events, and the risk factors have a close and prompt influence on each other. The risk factors of the conduction node and the starting node within the network have a dominant position. The results obtained demonstrate that schedule delay risk, construction cycle risk and cost overrun risk are the starting risk factors of urban river ecological management projects. Furthermore, the project complexity risk, quality assessment risk and construction accident risk have important conduction roles. Therefore, according to the key nodes of the risk network, searching for approaches to prevent risk generation is a crucial part of the project risk control work.