Stakeholder-Associated Risks and Their Interactions in PPP Projects: Social Network Analysis of a Water Purification and Sewage Treatment Project in China

As a result of complex contractual relationships, multiple stakeholders with different interests are involved in public-private partnership (PPP) projects. Compared to traditional models, PPP projects have more uncertainty. This study integrated stakeholders and risk factors in PPP projects from a network perspective to better determine how to control risks. Using social network analysis (SNA), a case study was conducted to identify the critical risk factors, and mitigation actions are proposed. The results indicated that, compared to other stakeholders, local governments play the most important role in PPP projects. Managers should therefore pay more attention to political and legal risk factors and develop reasonable risk-sharing plans. This study expands PPP risk research from the individual level to the network level and provides a visualized, innovative research paradigm for PPP risk analysis. The results can also be used by project managers for decision-making, risk management, and other processes, thus helping to achieve the sustainable management of PPP projects.


Introduction
A public-private partnership (PPP), which refers to cooperation between governments and private entities, provides an efficient way to achieve value for money (VFM) in procuring public infrastructure or services [1]. PPPs have made great contributions to sustainable urban development. Compared to traditional models, PPPs can relieve governments' financial pressures and technical constraints by taking advantage of the private sector's capital and expertise, thereby improving the efficiency and performance of projects [2]. e PPP model was first proposed in the UK, initially to realize the privatization of public infrastructure projects by adopting a private finance initiative (PFI) model [3]. Since the 2008 global economic crisis, there has been increasing interest in adopting PPP policy in both developed and developing countries [4].
PPP was once considered a panacea for the financial and technical deficits of public investment [5]. However, as a result of characteristics such as enormous investment, longterm contract periods, and multiple stakeholders with different objectives, PPPs face greater uncertainties than traditional projects [2]. Practical experiences of infrastructure PPP projects have revealed many problems. Many such projects have encountered various crises, and there are numerous cases of failed PPP projects. For example, the D47 Motorway in the Czech Republic and the M9 Motorway in Pakistan were ultimately canceled [6]. Meanwhile, the failure of the Quanzhou Citong Bridge project in China provides a good example of a project being nationalized in advance [7]. Further, the Channel Tunnel Rail Link in the UK was a failure in that VFM was not achieved [6]. erefore, the complex, long-term, systematic nature of PPP projects inevitably gives rise to various risks and challenges.
In recent years, several studies have investigated the risk management of PPP projects [8]. Based on conventional risk-management processes, these studies can be categorized into three themes: risk identification, risk assessment, and risk response [9]. Many studies have examined risk identification in PPP projects, especially in the early stages of the research [10][11][12]. Such studies mainly used literature reviews [10], case studies [7], questionnaire surveys [13], and other qualitative methods to identify and classify the risks of various PPP projects. Risk assessment, meanwhile, has been shown to play a crucial role in PPP project success; accordingly, researchers have tried to construct suitable risk assessment models for PPP based on various theories and methods [14][15][16]. Regarding the risk-response theme, most studies have focused on risk-sharing principles [17,18], decision-making processes [19][20][21], and distribution methods [14,22]. Such studies have provided valuable information for managing risk in PPP projects. However, many studies are limited in that they only approach risk from a single perspective, do not analyze causal relationships, and do not consider the entire supply chain as a risk network.
With the maturation of stakeholder theory, stakeholder analysis has been applied in various research fields [23], including investigations of PPP projects [24][25][26][27][28]. Kerzner [29] suggested that "people" is the primary factor affecting project performance. Indeed, when looking at the risks identified in previous studies, most are associated with PPP project stakeholders. Stakeholders need to analyze their individual risks and make corresponding responses. Stakeholder-risk analysis can therefore help identify risk resources to develop a comprehensive risk list for PPP projects, thereby contributing to effective decision-making. Stakeholder analysis can support efficient communication in PPP project management. However, the interactions among stakeholders in PPP projects have not been clearly analyzed. Construction projects take place in nonlinear, complex, iterative, and interactive environments [30]. erefore, the impacts of stakeholders are best understood not as a twoparty framework but as a "network." Most prior studies have used linear impact analysis to evaluate the impacts of risks or stakeholders on PPP projects; however, there has been little consideration of the associated risks and stakeholders. Relatively few studies have specifically explored risk-stakeholder interrelationships in PPP projects.
is study aimed at analyzing stakeholder-associated risks in PPP projects from a network perspective. e rest of this paper is organized as follows. In the next section, the risk and stakeholder categories of PPP projects are identified through a literature review. en, an SNA model is proposed to analyze stakeholder-associated risks in PPP projects. In the fourth section, an exploratory case study is conducted, and the final section presents the conclusions and limitations.

Risks and Stakeholders in PPP Projects
With the worldwide application of PPPs, it is critical for participants to find appropriate ways to manage project risk. Researchers and practitioners both recognize that PPP projects face uncertainties because of their complex, longterm nature [31]. e body of research on PPP risk has grown significantly in recent years [32]. Risks must be accurately identified in advance to effectively analyze them and make quick responses. Eaton et al. [33] proposed that participants need to identify risks as early as possible in the life cycle of PFI projects to take measures to reduce them.
Current research on PPP risk identification usually classifies risks into different categories. Li et al. [34] divided PPP risk into "macrolevel," "mesolevel," and "microlevel" factors. Zheng et al. [35] proposed analyzing critical risk factors in two dimensions: "system" and "nonsystem." Li-Yin et al. [36] grouped risks into seven categories: "projectrelated risks," "government-related risks," "client-related risks," "design-related risks," "contractor-related risks," "consultant-related risks," and "market-related risks." Askar and Gab-Allah [11], meanwhile, identified four aspects of risk factors, including "political risks," "construction risks," "operating risks," and "market and revenue risks." Zhang [12] divided the barriers of PPP projects into six aspects: "social, political, and legal risk," "unfavorable economic and commercial conditions," "inefficient public procurement framework," "lack of mature financial engineering techniques," "problems related to the public sector," and "problems related to the private sector." Although there is still no standard classification of PPP risk, the approach of Liu et al. has been widely adopted (i.e., macro-, meso-, and microlevel risk) [37]. Macrolevel risks include those outside the project, such as political and legal risks, economic exposures, social risks, and natural risks. Mesolevel risks are those within the project, including project development risks, project financing risks, design risks, construction risks, and operation risks. Finally, microlevel risks concern the relationships between stakeholders and specifically include organizational risks and contract risks.
Identifying risk resources is necessary for reducing risks and ensuring PPP project implementation. However, it is difficult to track the risk resources of the identified PPP risks.
is is partly because some risks are related to different stakeholders; the main reason, however, is that stakeholder groups are still not comprehensive. PPP projects create a web of stakeholders with varying interests. Previous PPP risk studies have not sufficiently identified how multiple stakeholders bring various problems to PPP projects. erefore, it is worthwhile to review the role of stakeholders.
According to the previous research on PPP projects, the basic stakeholders are the public and private sectors [27,38,39]; other stakeholders have been subsequently added. Ng et al. [40], for example, added "people" as a major stakeholder while Budayan [41] added "consultant" as the third key stakeholder. Sun et al. [42] identified the public sector, the private sector, and passengers as stakeholders for evaluating cooperation efficiency. Debt and equity investors, the state, users, suppliers, and service providers have all been regarded as PPP project stakeholders [24]. Yan et al. [43] extended the list to include 13 key stakeholders (i.e., local government, private investor, government implementing agency, project company, banking and financial institutions, contractor, operator, supplier, prospecting and design unit, consultancy, end user, public, and insurance company). Amadi et al. [44] suggested that internal stakeholders, such as the public and private sectors, and external stakeholders, 2 Advances in Civil Engineering such as communities and trade unions, both play important roles in delivering PPP projects. Freeman defined stakeholders as the participants in the human process of joint value creation [45]. According to the Project Management Institute (PMI), stakeholders are involved in a project, and their interests will either affect or be affected by the development of the project. Olander [46] suggested that stakeholders are individuals or organizations who have a vested interest in the success of a construction project. Many subjects are involved in the long life cycle of PPP projects, and those subjects will have effects on or be affected by the projects. According to Freeman, the stakeholders involved in PPP projects comprise a huge hybrid, which only increases the difficulty of research. e present study aimed to examine risk management for the purpose of improving project management and promoting successful PPP project implementation. Accordingly, the focus needed to be on those who trigger risks in PPP projects. is article defines PPP project stakeholders as individuals or organizations who influence projects during the whole life cycle and are, in turn, affected by the implementation and the final results. is definition emphasizes the interaction between stakeholders and PPP projects.

Social Network Analysis
e concept of social networks and the social network analysis (SNA) method have attracted considerable attention from the social and behavioral science community [47]. is can be attributed to the focus on the relationships between social entities. As a system environment, a PPP project involves various relationships. e purpose of SNA is to explore the influence of relationship structures on behavior [48]; it emphasizes the importance of relationships and is suitable for analyzing relational data [47]. SNA can also perform precise quantitative analyses of various relationships, and it has been widely used in many areas, including the management of construction projects. For example, Yang et al. [30] applied SNA to stakeholder management in construction projects. Fang et al. [49] used it to investigate the risk relationships in large engineering projects, and Zhu et al. [50] studied value conflicts between local governments and the private sector in stoke PPP projects. However, the application of SNA to stakeholder-associated risk analysis in PPP projects remains unexplored.
Following Yang and Zou [51], Figure 1 shows the flowchart of the SNA method.
In the SNA process, the first step is to identify the boundary of the network. All networks consist of nodes and links. e boundary of a network is determined by the nodes within it. is step aims to identify those nodes, which, in this study, are stakeholders and their risks in PPP projects. Laumann et al. [52] summarized the methods for identifying the boundaries of complete networks according to nominalist and realist approaches. e nominalist approach identifies network members from an observer's perspective while the realist approach is based on the subjective judgment of network members. Two different methods are often used to complete this step: the classical experience-based method and the snowball-rolling method [51]. Using the classical experience-based method, decisions can be made in a relatively short time, but the stakeholders and the identified risks will be limited. e snowball-rolling method can provide a complete list of stakeholders, but it is time-consuming and may encounter practical and ethical challenges. e choice of method should depend on the project situation considering the advantages and limitations of each. e second step is to assess relationships in the network. Links representing the impacts between two nodes are defined in this step. In this study, this is used to determine the interrelations among the risks identified in the first step. A matrix can be used to express the relationship network [53]; it can be a binary or multivalue matrix. Workshops with project teams and other stakeholders, as well as Delphi surveys with key stakeholders, are often used to obtain a riskstructure matrix (RSM) [51]. Once the nodes and links are identified, a risk network for a PPP project can be drawn. e third step is to visualize the risk network. Nodes of different shapes and colors can be used to represent different stakeholders and risk categories. Arrows represent the interrelationships among PPP risks, and their thickness indicates the degree of impact. After establishing the PPP risk network, the next step is to analyze it. Various software packages have been developed to visualize and analyze relationship networks (e.g., UCINET, Netdraw, NetMiner, and Pajek). To decipher the structure of the PPP risk network, SNA indicators such as density, cohesion, block models, degree, betweenness centrality, and brokerage are calculated.
(i) Density is defined as the ratio of the actual number of relationships in a network to the maximum number of possible links [47]. For a directed network, the density can be measured by equation (1), where L represents the existing relationships and N the total number of nodes. e value range of this measure is [0, 1]. With the increase in the number of relationships in a network, the network density increases. e density of a complete network graph is 1:

Advances in Civil Engineering
(ii) Cohesion is an index based on the distance of nodes in a network [54]. e distance between two nodes refers to the number of links connecting them. Adjacency matrices (AdjM) are often used to calculate the distance between all actors to obtain the average distance. Node i and node j are both actors in a network. e cohesion can be measured by equation (2), where z is calculated by the average walks between each pair of nodes in the network [51]. It is a measure of the tightness of the network structure and reflects the complexity of the network: (iii) Block modeling analysis was first proposed by White et al. in 1976 [55]. It divides the actors in a network into different positions, named B 1 ; B 2 ;. . .; B B . ere is a corresponding rule Ø that divides the actors into different positions. If actor i is in position B k , then Ø(i) � B k . We use b klr to represent whether there is a relationship between B k and B l according to relation X r . It is assumed that b klr � 1 if there is a relationship and b klr � 0 otherwise. Block models are simplified expressions of a relationship network that represent the overall structure of the network. (iv) According to Burt's theory, the positions in a network can be categorized into four types [56]. e first type is "isolate," whose members have no contact with the outside. e second type, "sycophant," transmits more relationships to other positions than to itself, and it does not accept many relationships. e third type, "broker," is one in which its members both send and receive external relationships, but there are fewer contacts between internal members. e last, "primary," accepts both relationships from other positions and relationships from its own members.
(v) Degree indicates the number of other nodes directly connected to a node [47]. In a directed network, the degree of each node can be divided into in-degree and out-degree. e in-degree of a node refers to the number of direct relationships pointing to it, while out-degree refers to the number of relationships emitted by it. We use out-degree minus in-degree to represent the degree difference (equation (3)). e greater the difference, the stronger the impact of node i on others compared to the impact it receives: (vi) Betweenness centrality measures how far a node/ link falls in between two other nodes/links in a network [57]. It reflects the node/link's ability as a medium in a network [58]. Take the betweenness centrality of a node as an example. Assuming that node i, node j, and node k are three different nodes in a network, the number of geodesics linking j to k is expressed by g jk , and g jk (i) represents the number of geodesics passing through i. e absolute betweenness centrality of node i can be calculated by equation (4). In the same way, the betweenness centrality of a link can be obtained: (vii) In a tripartite relationship consisting of A, B, and C, if A has a relationship to B, B has a relationship to C, but A does not have a relationship to C, then B is a broker. ere are five kinds of brokerage relationships based on the groups to which A, B, and C belong. As shown in Figure 2, if B is a broker, and A, B, and C are in the same group, we call B the "coordinator;" if A and C are in the same group, and B who acts as a broker belongs to another group, we call B the "consultant;" if C and the broker B are in the same group, and A belongs to another group, we call B the "gatekeeper;" if A and the broker B are in the same group, and C belongs to another group, we call B the "representative;" if A, B, and C belong to three different groups, we call the broker B the "liaison." e results for the SNA indicators in Step 4 are used to identify risk mitigation actions for PPP projects. Density and cohesion are two overall descriptive indexes of the network [47]. Block models divide network risks into different parts according to structural equivalence. e out-degree of nodes can help identify risks that have a greater immediate impact on others while the in-degree can reflect the more susceptible risks to others. Betweenness centrality helps to identify risks and the relationships that have stronger control over the relationships passing through them. Brokerage identifies the risks that play critical roles between different categories. erefore, the risks with a higher degree, higher betweenness centrality, and higher brokerage value, as well as relationships with higher betweenness centrality, should be mitigated with higher attention.

Case Study
is research used a single case study. One reason is that this study aimed to address a "how"-type question to understand how risks are connected in PPP projects. At the same time, since PPP models are being widely used around the world, an exploratory case study was an appropriate approach [59]. e case selection was not random. To make the stakeholder and risk analysis more meaningful, a typical case with high project complexity involving numerous stakeholders was chosen. e case is a water purification and sewage treatment PPP project in the Changchun City Airport Economic Development Zone in China. e contract sum was over $21 million.
is project consists of five subprojects: a water purification plant project, water supply pipe network project, core area sewage treatment plant project, northern sewage treatment plant project, and tailwater wetland project. It was launched in December 2017. A foreign-investment company won the bid in April 2018 and then formed a special-purpose vehicle (SPV) together with a financing platform company. Next, in June 2018, the government signed a concession agreement with the SPV; the contract period may last 30 years. Given the long-term payoff period, vast investment, complex contractual relationships, and numerous stakeholders with contradictory interests, this project is bound to face a number of potential risks [2]. Such risks could include a failure to acquire the land within the stipulated time [34], the actual cost of the project during the construction phase exceeding expectations [60], and a mismatch between the technology used in the operation of the project and the actual situation [61].

Identification of Stakeholders and eir Risks.
In the SNA method, the first step in building a risk network for this case project is identifying stakeholders and their risks. is study used the classical experience-based method. Predefined categories of risks and stakeholders were given in the previous section. e core stakeholders in this PPP project could easily use them as a reference to identify stakeholders and risks.
To identify project stakeholders, a four-hour group discussion was conducted with key project participants, including two senior officers from the local government, two senior managers from the financial platform company, the chief operating officer (COO) of a private investment firm, the vice president of a commercial bank, and a vice general manager from a construction company. Figure 3 shows the structure of stakeholders in this PPP case project. e SPV was formed by the private investor and a financial platform company authorized by the local government; then, the local government granted this SPV a concession. A state-owned commercial bank was the main creditor for the project's financing sources. e SPV commissioned different design units and contractors to design and construct this PPP project. Suppliers provided the main equipment and material for the project. e SPV as the operator was responsible for the operation and maintenance of the built-up PPP project according to the concession agreement. Consultancies provided intellectual support for the successful implementation of the project. e ultimate purpose of the project is to provide high-quality clean water and sewage treatment services to the public. e seven respondents who participated in the group discussion provided contact persons of the 10 stakeholders in the case project. Semistructured interviews were used to identify the risks related to each stakeholder.
irty-five semistructured interviews were conducted from June 2019 to October 2019; each lasted more than 30 minutes. Questions about the risks related to each stakeholder were asked. According to the risk categories, a total of 37 risks associated with these 10 stakeholders were identified. ese identified risks were coded numerically as SaRb, where Sa represents a stakeholder and Rb represents the risk related to that stakeholder. A risk checklist was developed, as shown in Table 1.

Determination of Risk
Interrelations. Based on the identified risks, expert scoring was used to further identify the relationships between risk factors. A total of 20 experts, including scholars and management personnel, were asked to determine whether there were impacts between each pair of risks. Questionnaires were collected through interviews and e-mail. Based on the experts' professional knowledge and practical experience, a value of 0-1 was assigned to the interrelations among the identified risk factors. If it was determined that the risk factor in a row had an impact on the risk factor in the column, it was represented by 1; otherwise, 0.
e assignment results from the 20 experts were then processed. If more than 10 experts assigned a value of 1 to the same relationship, the relationship was determined to be 1; otherwise, it was 0. e results were then given back to the experts so they could adjust their judgments. is process was repeated until an agreement was reached.   F i n a n c i n g I n t e r e s t a n d a m o r t i z a t o i n Figure 3: Structure of stakeholders in the water purification and sewage treatment PPP project.  Risk factor S1R1 S1R2 S1R3 S1R4 S1R5 S1R6 S1R7 S1R8 S6R9 S6R10 S10R11 S10R12 S1R13 S1R14 S2R15 S2R16 S2R17 S4R18 S7R19 S7R20 S8R21 S8R22 S8R23 S8R24 S9R25 S3R26 S10R27 S3R28 S3R29 S4R30 S1R31 S4R32 S5R33 S4R34 S5R35 S5R36 S5R37 S1R1

Visualization of the Risk Network.
After identifying the risks and their interrelations, the risk network for the PPP case project was established. NetDraw was used to visualize the risk-structure matrix. e risk network was depicted in a graph with 37 nodes and 378 arrow lines, as shown in Figure 4. e colors of the nodes represent different stakeholders, and the node shapes show the risk levels. e arrows indicate the directions of the relationships between risk factors.

Analysis of the PPP Risk
Network. Ucinet 6.0 was used to calculate the indicators of the risk network in the case project. Density and cohesion were calculated first. e density of the PPP risk network is 0.298, which means the risk network is dense; there are relatively more interrelations between the PPP risk factors [49]. e cohesion of the PPP risk network is 0.615 > 0.298, which means the PPP risk network has high complexity [51].
Block modeling analysis was used to divide the risk factors into different positions and explore the relationships between them [47]. is is a simplified expression of the risk network in the case project, and it represents the overall structure of the network. e steps for building a PPP risk network block model are as follows: first, the CONCER method was used to partition the risk factors into blocks; then, the overall network density was used as an α-density index to determine the values of the blocks. Considering the effect of the final partition, the number of nodes in each block should generally be greater than three. erefore, the above risk factors were divided into four subgroups, as shown in Table 3. Table 4 shows the density matrix of the block models. Comparing the values in the density matrix with the overall network density, values greater than 0.298 were replaced with 1 and values less than 0.298 with 0. e image matrix of the risk network was obtained as shown in Table 5. Investigating how messages were sent and received between blocks based on Burt [56], and it was found that the risk factors in Block 1 sent more relationships to other blocks but received no foreign relationships. So Block 1 is a "sycophant." Blocks 2, 3, and 4 accepted both relationships from other blocks and their own; therefore, they are "primaries." e risk factors in Block 1 are at either macrolevel or microlevel.
For the risk network, the degree of a risk factor indicates the links between it and its neighbors. In-degree refers to the number of other risk factors that can have a direct impact on it, and out-degree refers to the number of other risk factors that can be directly influenced by it. As shown in equation (3), degree difference is equal to out-degree minus in-degree. e greater the difference, the stronger the risk factor's impact on others compared to the impact it receives. Seven risk factors with a high out-degree and high degree difference were identified, as shown in Table 6. S5R35 ("inadequate distribution of risks" associated with consultancy) had the highest out-degree of 31, followed by S1R2 ("corruption" associated with local government) and S1R1 ("unstable government" associated with local government). ese identified risk factors all belong to Block 1, which is the "sycophant." In this PPP risk network, the greater the betweenness centrality, the stronger the control of the risk factor/link over the relationships passing through it. Table 7 shows the top 10 risk factors and risk relationships with the highest betweenness centrality. e calculation results show that S1R7 ("government intervention" associated with local government), S5R35 ("inadequate distribution of risks" associated with consultancy), and S1R2 ("corruption" associated with local government) have the highest betweenness centrality, and all of the most important links are related to them. e trigger factors in the risk relationships should receive more attention. Comparing the risk factors in Tables 6 and 7, S1R14 ("delay in approval" associated with local government), S10R27 ("revenue risk" associated with the public), S5R37 ("contract change risk" associated with consultancy), S2R15 ("high financing costs" associated with financial platform company), S2R16 ("project financial attractiveness" associated with financial platform company), S10R11 ("public opposition risk" associated with the public), S4R18 ("design change" associated with SPV), and S8R23 ("schedule delay" associated with contractor) show low outward influence but still play important intermediary roles.
ese risk factors with high betweenness centrality values are located in the geodesics of many other pairs of nodes. e connections between other nodes are established through them. ese risk factors are neither the initiators nor the ultimate recipients of the risk transmission. ey are in the middle of the risk transmission, playing the role of connecting risk initiators and recipients.
Brokerage roles, including coordinator, gatekeeper, representative, consultant, and liaison, were determined based on analyzing the ego network from the whole network [62]. Brokerages often hold secrets among multiple groups and occupy important positions in a network. Given a onemode network and a partition vector, brokerage analysis can be conducted. Table 8 shows the top 10 risk factors with the highest brokerage values. Stakeholder categories and risk categories were selected as the partition vectors. ese risk factors are regarded as playing critical roles in connecting different groups. e identified risk factors are basically consistent with the betweenness centrality results. Only one risk factor, S1R31 ("lack of supporting infrastructure" associated with local government), was newly identified as an important risk due to its brokerage role.

Risk Mitigation Actions.
rough the above SNA, a list of critical risk factors was finally obtained, as shown in Table 9. ey either have the most direct effect on other risk factors or have strong risk transmission ability according to the results for degree, betweenness centrality, and brokerage. To mitigate risk, these 17 risk factors, related to six different stakeholders in the PPP project, should be prioritized.
Seven are caused by local government. Local government plays an important role in managing PPP risks. A stable political and legal environment is necessary for the successful implementation of PPP projects. e Chinese government should therefore speed up the formulation and promulgation of laws related to PPP. At the same time, the local government should clarify its responsibilities and strengthen its internal management to avoid excessive interventions, delays in approval, and corruption. In this case project, the local government should ensure that all supporting infrastructures are complete before the project operation period.
Two project financing risk factors associated with the financial platform company were identified as critical factors. Fully exploring the profitability of the PPP project, the financial platform company should comprehensively analyze possible lenders for the project to expand the financing channels. At the same time, the company could ask the local government to provide appropriate guarantees for the PPP project, thereby reducing costs and improving the project's financial attractiveness.
As the core stakeholder, the SPV carries out the actual management of the PPP project. Based on the SNA results, the SPV of this case project should clarify the project objectives at the beginning and avoid changing the project design at will. e SPV should also seek to ensure effective communication between project participants. It should propose a feasible project communication plan with related measures, such as conducting meetings, regularly reporting on the project's progress, and carrying out irregular S1R1 S1R2 S1R3 S1R4 S1R5 S1R6 S1R7 S1R8 S6R9 S6R10 S10R11 S10R12 S1R13 S1R14
Lastly, the contractor should make a reasonable project schedule plan and choose a suitable construction plan to ensure the construction is completed on schedule.
In addition to resolving the above critical risk factors, cutting off the main interactions between risk factors is also an important means to mitigate the risk of the PPP project. Cutting the links can fragment the network and reduce the chain reaction between risk factors. Stakeholders should focus on the causal relationships between the risk source owners and the risk receivers and enhance communications between them. Key risk relationships identified with a high link of betweenness centrality values, as shown in Table 7, should receive more attention. Since the identified links are all related to risk factors in Table 9, the abovementioned actions for these critical risk factors can effectively reduce these risk relationships; therefore, specific control measures for these relationships are not proposed.
By undertaking the above actions, the critical risk factors can be resolved, and the main interactions can be cut off. It is meaningful to verify the impact of the above risk mitigation actions on the risk network. By removing the three most important risk factors (S5R35, S1R7, and S1R2, based on degree, betweenness centrality, and brokerage values) and cutting off the most important risk relationship (S1R14 ⟶ S1R2, with the highest betweenness centrality of link), the density of this case project's risk network was reduced from 0.298 to 0.246, and the cohesion value was reduced from 0.615 to 0.533. is outcome means that there are fewer risk interactions in the new risk network, and the complexity of the risk network has been reduced.

Discussion and Conclusion
is paper first defined the stakeholders in PPP projects and then identified risk categories based on the literature. An SNA model was then proposed to analyze stakeholder-associated risks in PPP projects. Lastly, a case study was conducted for a water purification and sewage treatment PPP project in the Changchun City Airport Economic Development Zone in China. To identify how to better prevent and control risk, this study integrated stakeholders and risk factors in PPP projects from a network perspective. In this way, this study expands the research on PPP risk from the individual level to the network level, making up for the limitations of previous studies. Social network analysis is suitable for building and discussing a risk transmission network for PPP projects to discover the key risk factors and risk relationships. e advantages of using SNA for risk analysis are as follows: first, the risk network can be visualized. Second, it fully considers the influence of risk relationships in the risk assessment process.
ird, the mitigating actions can be proposed from two aspects of risk factors and risk relationships. Last, the effectiveness of risk mitigation actions can be tested. is research provides a visualized, innovative research paradigm for PPP project risk analysis. Project managers can use the results for decision-making, risk management, and other processes.
ere are several risk transmission chains in the risk network. Risk is transferred from the risk initiators to the intermediary risk factors and finally to the ultimate risk recipients. Block modeling analysis and the degree difference help to identify the source risks in this risk network. ese risk factors will induce the generation of subsequent risks. According to the degree results, all identified risk factors belong to Block 1, and the block models indicate that the risk factors in Block 1 are at the macrolevel and microlevel. erefore, macrolevel risks and microlevel risks are more inclined to the identity of risk initiator. e risk transmission process must contain many intermediary risk factors. For example, "government intervention" is often in the chain between "policy risk" and "revenue risk." In other words, a change in policy may lead to local government intervention on the PPP project, which may lead to a revenue deficiency. A "government intervention" associated with the local government is neither the initiator nor the ultimate recipient; it establishes a connection between "the policy risk" associated with the government and "the revenue risk" associated with the public. e intermediary risk factors can be all three risk levels.
By conducting an SNA of the case project, 17 factors were identified as the most influential risk factors. Macrolevel, mesolevel, and microlevel risks were all involved and are therefore important in the PPP risk network. Among   them, political and legal risks associated with local government were seen most frequently. is means that, compared to other stakeholders, local governments play the most important role in PPP projects, and political and legal risks are key to PPP project success. e inadequate distribution of risks associated with consultancy ranked second in the results for betweenness centrality and brokerage and first in the results for degree centrality. is highlights the significance of reasonable risk sharing. Construction and operation risks were not as important as perceived. Although these conclusions need to be further verified through additional case studies, this study's findings can nevertheless provide a reference for similar PPP projects in China.
is study has some limitations. First, a 0-1 value was used to evaluate the relationships between risk factors. is only considered the existence, not the strength, of the relationships. In fact, there are differences in the degree of influence between risk factors. In the risk transmission process, risk factors can only be induced when the degree of influence exceeds a certain threshold. Future research should consider the weight of the relationships between risk factors. Meanwhile, this study built a static risk network for the PPP project. As a long-term process, different stakeholders become involved in different phases of PPP projects. e risk network of a PPP project should be dynamically monitored during its whole life cycle. In the future, we should pay attention to changes in the PPP risk network in different stages. Finally, additional case studies should be conducted to corroborate the conclusions of this research.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest regarding the publication of this paper. Public opposition risk e public Social risks S10R27 Revenue risk e public Operation risks