Structural Dimensions and Measurement of Trust Networks among Construction Project Participants

Abstract

The formation and stable existence of interorganizational trust and its network structure can promote the sustainable development of construction projects and thus become the core elements of the stakeholder relationship governance mechanism. However, existing research has not reached an agreement on the structural characteristics and key dimensions of trust networks, which makes it difficult to conduct in-depth empirical research on the degree of trust of all project participators. Based on social network theory, this study analyzes the connotation, dimension and measurement method of trust networks of project participants. The results show that the structure of trust networks can be divided into density and centralization. Among them, the trust network’s density reflects the universality and stability of the trust relationship between the participants, while centralization mainly reflects the heterogeneity of the trust relationship.

1. Introduction

Construction projects require the full cooperation of many participating parties to complete complex and interconnected tasks in order to achieve the sustainable goals of the project. However, practical situations such as buck-passing and collusion among participants frequently occur, thereby resulting in little cooperation, poor management performance and suboptimal realization of project value [1]. In recent years, with the continuous development of major construction projects, cooperation between the participating parties has increasingly become an important prerequisite for the successful completion of projects and the realization of project value and sustainability [2].

In practice, in the process of project implementation, the participants must take the form of an “engineering community”—that is, a cooperative social network [3]. Therefore, when the specific opportunistic behaviors and other factors of the project participants are taken into consideration, any problems or liabilities can be examined through the principle of “universal connection”—that is, the assumption of a specific liability by one or several participants does not necessarily exempt other participants from liability. To solve the above problems, inter-organizational trust, as the core factor in relationship management, has been emphasized in previous studies as having a profound impact on opportunistic behavior, transaction costs, cooperation efficiency and other factors [4,5]. However, most of the previous studies take the binary trust perspective of the construction owner and contractor, thereby ignoring the trust network structure formed by the participants [6]. In this regard, there is a shortage of methods through which to measure the characteristics of the trust network structure of each participant in construction projects and thus a lack of systematic quantitative tools in the empirical research. As such, the influence of trust networks on each concept has yet to be fully revealed [7]. Moreover, some scholars tend to emphasize the trust atmosphere of the social environment and assert that there is a general lack of social trust on this basis [8]. However, studies from this particular management context in China’s construction and engineering sectors may suggest the opposite—that is, that it is the objective existence of a trust network structure with Chinese characteristics that has contributed to the cooperation between project participants and thus to the rapid development of the construction and engineering sectors in China in recent years. Based on the above, this study aims to develop a set of measurement scales with high levels of reliability and validity to provide a foundation for subsequent research on trust networks among engineering project participants.

2. Theoretical Background

2.1. Definition of Indicators of Structural Characteristics of Trust Networks

In practice, construction projects often involve a large number of participants. Projects and their implementation are by nature complex and changeable, so it is difficult to rely on only two parties to complete them [9]. Based on this, social network theory and its derivative perspectives such as the “structural hole” and “embeddedness” provide a more practical, realistic and intuitive research perspective on the management of each participant in construction projects [10]. In this theoretical framework, the interlocking trust relationships among the participants form a network structure, which is the origin of the “trust network” concept enumerated in this study. However, there is no specific measurement scale for trust networks [11].

Thanks to the development of social network theory and its many extensions, it is possible to portray the networked structure of trust relationships between participants in construction projects, which is complex and heterogeneous, using the social network analysis (SNA) method [12]. In the practice of SNA, the holistic structural characteristics of trust networks will emerge, including network density, agglomeration, central potential, average path length and other indicators [13]. Among them, network density indicates the prevalence of connections among the members of the network. The networked structure of social relations not only provides resources, rights, information and other factors for each participant, but also creates an objective environmental influence for each participant such that the decisions of each member are influenced by the environment in which they are embedded and the behavior of other members. Based on social network analysis, network density is regulated by the number of connections and nodes in the network. Notably, “centrality” is one of the central ideas in the social network analysis perspective that forms the overall centrality and node-specific centrality indices, which measure the network structure and reflect its centrality at different levels. Specifically, centralization portrays the degree of differentiation in the number of relational connections held by each participant and can be used to examine the distribution of relational connections in a social network. In general, a higher degree of centralization potential suggests a tendency to overcentralize network connections and a more uneven distribution of relational affinity between participants. From the perspective of SNA, network density and central potential are the most basic indicators of the totality of the network structure and reflect the prevalence and unevenness of relational connections in the network, respectively.

SNA and its related formulas can quantitatively measure density, central potential and other characteristics of a specific network structure, but specific data such as the number of nodes, the number of connections between nodes and the direction of relationships must be obtained using the corresponding formulas [14]. These data can be obtained through case studies, modelling and simulation, but the data obtained from the case studies are often only indicative of the specific circumstances of the case, while modelling and simulation often simplify the reality of the situation and depend upon a set of constraints or assumptions [15]. The data obtained by these methods characterize the complex and heterogeneous networked structure of trust relationships in construction projects and are thus difficult to present. Previous studies have used measurement scales to quantify specific indicators of the social network structure (i.e., self-reported measures of network characteristics have been widely used in relevant studies). For example, in analyzing the factors that influence contract enforcement and breach of contract between companies, previous studies have used the basic definitions of density and centrality in social network theory to set up measurement scales of six and five questions, respectively, to rate and determine the correlation between network density and centrality within the constructs of contract enforcement and criticality of obligations [16]. Similarly, researchers have used a measurement scale containing three and ten items to measure network centrality and density, respectively, in analyzing the role of SMEs’ structural network characteristics on their internationalization strategy, innovation and adaptability; they then analyzed 263 valid questionnaires using structural equation modelling (SEM). It was found that the link between SMEs’ network centrality and density in their home country as well as their international innovation was significantly moderated by network informality [17]. In addition, in a study on entrepreneurship in Chinese smart manufacturing firms, the researcher used four questions to measure network density and centrality, and the results of a structural equation-based analysis of the returned questionnaires showed that network-mediated centrality and network density were both significantly influential in determining firms’ entrepreneurial ability [18]. Based on the above, self-reported measures of social network characteristics can provide a more generalized sample source and a broader data pool for this study. Because social network analysis provides a detailed conceptualization of network characteristics in terms of both the overall network and the individual levels, the questions and scales constructed based on this theory have good validity and reliability. In view of this, this study develops, designs and tests this type of scale and provides a basic methodology for data collection to support empirical research.

2.2. Subdimensions of Network Density and Central Potential

A literature review identifies the specific dimensions that must be measured to characterize the network structure of each participant in a construction project. We note that the current research on trust networks is mostly in English, so this study uses the Web of Science database to collect the literature in this area, using “Network-level Trust”, “Trust Networks” and other similar phrases as subject terms or search keywords. There is also research in the Chinese literature on the use of scales to measure concepts such as social network centrality (including “central potential”) and density.

Although there is still relatively little empirical research on the structure of trust networks and their effects, the measurement scales from similar studies in the social network theory research can be used as a reference for this study. The studies were collected using the terms “social network scale” or “density and centrality scale” in the Chinese literature database. After eliminating studies from both sources that did not focus on trust networks or on the measurement scales of relationship networks, 12 relevant papers were identified and collated to identify the specific dimensions of trust network density and centrality, as shown in

Table 1. Reference to the secondary classification involved in the division of trust networks.

Classification	Secondary Classification	References									Total
		1	2	3	4	5	6	7	8	9
Trust Networks Density	Strength of relationship		√	√	√					√	4
	Universality	√	√	√		√	√	√	√		7
	Nodal distance					√		√	√		3
	Relationship maintenance	√	√	√			√				4
	Tightness	√	√		√		√				4
Trust Networks Centralization	Uneven	√	√	√	√	√			√		6
	Agglomeration	√	√			√			√		4
	Punctuality		√			√	√				3
	Intermediacy			√					√	√	3
	Proximity				√	√	√		√		4
	Differences		√	√							2

Notes: 1 = Ye [18]; 2 = Nyuur [17]; 3 = Frazier [16]; 4 = Kamiyarna [19]; 5 = Adali [20]; 6 = Giuliani [21]; 7 = Park [22]; 8 = Pasquale [23]; 9 = Choi [11].

[19,20,21,22,23].

Based on Table 1, it can be seen that the networked structure of trust relationships has received more in-depth analysis in the research on e-commerce, supply chain and corporate human management, and the relevant measurement scales in previous studies have similarly focused on these areas. The density indicators of trust networks can be interpreted and explained in terms of their prevalence, relationship maintenance, relationship strength, node distance and closeness. For example, the concepts of “relationship strength” and “node distance” have been used in the research on the Internet and e-commerce, which has led to a number of measurements of trust networks as well as algorithm optimization. In the supply chain and enterprise management research, the density of the networked structure of relationships between nodes is often deconstructed into dimensions such as “universality”, “closeness” and “relationship maintenance”. In addition, according to the basic definition of network density in social network theory and its quantification, “universality” indicates the existence of a limited number of nodes in a network of connections between nodes, which can be regarded as the expression of network density in terms of “mathematical relationships”. This means that the greater the number of connections between nodes in a networked structure of trust relationships, the more universal trust relationships exist in the network; when the number of connections reaches the maximum possible value, the trust relationships are considered to be universal. This allows for a better understanding of the dimension of “closeness”—that is, when the nodes are close together the network is tighter and there is a greater probability that two unconnected points can be “bridged” together by other nodes regardless of the existence of the relational connections between them. This is an expression of the “spatial configuration” of network density. Moreover, looking at network density from a time-series perspective reveals the “relationship maintenance” subdimension (i.e., that network density evolves over time). In fact, each node in a complex network structure exhibits multiple heterogeneous characteristics, and the connections between nodes are in a state of dynamic change, so the network density also changes as time advances. Furthermore, the relationship maintenance subdimension is an indication of the density of the network as well as its self-sustaining ability in a finite time interval. To summarize the above, this study adopts three dimensions to measure the density of the structural trust network characteristics of each participant in construction projects: universality, closeness and relationship maintenance.

The central potential of a network can be divided into three factors: degree, betweenness and closeness central potential [24]. The literature, as presented in Table 1, reflects this situation. However, the differences between these three central potentials are small so they can be considered a reflection of the unevenness of the relational connections in the network. For example, intermediary centrality potential reflects the difference between the intermediary centrality of the node with the highest intermediary centrality in each node as well as that of other nodes in the network. If the gap between this node and other nodes is large, the network has high intermediary centrality potential and the nodes may be divided into smaller groups such that they are not overly dependent on one key node for the transmission of resources, relationships and information, for example (i.e., the node is of central importance in the network). It should be noted that all three manifestations of network centrality reflect the unevenness of relational connections between nodes (i.e., when there is a node or faction with a high number of relational connections, while there are other nodes with few or no relational connections). When viewing the spatial configuration of network relations from a graphical perspective, centrality is a holistic indicator of the difference in centrality between the edge points and the center points of a network, while “agglomeration” can be considered as another explanatory dimension of network centrality based on the contents of Table 1. In fact, if the structure of a network of relationships is spatially concentrated, the centrality of the central points is high while that of the edge points is low (i.e., the centrality is high); if the relationships in a network are sparsely connected, there is no significant difference between the centrality of the central points and that of the edge points (i.e., the centrality is low). The spatial configuration of the “scale-free network graph” reflects the degree of sparseness or concentration. This study uses two dimensions to measure the centrality of each participant in a construction project: unevenness and clustering.

3. Research Design and Methodology

The development of scales for academic research should follow a standardized procedure [25]. This means that the initial scale and its items should be developed first; then the content reliability and structural validity of the scale items should be verified through a questionnaire, and inappropriate items should be removed to obtain a measurement scale; finally, the reliability and validity of the scale should be tested [26]. Specifically in this study, the scale items were first generated through a combination of deductive and inductive methods. The deductive study was based on a review of the relevant literature to generate the initial items of the scale, while the inductive study was based on an open-ended question to collect a wide range of respondents’ responses to the question, followed by a content analysis to identify and classify keywords or themes in the descriptive statements, and then to generalize the connotations of the new concepts [27]. Taken together, and drawing primarily on specific practices from previous related literature, the scale development for this study was carried out [28].

3.1. Development of the Initial Scale

According to the social network theory and its extended view, the overall structural characteristics of each participant in an engineering project can be divided into two core dimensions, namely, network density and central potential. Based on relevant studies, the density indicators of social networks can be divided into three subdimensions—universality, closeness and relationship maintenance—while the central potential indicators can be divided into two subdimensions—imbalance and agglomeration. On this basis, each measurement item can be sourced from the literature, followed by an initial measurement of the topics under review in this paper [29]. The initial measurement items are shown in

Table 2. Initial measurement items on the structural characteristics of the trust networks.

Classification	Secondary Classification	Item No.	Initial Measurement Items	References
Trust Networks Density (ND)	Universality	NDU1	There is mutual trust between all parties involved in the project	Nyuur [15]; Frazier [14]
		NDU2	The participants have always shown themselves to be trustworthy
		NDU3	No obvious obstacles to forming a relationship of trust with other parties when joining a new participant
		NDU4	All parties involved agree that a good relationship of trust is important to the project
	Tightness	NDT1	The participants are happy to work centrally, and a relationship of trust is formed during this period
		NDT2	Efficient sharing of project information and the formation of trust between participants
		NDT3	Frequent communication between project participants, during which a relationship of trust is formed
	Relationship maintenance	NDS1	Trust between project participants throughout the cooperation period
		NDS2	>No sporadic conflicts between the parties involved will lead to a breakdown in the relationship of trust
		NDS3	Satisfactory relationship of trust between the various parties involved
		NDS4	The parties involved want to maintain a relationship of trust long after the project has been completed
Trust Networks Centralization (NC)	Unevenness	NCB1	There are participants who are trusted or largely untrusted by other individual participants	Ye [16]; Pasquale [23]
		NCB2	The project participants apparently focus their trust relationship on a specific participant
		NCB3	Some participants pay extra attention to building and maintaining trusting relationships
		NCB4	Some participants expressed or showed contempt for the relationship of trust
	Agglomeration	NCC1	Differences in trust relationships between project participants
		NCC2	A small faction of participants who clearly trust each other in the project
		NCC3	A participant is the “bridge” position for the relationship between other nodes

.

The initial measurement scale consists of 18 questions. The trust network density dimension consists of eleven items and the central potential dimension consists of seven items. A questionnaire was used for data collection. To improve accuracy, the initial measurement scale was pretested by seven experts. Specifically, the practical meaning of trust relationships in the Chinese cultural context was to be considered, so the experts involved in the pretest included academic experts from major universities and professionals from the construction industry in China. The university experts were selected based on their research in the field of engineering project governance (i.e., they were selected through the Chinese academic literature database for their published work in the field of construction contract or relationship management), while the experts from engineering practice were mainly keynote speakers at industry summits in real estate, engineering law, supervision and cost management. More than twenty potential experts who met the criteria were contacted by telephone and email, and six academic experts from universities and five professionals were finally invited.

Some experts used on-site interviews to conduct the research, while others used open-ended questionnaires. The content of the interview and survey was based on the 18 measurement questions summarized in Table 2, and the experts were asked to judge the necessity and accuracy of the questions based on whether they “fully reflect the content of the networked structure of the trust relationship between the participants of the project.” At the beginning of the interview and survey, the scope and meaning of the trust network of participants in engineering projects established in this study were explained to each expert, and the basic definitions of concepts such as density and central potential were explained from the social network theory perspective. In doing so, the main objective of this study and the basic meaning of “trust network” were communicated such that the participants could assess whether each item reflected the actual practice of project engineering in China and thus the trust network density and central potential as well as whether there is any duplication or missing content.

At the end of the interview process, open-ended responses from the experts were collated and the initial scale was refined in two ways. First, in terms of content, most of the university experts emphasized that the density and centrality of the network structure can be accurately measured and calculated in the context of SNA, but the trust relationship itself is difficult to quantify. It is therefore necessary to develop a scale for the structural indicators of the trust network and provide a concise explanation of the trust relationship in terms of preliminary scales and specific item descriptions, to help subjects grasp the meaning of “trust” and give accurate answers. Many experts from the field of construction emphasize the importance of clarifying the “specific scope of participants” (i.e., the need to clarify which types of enterprises are included in the “participants” mentioned in the scale questions) to help them make accurate judgments. This suggests that it is necessary to clarify which types of companies are included in the questions. However, in terms of the specific content of the questions, most experts believe that question NDU3 (new node trust relationship establishment) is related to the dynamic nature of trust relationships—that is, the addition of new trust relationships will lead to changes in both density and central potential—so this content will not accurately reflect the basic meaning of either. In addition, questions NCB3 (participants value trust relationships) and NCB4 (participants value trust relationships) differ and belong to the concept of “stability,” which can be combined into NDS1 (i.e., there is no need to list these two items separately). Experts mostly believe that NDS3 (satisfaction with trust relationships) and NDS4 (continuation of trust relationships after project completion) cannot directly influence or reflect the density and central potential of the participants and can therefore be ignored.

3.2. Data Collection

The scale for measuring the structural characteristics of the trust network of each participant in an engineering project asks the participant to recall the specific engineering project in which they have participated in the past, to select the most impressive one and to give an overall assessment of the networking of the trust relationship of the entire project team consisting of each participant. The questionnaire was administered on a five-point Likert scale (1 = completely disagree; 5 = completely agree). The questionnaire was sent in paper form and the respondents were academic experts as well as participants in and attendees of major academic conferences, industry summits and various channels of continuing education and training in the field of engineering management.

The total number of questionnaires returned was 119 out of 230 sent. The questionnaires that showed the same values throughout, had obvious patterns of answers or had incomplete answers were considered invalid. Thus, 91 valid questionnaires were obtained after removing the invalid questionnaires, for a return rate of 51.74% and a validity rate of 39.57%. A statistical analysis of the background information of the valid questionnaires revealed that 61.54% of the subjects had five or more years of experience in the field, 78.02% had participated in four or more projects, and 60.44% were project managers, thus indicating that the subjects in this study had rich working experience and a deep understanding of project management practices, which ensures the accuracy of the data collected in this study. In addition, an analysis of the type of project chosen by the participants reveals that 58.24% of the projects were led by government investment and 20.88% were government–social capital cooperation projects. This shows that the collected data will reflect the situation in construction projects led by or with the participation of the government. Such projects will be supervised by various government administrative departments and provide services to government departments and the general public after completion. In practice, such projects tend to have a large number of participants or stakeholders and a broad social influence (i.e., the number of nodes in the trust network structure is high). In addition, among the types of construction contracts chosen by the participants, 39.56% were lump-sum contracts, 10.98% were cost-plus-award contracts and other types of contracts and nearly half of the contracts were unit price contracts.

4. Data Analysis

4.1. Exploratory Factor Analysis

4.1.1. Reliability Analysis and Question Purification

The exploratory factor analysis was conducted using SPSS 24.0 software and mainly used the coefficient of internal consistency test (i.e., Cronbach’s α) as a measure of reliability and the single item–total correlation correction coefficient (CITC indicator) to purify the measured items. A Cronbach’s α value ≥ 0.70 indicates high reliability, while questions with a CITC value of no less than 0.5 should be retained [30]. The Cronbach’s α value for the thirteen items of the trust network structural characteristics Scale was found to be 0.913. Specifically, the Cronbach’s α values for the dimensions of universality, closeness, relationship maintenance, unevenness and agglomeration were 0.804, 0.761, 0.805, 0.837, and 0.867, respectively, all of which are greater than the threshold of 0.7, thus indicating that the dimensions have high reliability [31]. In addition, according to

Table 3. Results of confidence analysis.

	Average of Scales after Deletion of Items	Scaled Variance after Removal of Terms	Corrected Term to Total Correlation	Cronbach’s Alpha after Deletion of Terms
NDU1	37.87	127.827	0.522	0.911
NDU2	37.78	129.018	0.529	0.910
NDU3	38.29	127.717	0.568	0.909
NDT1	38.42	130.135	0.309	0.922
NDT2	39.05	123.275	0.623	0.907
NDT3	39.08	115.805	0.779	0.900
NDS1	38.95	125.141	0.579	0.909
NDS2	39.16	115.250	0.807	0.899
NCB1	38.64	121.167	0.730	0.903
NCB2	38.36	121.389	0.731	0.903
NCC1	38.68	120.731	0.711	0.903
NCC2	38.46	124.918	0.608	0.908
NCC3	38.23	115.002	0.819	0.898

, only NDT1 (each participant is happy to work centrally) has a value below the threshold of 0.5 (0.309) (i.e., it did not meet the test criteria and was deleted) [32].

4.1.2. Validity Analysis

After the reliability analysis, the scale actually retained 12 items, and the overall Cronbach’s α of the scale was raised to 0.922. The items had a high standard deviation, as the Bartlett’s sphericity test value was 796.56 and the significance level (p-value) was 0.000 (i.e., less than the 0.05 level), thus indicating that the correlation matrix is not a unit matrix. The net result of the above tests indicated that the data in this study were suitable for exploratory factor analysis [33]. Based on the above, exploratory factor analysis was conducted on the data to detect the divisions in the trust network dimensions among the participants in an engineering project. Specifically, factors with eigenvalues greater than 1 were extracted using principal component analysis with maximum variance rotation, and the specific results are shown in

Table 4. Results of principal component analysis.

Item No.	Factors Extracted
	1	2	3
NCC1	0.807	0.159	0.137
NCB2	0.790	0.346	0.174
NCC2	0.784	0.136	0.390
NCC3	0.773	0.335	0.374
NCB1	0.772	0.262	0.295
NDT2	0.143	0.867	0.120
NDS1	0.118	0.841	0.111
NDT3	0.390	0.835	0.128
NDS2	0.373	0.829	0.201
NDU2	0.235	0.128	0.826
NDU1	0.180	0.177	0.810
NDU3	0.364	0.101	0.743

Note: Title NDT1 has been deleted in accordance with the preceding.

and

Table 5. Results of exploratory factor analysis.

Classification	Factors	Item No.	Factors Loading	CITC	Characteristics	Amount of Variance Explained (%)	Amount of Cumulative Variance Explained (%)	Cronbach’s α
ND	Universal	NDU1	0.810	0.752	1.033	8.610	8.610	0.804
		NDU2	0.826	0.758
		NDU3	0.743	0.724
	Stability	NDT2	0.867	0.630	1.757	14.645	23.255	0.916
		NDT3	0.841	0.845
		NDS1	0.835	0.530
		NDS2	0.829	0.547
NC	Heterogeneity	NCB1	0.772	0.581	6.485	54.043	77.298	0.919
		NCB2	0.790	0.594
		NCC1	0.784	0.758
		NCC2	0.807	0.555
		NCC3	0.773	0.782

.

The following criteria were used to screen suitable items: (i) the factor loading of the item on its subject was ≥0.4; (ii) the cross-loadings between the item and other items were <0.4; and (iii) the connotation of the item should be consistent with the connotation of other items on the same factor. Only those items that met all three criteria were retained. According to the above criteria and in combination with Table 4 and Table 5, three main dimensions were obtained, and no items were deleted in the process [34]. The reliability of all constructs met the recommended threshold of 0.7. In addition, the reliability of each item was tested using the single item–total correlation correction coefficient, and Table 5 shows that the reliability of each item met the recommended threshold of 0.5. In the initial classification of the structural characteristics of the trust network of each participant in this study, the trust network density was divided into the three dimensions of universality, closeness and relationship maintenance, and the central potential indicator was divided into the two subdimensions of unevenness and agglomeration. However, the results of an exploratory factor analysis showed that the two dimensions of trust network density (i.e., closeness and relationship maintenance) can be combined into the same factor, as can those of central potential, and the results are shown in Figure 1. Among them, trust network density can be further divided into two subdimensions of prevalence and stability, while network centrality potential can be used as a unidimensional construct that reflects the heterogeneity of trust relationships among the participants in the networked structure (i.e., the simultaneous existence of heterogeneity and complexity among the nodes in the network).

4.2. Validation Factor Analyses

Validation factor analyses were conducted on the sample data to examine the convergent validity and discriminant validity of the scale. The partial least squares structural equation modelling (PLS–SEM) approach has been noted to have advantages such as lower computational complexity when evaluating multidimensional models [35]. In addition, the Shapiro–Wilk (S–W) test and the one-sample Kolmogorov–Smirnov (K–S) test were conducted separately, and the results indicated that the significance indicator values (p) for each question item were below the threshold of 0.05. Thus, the sample data exhibit nonnormal distribution characteristics and it is appropriate to use the PLS–SEM method for data analysis [36]. The validity of the measurement scale was tested using SmartPLS 3.3.3 software, while a two-stage estimation method was used (i.e., the first-order and second-order constructs were assessed separately) [37].

4.2.1. First Stage Conceptual Assessment

The measured combined reliability (CR) values for the three first-order constructs of the universality, stability and heterogeneity of the trust network were 0.885, 0.941 and 0.940, respectively, and all exceeded the recommended threshold of 0.7 and thus had high reliability, as shown in

Table 6. Results of the validation factor analysis.

First Stage Conceptual Assessment					Second Stage Conceptual Assessment
Secondary Classification	Item No.	Factors Loading	AVE	CR	Dimensional	AVE	CR
Universal	NDU1	0.833	0.720	0.885	Trust Networks Density	0.545	0.892
	NDU2	0.863
	NDU3	0.850
Stability	NDT2	0.875	0.799	0.941
	NDT3	0.933
	NDS1	0.830
	NDS2	0.933
Heterogeneity	NCB1	0.884	0.757	0.940	—	—	—
	NCB2	0.873
	NCC1	0.873
	NCC2	0.793
	NCC3	0.924

. In addition, each question item of the three constructs had high factor loadings, and the average extracted variance (AVE) values of each construct exceeded the recommended threshold of 0.5 and thus had high convergent validity [38]. Moreover, the square root of the AVE value for each first-order construct was found to be greater than the correlation between the construct and the other constructs, as shown in

Table 7. Discriminant validity of first-order constructs.

Secondary Classification	Heterogeneity	Universal	Stability	Average Value	Standard Deviation
Heterogeneity	0.870 *			3.273	0.187
Universal	0.616	0.849 *		3.769	0.270
Stability	0.585	0.390	0.894 *	2.687	0.089

Note: The values marked with * indicate the square root of the AVE value for each concept.

. The results indicate that each question item has the highest factor loadings on the construct to which it belongs, thus indicating that the first-order constructs are significantly different and have high discriminant validity.

4.2.2. Second Stage Conceptual Assessment

Trust network density is a second-order construct, and Table 6 shows that the CR value for this construct is 0.892, which is greater than the recommended threshold of 0.7, and the AVE value is 0.545, which is greater than the recommended threshold of 0.5. These results indicate that the trust network density has relatively good reliability and convergent validity. In addition,

Table 8. Path coefficients between trust network density and its first-order constructs.

Paths	Factors	T-Statistic	p-Value
ND → Universal	0.738	15.47	0.000
ND → Stability	0.909	69.387	0.000

shows that there is a significant correlation between trust network density and both of its first order variables. For example, the path coefficient between trust network density and relationship prevalence is 0.738 (p < 0.001) and that between trust network density and relationship stability is 0.909 (p < 0.001).

4.3. Reliability and Validity Tests

To verify the reliability of the scale, the Cronbach’s α coefficient was used to test the internal consistency and reliability of the multidimensional scales. The Cronbach’s α coefficients for the overall scale and each of its dimensional subscales were tested using SmartPLS 3.3.3 software, and the results are shown in

Table 9. Results of reliability and validity tests for structural features.

	Trust Networks	Density	Heterogeneity	Universal	Stability	Cronbach’s α	AVE
Trust Networks	0.735					0.920	0.540
Density	0.924	0.738				0.856	0.545
Heterogeneity	0.924	0.709	0.870			0.919	0.757
Universal	0.733	0.738	0.616	0.849		0.806	0.720
Stability	0.808	0.909	0.585	0.390	0.894	0.915	0.799

Note: The diagonal values indicate the square root of the AVE values for each concept.

. Based on the results of this test, it can be concluded that the relevant indicators are within a reasonable range of thresholds and that the internal consistency between the items in this study is good and thus the model has good reliability.

The content validity and validity of the scale were ensured by following a standardized and rigorous scale development process, while construct validity was measured by testing whether the square root of the AVE for each dimension was significantly higher than the standardized correlation coefficient between that dimension and the other dimensions. The results of this analysis showed that the 12 items retained by the exploratory factor analysis in this scale had fully standardized factor loadings greater than 0.5 on the corresponding latent variables and reached the significance level, the corresponding AVE values were greater than 0.5, and the square root of each latent variable’s AVE was greater than its standardized correlation coefficient with the other latent variables, as shown in Table 9. These findings indicated that the constructs of this scale passed the test and thus had good validity.

5. Results Discussion

This study develops a scale for measuring the structural characteristics of trust networks among participants in engineering projects. The structural characteristics of trust networks include two core dimensions—network density and network central potential—and the measurement of trust network density contains two subdimensions—stability and the universality of trust relationships. Trust network central potential is a unidimensional construct that reflects the heterogeneity of the relationships among participants in engineering projects. The factors extracted from the data analysis performed in this study are similar to those highlighted in our literature review, thus indicating that in the engineering practice, the networked structure of trust relationships is mainly reflected through the abovementioned network factors of stability, universality and heterogeneity.

(1)

A universal trust relationship between project participants is the foundation of any networked structure. If a universal trust relationship cannot be achieved between the participants, the number of connections between the nodes in the networked structure will be reduced or even disappear (i.e., the network density value in the social network analysis will be close to zero). The universality of trust relationships in a network is therefore a core subdimension of network density. The existence of stable trust relationships among participants will help to maintain network density. Importantly, the network structure is always heterogeneous; so, in practice, it will always dynamically change as the project progresses. In this way, the density of the trust network will change with time, so the stability of the relationships will be an important indicator of its density. The results of the validation factor analysis show that the path coefficients between trust network density and its two subdimensions (i.e., universality and stability) are 0.738 and 0.909, respectively, thereby suggesting that universality and stability are both strong explanatory factors of trust network density. The results of the above analysis suggest the following: (a) The existing studies in the social network theory literature have emphasized the inhibitory effect of trust relationships on opportunistic behavior, which is also the basis for improving each participant’s efficiency. Thus, the trust relationships of each participant constitute a network structure, and the stability of the relationships between each participant is particularly important. This is why the path coefficient between the density of the trust network and its subdimension (i.e., stability) is high, which emphasizes the importance of a stable trust relationship in improving cooperation and suppressing opportunistic behaviors in engineering projects. (b) In fact, the parties involved in an engineering project do not all trust each other. In this reality, the trust relationship that prevails between the parties corresponds to a high level of trust network density. Conversely, a low level of network density or even the absence of a trust network structure is indicated. Thus, the dimension of universality is a fundamental perspective, it can indicate that a trust network actually exists. However, it is clear from our analysis of the path coefficient data that this universality is less important than stability in the measurement of trust network density. This is because the stability dimension is more indicative of a sustainability or time-series nature than the universality dimension which is the nature of cross-sectional data. Therefore, although the universality dimension is a foundational perspective, it is not as important as the stability dimension;

(2)

According to graph theory and social network theory, the unevenness and complexity of the relationship between nodes in a network is reflected by the central potential of the network, which is also in line with the “heterogeneity” characteristic in ecology and the general social consensus. That is to say, there is a natural imbalance in the distribution of trust relationships between individual participants—that is, there is not an equal strength of trust between all participants in a project [39]. On the contrary, in practice, there is a core of participants who are able to gain more trust from other participants, and there are also individual participants who are unable to gain trust from any other participant. Specifically, the contractor and the developer are always the core binary subjects in engineering projects [40]. The trust relationship induced by this relationship is more binding than those of other participants, and the network of construction projects is characterized as a “scale-free network” without a loss of generality (i.e., their high central potential is often more obvious). Heterogeneity is the core dimension of the central potential of trust networks. The literature review in this study classifies the central potential of trust networks into two subdimensions—unevenness and agglomeration—while the results of the exploratory factor analysis show that both belong to the same factor. The main reason for this finding is that the relationships between and behavior of the parties involved in a construction project are heterogeneous, and the networked structure of the trust relationship is complex and variable; thus, its central potential is variable and difficult to measure. This is also reflected in the statistics presented in the literature review, where there is a similar amount of support for a differentiated dimensional approach.

Previous research has shown that centralization is a holistic measure of the structure of a relationship networks [12]. Differences in data on the centralization indicator across trust networks, or fluctuations in the centralization indicator over time within the same trust networks, are rooted in the heterogeneous nature of trust relationships: the aforementioned imbalance in the distribution of trust relationships across individuals—that is, a higher centralization indicates the presence of a participant in the trust networks that is able to obtain more trust relationships than any other participant [13]. The reasons for the emergence of this phenomenon can be explained by factors such as the complexity, unevenness and aggregation of trust relationships, but the underlying causes of these factors all point in one direction, namely, the heterogeneous nature of trust relationships [39]. Based on this fact, it is easy to understand that the results of the exploratory factor analysis show a unique factor in the measurement of central potential—that is, central potential is a unifying concept that encompasses multiple perspectives such as complexity, unevenness and agglomeration.

Based on the above, this study constructs a scale to measure the structural characteristics of trust networks in engineering projects containing twelve items, including seven items for network density and five for central potential. The specific measurement scale constructed in this study and the corresponding items are shown in

Table 10. Measurement items on the structural characteristics of the trust networks.

Classification	Items No.	Measurement Items
Trust Networks Density (ND)	ND1	There is a general relationship of mutual trust between the various parties involved in the project.
	ND2	The participants have always tried to show that they are to be trusted.
	ND3	All parties involved agreed that the relationship of trust had a significant impact on the project.
	ND4	Project information is often shared efficiently and trusting relationships emerge between the participants.
	ND5	Frequent communication between the participants and the emergence of a trusting relationship between the participants.
	ND6	The relationship of trust between the project participants is maintained and continues throughout the period of cooperation.
	ND7	The parties involved in the construction will not easily be in conflict over disputes leading to a breach of trust.
Trust Networks Centralization (NC)	NC1	There are participants who are only trusted or largely untrusted by other individual participants.
	NC2	The majority of participants apparently focused their trust relationships on particular participants.
	NC3	There are significant differences in the level and depth of mutual trust between project participants.
	NC4	There are clearly groups or factions of participants in the project that trust each other.
	NC5	The presence of a participant can be an effective catalyst for building trust between other participants.

.

6. Conclusions and Limitations

This study combines multiple quantitative research methods to develop a scale to measure the characteristics of the trust network structure of each participant in an engineering project. The measurement structure is divided into two dimensions—network density and centralization. Trust network density is a composite construct, which can be further divided into two sub-dimensions—universal and stability. On this basis, combined with similar measurement items in previous studies, the measurement items of each construct of the trust network of participants in the engineering project are developed and verified. Among them, there are seven measurement items about the density of the trust networks and five related to the centralization of the trust networks. The theoretical contribution of this paper is mainly reflected in two aspects: first, this paper expands the existing relationship management research framework by examining the binary trust relationships between project developers and contractors from the perspective of social network theory, complements the research on relationship management and builds a complete network analysis framework; second, this paper presents a theoretical foundation for relationship management in engineering projects and provides a potential supplement to contractual governance mechanism as well as an integrated measurement tool for studying the influencing mechanism of trust networks among engineering project participants on the specific behaviors of each party.

The shortcomings of this study are as follows: (1) due to time, financial and social limitations, the sample size in this study is 91, which does not reach the theoretical requirement of over 200 and will thus affect the accuracy of the results; (2) the questionnaire in this study is not limited to specific project types and the sample data cover various types of construction projects, thereby resulting in the questionnaire used in this study being universal but lacking relevance. In fact, there are differences in the degree of ownership control, the number of stakeholders and the depth of participation by contractors in construction projects. For example, there are obvious differences in project management styles such as DBB, EPC and PMC, so a follow-up study can explore specific measurement scales for different types of projects as well as their financing mechanisms and management styles.