**1. Introduction**

The construction industry is a project-based industry. Construction projects are complex and usually involve multiple stakeholders. Among them, the project owner is the initiator of the construction project, and the contractor undertakes the construction tasks of the project [1,2]. The owner and the contractor collaborate on a specific project, and the collaborative relationship between them is essential to the success of the construction activity [3,4]. Due to the temporary nature of construction projects, an owner or a contractor constantly develops new collaborative relationships with new owners or contractors in new projects. The number of construction projects in China has grown substantially over the past decade. The contract value of new projects in 2021 was USD 5.12 trillion, three times that of 2011 [5]. The massive increase in the number of projects has involved more and more owners and contractors. Lee et al. [6] believed that owners and contractors had gradually formed a complex collaborative relationship network based on their intertwined

**Citation:** Wang, F.; Cheng, M.; Cheng, X. Exploring the Project-Based Collaborative Networks between Owners and Contractors in the Construction Industry: Empirical Study in China. *Buildings* **2023**, *13*, 732. https://doi.org/10.3390/ buildings13030732

Academic Editors: Rafiq Muhammad Choudhry and Annie Guerriero

Received: 18 December 2022 Revised: 16 February 2023 Accepted: 5 March 2023 Published: 10 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

collaboration in different projects. An organization's position in this collaborative network reflects its competitiveness in the construction market and its influence on the industry and determines its ability to access external resources and information [3,7].

As new projects are implemented, new participants and relationships are continuously embedded into the network. Therefore, the collaborative relationship network is dynamic, and this change will affect the exchange of information between owners and contractors and their future collaborative relationships [8,9]. According to the Industrial Marketing and Procurement (IMP) group, organizations should build long-term collaborative relationships to achieve mutual benefits and enhance competitiveness [10]. Studying the characteristics and evolution of the relationship network formed by owners and contractors in a certain period from a dynamic perspective helps understand their collaboration mechanism and the change of an organization's position in the construction market to provide a basis for formulating future collaboration strategies.

However, previous studies mainly focused on the one-time and short-term collaborative relationship between owners and contractors in particular projects [11,12]. There is a lack of industry-level exploration of the structural characteristics and evolution of the collaborative networks formed by numerous owners and contractors when they are involved in different projects. Although some studies on collaborative networks formed by different types of stakeholders in various projects involved owners and contractors, they focused on specific types of projects, such as skyscraper projects, BIM projects, and green building projects [13–15]. In fact, owners and contractors have formed intricate collaborative relationships based on their involvement in different types of construction projects. Studies based on broader boundaries can provide a more comprehensive insight into their collaboration.

Collaborative relationship network analysis is the foundation of organizational network governance, which is a long-term, selective, structured, and autonomous collection of organizations [16,17]. Unlike an organization concerned with maximizing its interests, organizational network governance focuses on the interactions between organizations and their performance in the network. Social network analysis (SNA) is a commonly used method to explore the macro-structural features of complex collaborative networks [18]. Meanwhile, the network motif analysis (NMA) method can be applied to analyze the local topology and micro-structural features of collaborative networks [19]. To bridge the knowledge gap in industry-level owner–contractor collaborative network research, we combined SNA and NMA to study the structural characteristics and dynamic evolution of the collaborative networks, which were established based on thousands of collaborative relationships among owners and contractors in the construction projects that won China's National Quality Engineering Award (NQEA) from 2013 to 2021.

This study aims to characterize the macro-structure and micro-structure of the collaborative networks formed by numerous owners and contractors involved in different projects and how they evolved over time by using the data of NQEA projects in China and combining SNA and NMA methods in order to help owners and contractors clarify their position in the partnership network and provide a reference for them to formulate future relationship cultivation strategies. The remainder of this study is organized as follows. In Section 2, the literature on the owner–contractor relationship and the collaborative network analysis in the construction field are reviewed. Section 3 presents the research methodology, and Section 4 explains the analytical procedures and data collection. In Section 5, the characteristics and evolution of the collaborative network formed by owners and contractors are analyzed based on SNA and NMA, followed by a discussion and some managerial implications.

### **2. Literature Review**

#### *2.1. Owner–Contractor Relationships*

The collaborative relationship between owners and contractors affects the implementation of construction projects. Previous studies have analyzed the relationship between the owner and the contractor from three aspects.

First, some scholars explored the owner–contractor relationship in different delivery systems adopted for construction projects. For example, Li and Feng [20] explored the strategies for enhancing the trust relationship between owners and contractors in project management contracting (PMC) projects. Sun et al. [21] argued that effective collaboration between owners and general contractors improved the level of BIM adoption in engineering, procurement, and construction (EPC) projects. Collecting questionnaires from 243 Chinese project professionals, Zhang et al. [22] demonstrated that the level of design provided by the owner had an impact on the quality of the contractor's design in the design–build (DB) projects.

Second, some scholars explored the factors that influenced collaborative relationships between owners and contractors. For example, Suprapto et al. [23] revealed that relational attitudes, collaborative practices, and teams' joint capability influenced the collaborative relationship between the owner and the contractor. Jiang et al. [24] found that reputation, competence, honesty, communication, reciprocity, and contracts effectively influenced the establishment of trust relationship between owners and contractors. Zhang and Qian [25] analyzed how the mediated power influenced opportunism in owner–contractor relationships. Tai et al. [26] analyzed the factors influencing owners' trust in contractors in construction projects. Suprapto et al. [27] found that shared team responsibility, execution-focused teams, common capability and structures, and senior leadership pair can be effective in improving the relationship between owners and contractors.

Finally, the interaction mechanism between the owner and the contractor is also one of the research focuses. For example, Zhang et al. [28] discussed the combined influence of the owner's power and contractual mechanism on the behavior of contractors in China. Qian et al. [29] emphasized that there is both cooperation and competition in the relationship between the owner and the contractor and that when the two are balanced against each other, greater value can be created in the project for maximum benefit. Based on a contract management perspective, Nasir and Hadikusumo [30] developed an integrated model to manage the relationship between the owner and the contractor. Zhao et al. [31] believed that there was a strong reciprocity relationship between the owner and the contractor, and the parties accepted and maintained specific cooperation.

Although previous studies support understanding the collaborative mechanism between the owner and the contractor, their relationships were typically regarded as a binary structure or explored in the context of a specific project. A construction project is implemented by a temporary organizational alliance, which forms a temporary collaborative network [32]. The owners and contractors are constantly expanding into new project-based partnerships as they engage in new projects. From an industry perspective, they gradually form a long-term organizational network with a specific structure in project-based collaboration [33]. Project-based industry-level collaborative networks are more complex and dynamic than project-level networks, which characterize collaborative relationships within a single project. Analysis of project-based industry-level collaborative networks not only helps to understand an organization's position in the industry and its competitiveness in the construction market, but also reveal the organization's collaboration preferences, which can provide a basis for the organization to choose partners [34,35]. However, there is still a lack of research on the characteristics of owner–contractor industry-level collaborative relationship networks and the evolution of the network structures.

#### *2.2. Collaborative Network Analysis in the Construction Field*

In today's business environment, collaboration is seen as a way for organizations to acquire new business opportunities and facilitate the formation of a networked society [36]. Organizations can improve their market competitiveness by strengthening their position in the network [9]. As a result, the strategic focus of organizations has shifted from focusing solely on their operational performance to network-based collaboration and competition [37,38]. It is increasingly important to understand the relationship structure of the collaboration network and the position of the organization in the network.

Some scholars have adopted the social network analysis (SNA) method to study the collaborative network in the construction field from the industry perspective. The collaborative network formed by multiple different types of stakeholders is one of the research focuses. For example, Han et al. [13] studied the structural characteristics of the collaboration network formed by different owners, general contractors, design firms, and project managers involved in 422 skyscraper projects worldwide from 1990 to 2010. Tang et al. [14] explored the collaborative relationship network formed by owners, design consultants, and major contractors in Hong Kong's BIM projects from 2002 to 2017. Qiang et al. [15] explored how the collaborative networks formed by owners, contractors, and designers in the implementation of multiple green building projects evolve over time based on the SNA method. In addition, some scholars have studied the collaborative network formed by one or two kinds of stakeholders (such as the contractor–subcontractor collaboration network and the contractor–contractor collaboration network). For example, Tang et al. [35] studied the collaborative relationship between contractors and subcontractors in China's construction industry based on the data set of projects that won the China Construction Engineering Luban Prize, and the results provided a reference for contractors to choose subcontractors. Akgul et al. [39] used the SNA method to investigate the collaborative relationship of contractors in Turkey while participating in overseas projects based on the data from 449 projects in 46 countries. Liu et al. [40] used some indicators of the SNA method to characterize the collaborative network among contractors in China's construction industry. Liu et al. [41] analyzed the characteristics of the collaborative network among China's construction firms using the SNA method based on 251 international construction projects constructed by China's 156 construction firms in cooperation. Park et al. [42] investigated the collaborative networks of Korean construction firms formed in 389 overseas projects using the SNA method.

The above studies used the SNA method to describe the complex relationship and macro-structure characteristics of the collaborative network in the construction field. The research results can clarify the organization's influence in the owner–contractor collaborative network and provide a reference for organizations to develop cooperation strategies. The existing research mainly focuses on contractor–subcontractor collaborative networks, contractor–contractor collaborative networks, and collaborative networks among multiple types of stakeholders. The owner and the contractor are the main stakeholders in the construction project. They gradually form a certain relationship network by participating in multiple projects. Understanding the characteristics of the relationship network between the two is helpful for the owner to select contractors and the contractor's bidding decision. Although previous studies on collaborative networks of multiple types of stakeholders involved owners and contractors, they focused on a specific project type. At present, there is still a lack of research on the relationship network of owners and contractors at the industry level based on extensive project data. Moreover, the collaborative networks studies based on SNA focus on exploring the macro-structural features of the network but cannot reveal the local patterns of collaboration.

To explore the micro-structure of complex networks more deeply, researchers shift their attention from focusing on the global properties of the network to local properties. Milo et al. [43] proposed network motifs to reflect a particular local pattern of network interactions, providing new insights for understanding the network structure and relational characteristics. Network motif analyses (NMA) have been applied to explore biochemical networks, ecological networks, neurobiological networks, traffic networks, and energy networks [44–47]. There are also a few scholars who use it to explore the local structural characteristics in organizational networks [48]. It would be meaningful and interesting to

explore the local relationship patterns of owner–contractor collaboration networks based on the method of NMA to discover the evolution of their collaborative patterns from a local network perspective. The introduction of NMA can overcome the limitation of SNA, which focuses on exploring the macro-structure characteristics of the network rather than the local properties. Therefore, we will combine SNA and NMA to analyze the owner–contractor collaboration network and to reveal the characteristics and evolution of the macro-structure of the overall network and the micro-structure of the local network.

#### **3. Methods**

The collaborative relationship between owners and contractors based on different projects involves a complex network connecting different organizations. To fully understand this relationship's structural characteristics and evolution laws, SNA and NMA are applied in the study. Specifically, SNA is used to capture the overall structural characteristics and node locations of the owner–contractor collaborative network from a macro-level. MNA is applied to discover the structure of subgroups in networks and reveal local collaborative patterns from a micro-level.

#### *3.1. Social Network Analysis (SNA)*

The measurement for the macro-structure of the owner–contractor collaborative network based on SNA includes the network-level and the node-level indicators.

#### 3.1.1. Network-Level Measurement

In the SNA method, four network indicators, including density, average degree, average distance, and clustering coefficient, are generally used to analyze the characteristics and evolution of the network.

#### (1) Density

Density refers to the ratio of the actual number of connections to the maximum possible number of connections in the network and can measure the degree of interconnection between nodes in the network [49,50]. The value of density is between 0 and 1. When all nodes in the network are connected to each other, the value of density is 1. When the nodes in the network are all isolated, the density value is 0 [51]. The calculation formula of density *D* is as follows.

$$D = \frac{2E}{N(N-1)}\tag{1}$$

where *E* refers to the number of connections between these nodes, and *N* refers to the number of all nodes in the network.

#### (2) Average degree

The average degree refers to the average number of connections to a node in the network, reflecting the network's tightness [34]. The larger the value of the average degree in the collaborative network, the tighter the network is [52]. The average degree *AD* is formulated as follows.

$$AD = \frac{E}{N} \tag{2}$$

### (3) Average distance

In the undirected network, the number of connections in a path between two nodes is defined as the length of the path, and the length of the shortest path is defined as the distance between the two nodes [53]. The average distance of a network is the average of the shortest path length between pairs of nodes in the network, and it is used to measure the ease of communication between nodes [54]. The average distance *L* is calculated as follows.

$$L = \frac{\sum\_{i \ge j} d\_{ij}}{N(N+1)/2} \tag{3}$$

where *dij* represents the shortest path length from node *i* to node *j*.

(4) Clustering coefficient

The clustering coefficient of a node is the ratio of the number of actual connections between the node and its neighbors to the number of the maximum possible connections between those nodes. The clustering coefficient of the whole network is the average of the clustering coefficients of all the nodes [55]. The clustering coefficient is used to describe the extent to which a node is embedded in the network's local group and reflects the aggregation extent of networks [56]. The value of the clustering coefficient ranges from 0 to 1. The clustering coefficient (*CC*) is 1 when all nodes are interconnected in the network, while *CC* is 0 when all nodes are not connected. *CC* is expressed as follows.

$$\text{CC} = \sum\_{i=1}^{N} \frac{2\varepsilon\_i}{k\_i(k\_i - 1)}\tag{4}$$

where *ki* is the number of neighbors of the *i*th node, and *ei* refers to the number of connections between these neighbors.

#### 3.1.2. Node-Level Measurement

In the network, the transmission of information is affected by the location of nodes. Centrality is a commonly used indicator to measure the location and status of nodes in the network, which helps figure out the core nodes, i.e., nodes that are relatively more connected with other nodes [57]. Betweenness centrality and degree centrality are two indicators commonly used for centrality analysis [58,59].

#### (1) Degree centrality

Degree centrality refers to the number of direct connections a node has to other nodes [60]. Additionally, the normalized degree centrality is defined as the ratio of the number of direct connections of a node and the total number of connections in the network [61]. Generally, the higher the degree centrality a node has, the greater its influence is on the network [62]. The normalized degree centrality *CD*(*i*) is calculated as follows.

$$\mathbf{C}\_{D}(i) = \frac{\sum\_{j=1}^{N} \mathbf{c}\_{i,j}}{N-1} \tag{5}$$

where *ei*,*<sup>j</sup>* is the number of connections between node *i* and node *j*, and *N* is the total number of nodes in the network.

#### (2) Betweenness centrality

Betweenness centrality reflects the extent to which a node is located on the shortest paths between pairs of other nodes [63]. The greater the betweenness centrality of a node, the more it can influence the connections between other nodes [64]. The normalized betweenness centrality *CB*(*i*) can be calculated as follows.

$$\mathcal{C}\_{B}(i) = \sum\_{j$$

where *gjk*(*i*) refers to the number of shortest paths traversing node *i*, and *gjk* is the total amount of the shortest paths between node *j* and node *k*.

#### *3.2. Network Motif Analysis (NMA)*

Network motifs are small connected subgraphs of 3–7 nodes that occur in real networks, the number of which is significantly higher than that in random networks [65,66]. Conversely, subgraphs that appear less frequently than in random networks are defined as anti-motifs [43]. The Z-Score is a statistical significance indicator, which is often used

to determine the network motif and assess the importance of the motif structure in the network [67]. The Z-Score for each subgroup is represented as follows.

$$Z\_i = \frac{N\_{real\_i} - N\_{rand\_i}}{\sigma\_{rand\_i}} \tag{7}$$

where *Nreali* represents the number of occurrences of subgraph *i* in the real network; *Nreali* represents the mean of the number of occurrences of subgraph *i* in the iterated random network; *σrandi* represents the standard deviation of the number of occurrences of subgraph *i* in the random network.

Typically, *Zi* > 0 represents that the number of occurrences of subgraph *i* in the owner–contractor collaborative network is greater than that in the corresponding random network. In this case, subgraph *i* is defined as a motif; otherwise, *i* is an anti-motif [43].
