*3.3. Analytical Procedures*

We collected a longitudinal data set of the projects that won the National Quality Engineering Award (NQEA) in China and used the SNA and NMA methods to study the structural characteristics and evolutionary laws of owner–contractor collaborative relationship networks. Figure 1 depicts the analytical procedures, which consist of four steps: (i) Obtain the information on the owners and contractors of NQEA award-winning projects, (ii) Construct the owner–contractor relationship matrix based on the processed data and develop the owner–contractor snapshot network, (iii) Analyze the macro-structural characteristics of owner–contractor collaborative networks by using SNA, (iv) Discover the local collaborative patterns by using NMA.

#### **Figure 1.** Analytical procedures.

#### *3.4. Data Collection and Processing*

China's NQEA is an award established to encourage construction companies to improve project quality. It was established in 1981 as China's construction industry's earliest and highest level national quality award. Generally, NQEA is awarded annually. The applicants include owners, contractors, designers, and some other enterprises participating in projects. The award projects must meet requirements such as excellent design, high construction quality, effective management, advanced technology, energy saving, and environmental protection. Projects in seven fields, including construction engineering, industrial engineering, traffic engineering, water conservancy engineering, and municipal

engineering, are involved in NQEA. Among them, construction engineering projects account for 70% of the total number of award projects. The information on award projects, including project name, project type, year of winning the award, and project participants, is available on the official website (http://www.cacem.com.cn/ (accessed on 15 July 2022)) of the China Association of Construction Enterprise Management.

The NQEA project information provides a valuable data set for exploring the owner– contractor collaborative network. In this study, the data of 1371 construction projects that won NQEA from 2013 to 2021 were used to analyze the characteristics and evolution of the owner–contractor collaborative network in China's construction industry. These projects involved 1283 owners and 1560 contractors. The number of owners is smaller than that of projects because some NQEA projects have the same owners. In total, 1560 contractors are all the contractors included in the NQEA projects data set. Since some projects involve multiple contractors, the number of contractors is greater than that of projects. The descriptive statistics of the projects are shown in Table 1.


**Table 1.** Basic information on awarded projects.

We processed the project information collected in accordance with the following principles. First, for some large contractors with multiple tiers of subsidiaries, only the first-level subsidiaries were regarded as network nodes in this study. For example, China Construction Second Engineering Bureau Ltd., China Construction Third Engineering Bureau Ltd., China Construction Seventh Engineering Bureau Ltd., and China Construction Eighth Engineering Bureau Ltd. are all first-tier subsidiaries of China State Construction Engineering Corporation, one of China's largest construction companies. Therefore, they were displayed as different nodes in the collaborative relationship network. Second, we regarded the collaborative network between owners and contractors as an undirected and unweighted network. In other words, we only considered whether there was a collaborative relationship between an owner and a contractor, regardless of how many times they had collaborated. Third, we coded the enterprises in the network with an "O" for owners and a "C" for contractors and used different numbers to represent different enterprises. For example, C1446 represented China Construction Third Engineering Bureau Co., Ltd., and O68 represented Beijing Wangjing Souhou Real Estate Co., Ltd.

To understand the evolution of the network, a dynamic analysis of the network is required. For analyzing longitudinal networks, it is crucial to determine the optimal window size, which refers to the time interval between two snapshots. The NQEA is awarded annually, so we set each year as a time window to generate nine network snapshots over the study period from 2013 to 2021. Each network snapshot contains the awarded projects and the owners and contractors involved in that year. We constructed a two-mode network at each snapshot point. The network nodes were divided into two different sets in a two-mode network: the project set and the organization set. Figure 2a shows a schematic diagram of a two-mode network, where the square nodes represent the awarded projects, and the round nodes represent the awarded organizations. If a circular node is interconnected with a square node, the award-winning organization is involved in the construction project. Since project implementation depends on the organizations' collaboration, there are interconnections between the organizations involved in the same project. In addition, an organization may be involved in multiple projects and form a complex network of relationships with other organizations through different projects. For example, the black node C3 in Figure 2a is involved in both projects P1 and P2. Since this study aims to explore the collaborative relationship network between organizations, we converted the two-mode network consisting of the project set and organization set into the one-mode network containing only the organization set (see Figure 2b). Then, we established nine owner–contractor collaborative relationship matrices with the row and column 290 × 290, 303 × 303, 391 × 391, 372 × 372, 462 × 462, 556 × 556, 515 × 515, 590 × 590, 653 × 653, respectively. If there was a collaborative relationship between company *i* and company *j* at the snapshot time point, *rij* = 1; otherwise *rij* = 0.

**Figure 2.** Schematic diagram of project organization network: (**a**) two-mode network; (**b**) onemode network.

## **4. Results and Discussion**

#### *4.1. Whole Network Topology*

According to the established owner–contractor adjacency matrix, the topological diagrams of the collaborative relationship in nine snapshots are produced by Gephi software to show the evolution of the collaborative network (as shown in Figure 3). In Figure 3, the color of the nodes represents the type of companies, with green nodes representing the owners and pink nodes representing the contractors. The size of the node reflects the number of connections to this node. Specifically, the larger the node, the higher the number of connections to this nod, and vice versa. We can see from Figure 3 that the network structure at different snapshots is quite different. The number of nodes and connections in the collaborative network increases over time, which results in a larger network size. Furthermore, several significant components with many connected nodes can be found in each network.

**Figure 3.** *Cont*.

**Figure 3.** The topology diagram of different network snapshots.
