*4.2. Network-Level Analysis*

4.2.1. Density

As an important indicator of the SNA method, network density reflects the connectivity of the network [51,52]. Figure 4 displays the evolution of the density of the owner–contractor collaborative relationship network over time. It can be seen that the density values for 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, and 2021 are 0.013, 0.013, 0.010, 0.011, 0.008, 0.008, 0.008, 0.008, and 0.007, respectively, indicating that the density was low and decreased during the study period. This is different from some research conclusions on the collaborative network [8,34,35]. For example, Tang et al. [34] studied the collaborative relationships between contractors and subcontractors, and the results showed that during the study period, the contractor–subcontractor collaborative network became denser and more connected between nodes. This may be because it is more flexible for contractors and subcontractors to establish collaborative relationships, and it is easy to collaborate multiple times. However, the owners of different projects are often different, and the contractors are usually selected by means of bidding, which makes establishing a collaborative relationship between the owners and the contractors more restricted. Therefore, the value of density of the owner–contractor collaborative network did not increase over time. A low network density indicates that some owners and contractors have little communication, which is not conducive to exchanging information and sharing knowledge in the collaborative network [58]. The gradual decrease in network density reflects the worsening of network connectivity. This is because some groups have appeared in the evolution of the network. The organizations within the group are closely connected, but they are less connected with the organizations outside the group, causing an island effect, which results in low connectivity of the network. Most of these groups with island characteristics are composed of medium-sized contractors that won few NQEA. Organizations in the island group should fully understand their dilemmas and strengthen cooperation with other organizations to improve the overall connectivity of the collaborative network.

**Figure 4.** The density of the collaborative networks in 2013–2021.

#### 4.2.2. Average Degree

The average degree is an indicator, which describes the compactness of the network and is the average number of connections (collaborative relationships) of a node (owner or contractor) in the collaborative network [68]. The higher the average degree, the more compact the network [69]. Figure 5 depicts the number of owners, contractors, and connections in the collaborative network from 2013 to 2020. During the study period, the number of nodes (contractors and owners) and connections in the network had increased, and the number of connections had increased more than that of nodes. This may be because the connection between nodes involves not only the collaboration between the newly joined contractors and owners but also the collaboration between the existing contractors in the collaborative network and the newly joined owners.

**Figure 5.** The number of owners, contractors, and connections in 2013–2021.

Figure 6 shows the change in average degree during the study period. It can be seen that the average degree of the collaborative network had increased over time, indicating that the collaborative network was becoming more and more compact. In 2021, the average degree of the owner–contractor collaborative network was 4.802, indicating that each node collaborated with at least four nodes, on average. Liu et al. [40]'s study on the collaborative relationships between contractors showed that the average degree of contractors' collaborative network in 2011 was 11.20, which is higher than the average degree of the owner–contractor collaborative network obtained in this study. Generally, a contractor can undertake several projects simultaneously or participate in a project together with other contractors. With the increase in the number of projects, the number of connections between different contractors also increased. Therefore, the average degree of the collaborative network of contractors is relatively high. However, for the collaborative network of owners and contractors, although the contractors of different projects may be the same, the owners are often different. This results in a relatively small number of relationships embedded in the collaborative network between owners and contractors, with a low average degree of the network.

**Figure 6.** The average degree of the collaborative networks in 2013–2021.

#### 4.2.3. Average Distance

In the organization network, the average distance refers to the average of the shortest path length between two organizations, which reflects the difficulty in communication between the two organizations and the possibility of information exchange [70]. Figure 7 depicts the variation of the average distance in the collaborative relationship network, as shown by the black line. In 2021, the average distance of the network was 3.719, which meant that it took about four steps from one node to another node. We can see from Figure 7 that the average distance of the collaborative network between owners and contractors in 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, and 2021 was 3.298, 3.269, 3.864, 3.230, 3.615, 3.557, 3.580, 3.389, 3.719, respectively. The value of the average distance in 2021 is greater than that in 2013, which means that compared to 2013, more intermediate nodes are needed to establish connections between two companies in the collaborative network in 2021. This is because some newly joined companies in the collaborative network happened to be located on the shortest communication path between the other two companies, resulting in the need for the two companies to communicate through more intermediaries.

#### 4.2.4. Clustering Coefficient

The clustering coefficient can be used to reflect the degree to which nodes in the network are clustered. In general, nodes clustered in a group can communicate and collaborate more effectively [71]. Figure 8 depicts the change in the clustering coefficient of the collaborative relationship network during the study period. The clustering coefficient gradually increased from 2013 to 2021. In 2021, the clustering coefficient value was 0.935, which meant that the owner–contractor network was highly clustered. This is because most of the NQEA projects are large in scale, and the owners usually contract out the construction tasks to several contractors to complete together, which makes them form a closely collaborative group, and many highly aggregated groups improve the aggregation degree of the whole network.

**Figure 7.** Evolution of the average distance of the collaborative networks in 2013–2021.

**Figure 8.** Change of the clustering coefficient of the collaborative networks in 2013–2021.

We further analyzed whether there was a small-world network in the owner–contractor collaborative network. Watts and Strogatz [72] and Neal [73] pointed out that if a network formed based on a specific rule had a larger clustering coefficient and a lower average distance than those of a random network with the same number of connected nodes and density, this indicated that the network had small-world characteristics. We randomly generate 100 networks with the same nodes and density as the owner–contractor collaborative network and calculate their average distances and clustering coefficients. Figures 7 and 8 show the mean distance and clustering coefficients of these 100 random networks, respectively, as shown by the red line. It can be seen that compared to random networks, the owner–contractor collaborative networks have lower average distances and higher clustering coefficients, that is, the collaborative networks have the characteristics of a small-world network. In a small-world network, the connection between two organizations requires only a few intermediary organizations, facilitating technology dissemination, capital accumulation, and personnel collaboration between the owners and contractors.

#### *4.3. Node-Level Analysis*

#### 4.3.1. Degree Centrality

Degree centrality is the number of adjacent connections a node has in the network, reflecting the direct connection between nodes and other nodes [74]. In a collaborative network, the node with a high degree centrality has robust interactivity, significant influence, high participation degree, and it is at the core of the network [75].

Table 2 shows the top 15 companies ranked by the degree centrality of the collaborative network in nine snapshots. It can be seen from Table 2 that the degree centrality of C1442, C1446, and C1443 has consistently been ranked in the top three during the study period. This indicates that they are at the network's core and can be called core nodes. Compared with the other contractors, they have more experience in collaborating with owners and contractors. These companies exhibit the preference attachment effect, i.e., contractors who have won the NQEAs are more likely to acquire new projects and form partnerships with new owners.


**Table 2.** Top 15 companies ranked by degree centrality (DC).

C1446, C1442, and C1443 refer to China Construction Third Engineering Bureau Corporation Limited, China Construction Eighth Engineering Bureau Corporation Limited, and China Construction Second Engineering Bureau Corporation Limited, respectively, all of which are the subsidiaries of China State Construction Engineering Corporation Ltd. (CSCE). CSCE is one of the largest construction contractors in China, ranking seventh in ENR's 2021 Top 250 International Contractors list. C1446, C1442, and C1443 are the three subsidiaries with the most potent comprehensive competitiveness of CSCE. In 2021, the newly signed contract values of C1446, C1442, and C1443 were around USD 88 billion, USD 94 billion, and USD 59 billion, respectively, and the operating income was around USD 44 billion, USD 53 billion, and USD 30 billion, respectively. The three companies have

branches in many cities in China, which provide conditions for extensive participation in project bidding and establishing collaborative relationships with owners. They all have advanced technology and excellent R&D talents and have won many high-quality engineering awards. From 2013 to 2021, C1446, C1442, and C1443 have won 106, 116, and 112 NQEAs, respectively.

#### 4.3.2. Betweenness Centrality

Betweenness centrality is an indicator, which measures the degree to which a node acts as an intermediary, that is, the degree to which a node influences the flow of information between other nodes [76]. The higher the betweenness centrality of a node, the greater its influence on the information flow between other nodes [77].

Table 3 lists the top 15 organizations in terms of betweenness centrality at each snapshot point. It can be seen from Table 3 that C1442, C1443, and C1446 always had a high value of betweenness centrality over time. This means that these companies act as bridges in the owner–contractor collaborative network. It is worth noting that C1153 (Suzhou Golden Mantis Building Decoration Co., Ltd.), as a private company, also had a high betweenness centrality in the owner–contractor collaborative network. In 2015, C1153 had the most significant betweenness centrality. C1153 (Suzhou Golden Mantis Building Decoration Co., Ltd.) is a large listed company with building decoration and renovation as its primary business. It has been ranked as one of the top 100 building decoration companies in China for 19 consecutive years, and its business has spread to various cities in China and many overseas markets. From 2013 to 2021, the number of NQEA won by C1153 has increased yearly, totaling 41 awards. This is due to its continuous development in building decoration with a large team of interior designers and excellent decoration and renovation construction teams. These advantages increase C1153 s bidding competitiveness and make it easy to be favored by owners.


**Table 3.** Top 15 companies ranked by betweenness centrality (BC).

We further analyze the attributes of the top 15 contractors ranked by degree centrality and betweenness centrality, as shown in Table 4. As can be seen from Table 4, among the top 15 contractors, there are more state-owned enterprises (SOEs) than private enterprises (PEs). This indicates that SOEs play a dominant and critical role in the owner–contractor collaborative network. Han et al. [78] also found that SOEs have high centrality and are the primary carrier of technological innovation in China's construction industry in the study on the collaborative innovation network of China's construction industry. State-owned construction enterprises often have substantial financial resources, government support, and extensive experience in contracting large-scale engineering projects. These advantages

make it easier to develop collaborative relationships with owners and often collaborate with other subcontractors as a general contractor.


**Table 4.** Number of SOEs and PEs in the top 15 contractors in terms of degree centrality and betweenness centrality in 2013–2021.
