Average path length (Mao and Zhang, 2017) is the average geodesic distance between all pairs of nodes in the network. A longer average path length indicates greater connectivity within the network. The formula for calculating the average path length L is as follows:

(1)$$L=\frac{1}{\frac{1}{2}n(n-1)}\sum _{i>j}{d}_{ij}$$

where $d_{ij}$ is the distance between node i and node j.

Network density is the ratio of actual connections to all potential connections in a network (Sasaki et al., 2015). A higher network density indicates more frequent interactions between nodes, as well as faster and more efficient transmission of knowledge and information. The closer the ratio is to 1, the higher the cohesiveness of the network and the closer the connections between nodes. The formula for calculating network density D is as follows:

(2)$$D=\frac{2M}{n(n-1)}$$

where M is the actual connections, n is the number of nodes, and $\frac{n(n-1)}{2}$ is the potential connections in the network, with D ranging from [0,1].

Network centralization serves as an indicator of the cohesiveness within the entire network topology and constitutes a quantitative assessment of group influence (Singh et al., 2017; Ruhnau, 2000). A higher degree of centralization signifies that nodes exhibiting greater betweenness centrality exert more pronounced and resilient control over other nodes within the network. The formula for calculating network centralization C_b is as follows:

(3)$$C_b=\frac{{\sum }_{i=1}^n\left(C_{abmax}-C_{abi}\right)}{n^3-4n^2+5n-2}$$

where n is the number of network nodes, $C_{abmax}$ is the maximum betweenness centrality of the network node, $C_{a{b}_i}$ is the betweenness centrality of the other network nodes in the map, and $C_b$ is the overall network centralization.

From the research on network centralization, we can conclude that there are multiple subgroups with core nodes in the network. Using the External–Internal (E-I) index, we can examine whether the formation of subgroups affects communication and collaboration. The E-I Index is the ratio of the density within a coherent subgroup to the overall network density. The closer the result is to 1, the more connections tend to occur outside the subgroup; the closer the result is to –1, the fewer the connections between subgroups and the more concentrated they are within the subgroup. A result of 0 indicates that connections in the network are randomly distributed. The formula is as follows:

(4)$$\mathrm{E}-\mathrm{I}=\frac{EL-IL}{EL+IL}$$

where EL is the number of connections between subgroups, IL is the number of connections within subgroups, and the range of values is [–1,1].

Node centrality reflects the importance of a node within the entire network. This study primarily illustrates it using the degree centrality indicator. Degree centrality refers to the number of nodes directly connected to a given node. The higher the degree centrality, the more connections that node has. Such nodes are usually located at the center of the network and have a significant influence on other nodes. Core nodes in the network are identified based on the relative size of their degree centrality (Liu et al., 2019; Liu et al., 2023a).

Based on the cooperative patents of China’s rail transit equipment industry from 1986 to 2018, this study adopts multi-time-slice static comparison combined with social network analysis. The combination of these methods improves both the refinement of the time dimension and the depth of structural relationships. It not only retains the evolution tracking ability of dynamic analysis but also integrates the micro-level in-depth description advantage of static analysis, making it a panoramic tool for social network research. At the organizational level, the co-patent networks over the years are constructed, the core indicators of the networks in each year are analyzed, and the temporal evolution trend of the network structure is identified through horizontal comparison across the years. At the regional level, based on national policies, industrial cycles and major technological milestones, the research period is divided into three stages: 1986–2001, 2002–2008, and 2009–2018. The co-patent networks of each stage are constructed, and the core indicators of each stage’s network are analyzed. Through horizontal comparisons between stages, the spatial evolution trend of the network structure is identified.

Network nodes of the I-U-R co-patent networks in the rail transit equipment industry include enterprises, universities, and research institutes. Collaborative patents link nodes with each other, and the degree of association between nodes is directly related to the frequency of collaboration. For example, if the number of collaborative patents between enterprise A and research institute B is n, then the degree of association between the two is n. The collected data are sorted and imported into an Excel spreadsheet. If A and B have a collaborative patent, it is counted as 1. If enterprise A, university B, and research institute C jointly apply for a patent, the collaboration is split into three pairs—namely, enterprise A and university B, enterprise A and research institute C, and university B and research institute C—each counted as 1. Excel is then used to measure the connections between all patent applicants, forming an n$\mathrm{\times }$n symmetric matrix $A_{ij}$, as shown in Eqn. 5.

(5)

After converting the I-U-R collaborative patent information of the rail transit equipment industry from 1986 to 2018 into the above symmetric matrix, the co-patent network matrices are obtained. The sizes of the matrices are as follows: 9 $\times$ 9, 10 $\times$ 10, 26 $\times$ 26, 14 $\times$ 14, 11 $\times$ 11, 15 $\times$ 15, 33 $\times$ 33, 21 $\times$ 21, 2 $\times$ 2, 9 $\times$ 9, 7 $\times$ 7, 14 $\times$ 14, 4 $\times$ 4, 2 $\times$ 2, 4 $\times$ 4, 6 $\times$ 6, 17 $\times$ 17, 14 $\times$ 14, 15 $\times$ 15, 33 $\times$ 33, 20 $\times$ 20, 12 $\times$ 12, 23 $\times$ 23, 68 $\times$ 68, 78 $\times$ 78, 102 $\times$ 102, 111 $\times$ 111, 115 $\times$ 115, 119 $\times$ 119, 121 $\times$ 121, 140 $\times$ 140, 185 $\times$ 185, 265 $\times$ 265, respectively. The I-U-R co-patent networks in the rail transit equipment industry are typical social networks. The relationships between nodes are cumulative; that is, once patent applicants i and j establish a relationship at a certain point in time, the relationship persists and becomes embedded in their respective social networks. Finally, the processed data is imported into the Gephi software (Version 0.10.1, Gephi Consortium, Ile-de-France, Paris, France) to construct the I-U-R co-patent networks of the rail transit equipment industry from 1986 to 2018, as shown in Fig. 3. Although the scale of the co-patent networks has fluctuated over the years, it has generally shown an expanding trend. From 1986 to 2004, the co-patent networks consisted of simple points and lines. Since 2005, the basic topology began to emerge, and in recent years, the network developed into a relatively larger structure centered around the China Academy of Railway Sciences and China Railway Corporation. The number of network nodes increased significantly—from 9 nodes in 1986 to 265 nodes in 2018—with some fluctuations in certain years, showing that many companies, universities, and research institutes have participated in I-U-R co-patent networks.

Fig. 3.

The I-U-R co-patent networks from 1986 to 2018.

A high-density network can speed up the flow of knowledge, information, and resources within the network, improving mutual learning and innovation activities among the various applicants. Table 1 presents the density of the I-U-R co-patent networks in the rail transit equipment industry from 1986 to 2018. The network density over this period exhibits a general downward trend, with fluctuations in certain years. By observing the scale and density values of the co-patent networks from 1986 to 2018, we can see that while the network scale continues to expand, the density values of the co-patent networks gradually decrease, indicating that the overall network has become more diffuse. Each patent applicant, influenced by resource limitations and other factors, can only establish and maintain a certain number of collaborative relationships. As the network scale expands rapidly, and more patent applicants enter the network, the resources available to support individual partnerships become more constrained. When the cost of forming a new collaboration exceeds the incremental income, applicants tend to maintain existing partnerships rather than form new ones. As a result, the co-patent networks exhibit low density, indicating that network functionality could be improved and that there remains considerable room for further development within the co-patent networks. Entities within the network can further develop their respective strengths and establish more extensive and deeper patent collaboration relationships with other entities. Additionally, in 1994 and 1997, the number of collaborative patents was very small, and all network nodes were linked, resulting in an exceptional case where the network density reached 1.

Table 1 shows that the network centralization of I-U-R co-patent networks in the rail transit equipment industry has generally been rising. In 2005, clear central nodes began to appear in the network. By 2018, network centralization reached 12.08, indicating that resources within the network had started to concentrate around specific core nodes. Although the density of the co-patent networks gradually decreases as the network expands and becomes more diffuse, centralization continues to increase, indicating that some network nodes are emerging as core nodes, and the number of such core nodes shows an increasing trend. This pattern indicates that I-U-R patent collaboration in the rail transit equipment industry exhibits a small-scale aggregation effect, with group formation centered around individuals or entities with strong innovative capabilities as the core. These groups, in turn, form a larger group through strong alliances.

Taking into account both network density and network concentration, we can see that a decrease in network density does not necessarily indicate a weakening of cooperation. Network density has an inverted U-shaped relationship with cooperation efficiency (Gilsing et al., 2008). When network density is too low, it can create information islands, hindering cooperation; when network density is too high, it can lead to redundant connections, thereby reducing cooperation efficiency. When network density is moderately lowered, cooperation efficiency is highest. The decline in I-U-R co-patent network density in China’s rail transit equipment industry reflects the optimization of the network structure. For instance, key innovation entities play an increasingly significant role, and a small-world network has already begun to form.

Table 1 also shows that the E-I index is less than 0 from 1986 to 2018, except in 1994, 1998, 1999, and 2000. This is because there were fewer collaborative patents in those four years, making the network distribution close to random and the presence of subgroups less apparent. The E-I index of the I-U-R co-patent networks in the rail transit equipment industry is close to –1, indicating fewer connections between subgroups in the network, meaning that resource exchange and sharing occur primarily within small groups. Members outside a given group rarely have the opportunity to exchange and collaborate with members of the group. The E-I index shows an upward trend in 2016–2018, indicating that connections between different groups are improving. Cooperation within subgroups in the I-U-R co-patent networks of China’s rail transit equipment industry is not necessarily detrimental to the dissemination of innovation. In the context of core technology development, intellectual property protection, and a stable market environment, internal cooperation within subgroups effectively promotes technological iteration through resource integration and collaborative innovation. However, to break through technical barriers, adapt to international markets, or introduce cutting-edge technologies, collaboration across subgroups becomes a necessary supplement. The policies and industry structure promote the efficiency and scope of industry innovation dissemination by encouraging a mixed model: internal cooperation within subgroups as the primary approach, and external cooperation among subgroups as the secondary approach.

In contrast to the above analysis of the structural characteristics of the co-patent networks, the I-U-R co-patent networks in the rail transit equipment industry are divided into the following three stages. This study selects 2001 and 2008 as cutoff years because these years were each associated with national policies, industrial cycles, and major technological milestones. In terms of national policies, in 2001, the “Implementation Plan for the Domestication of Urban Rail Transit Equipment” directly promoted the development of domestic equipment manufacturing and ended the high dependence on imported equipment. Meanwhile, the “Tenth Five-Year Plan” (2001–2005) proposed accelerating railway technological transformation, and the construction of high-speed rail in China officially began. The “Mid-to-Long Term Railway Network Plan” (adjustment in 2008) explicitly identified high-speed rail as a strategic emerging industry in China. Also, in response to the global financial crisis in 2008, China stimulated the economy through large-scale infrastructure investment, with high-speed rail becoming a key area of focus. In terms of technological milestones, around 2001, China gradually gained control over core technologies such as subway vehicles, signal systems, and traction power supply through technology introduction and cooperative production. At the same time, domestic production policies led to a significant drop in equipment prices. In 2008, China’s first independently designed high-speed rail entered service, marking the beginning of the high-speed rail era in China. This high-speed rail adopted technologies with fully independent intellectual property rights, forming the technical standard system of China’s high-speed rail. In terms of industrial cycles, 2001 marked the transition of China’s rail transit equipment industry from “reliance on imports” to “self-control and autonomy”. In 2008, it advanced from “self-control and autonomy” to “global leadership”.

The germination stage (1986–2001). The industry predominantly relies on technology importation, with core components exhibiting a high level of dependence on overseas supplies. The absence of targeted industrial policies at this stage resulted in a limited number of cooperative patents. In 2001, the launch of “Implementation Plan for the Domestication of Urban Rail Transit Equipment” provided a foundation for the subsequent rapid development of the industry. In the early days of the I-U-R co-patent networks, only a few enterprises collaborated with universities or research institutes, presenting one-to-one and one-to-many collaboration models. The overall network was disconnected and loosely distributed. At this time, enterprises, universities, and research institutes collaborated only to solve current technological innovation problems and obtain heterogeneous resources, without engaging in repeated collaborations. The joint stability among enterprises, universities, and research institutes was relatively low. During this stage, the number of network nodes and connections in the I-U-R co-patent networks was limited, and collaboration remained underdeveloped.

The transitional stage (2002–2008). With the advancement of localization policies (“Mid-to-Long Term Railway Network Plan” in 2004 and 2008; “Tenth Five-Year Plan” from 2001 to 2005), the I-U-R collaboration has shifted to technology digestion, absorption, and secondary innovation, and cooperative patents have focused on the localized transformation of core technologies. The industry has begun to shift from “reliance on imports” to “self-control and autonomy”, and the import dependence of core technologies was significantly reduced. As collaboration deepened among the leading patent applicants in the co-patent networks, the network gradually expanded, and collaboration among the patent applicants became more extensive. The collaboration between enterprises, universities, and research institutes became more in-depth, and all participants’ recognition of and reliance on the co-patent networks increased. At this time, the collaboration model remained largely unchanged. The overall network remained disconnected, though parts of it became connected, presenting a core-edge network structure. Enterprises, universities, and research institutes used innovation networks to obtain heterogeneous resources, reduce information search costs, and lower transaction costs by strengthening collaboration, resulting in greater collaborative stability. During this stage, the number of network nodes and connections in the I-U-R co-patent networks grew rapidly, node strength began to increase, core nodes started to appear, and the overall level of collaboration improved.

The developmental stage (2009–2018). Under the advantages of multiple policies (“Decision of the State Council on Accelerating the Cultivation and Development of Strategic Emerging Industries” in 2010; “Twelfth Five-Year Development Plan for High-end Equipment Manufacturing Industry” from 2011 to 2015; “Made in China 2025” in 2015; “Railway 13th Five-Year Development Plan” from 2016 to 2020), the industry has entered the stage of independent innovation and global output, I-U-R collaboration focuses on cutting-edge technologies. Cooperative patents span the whole industrial chain, and the technological level has reached the globally leading standard, thereby entirely eliminating reliance on imports. With the further development of the co-patent networks, the network exhibited an agglomeration effect. The collaborative relationships among enterprises, universities, and research institutes often took the form of strong, repeated partnerships, which significantly promoted the transfer of tacit knowledge. At the same time, companies, universities, and research institutes fully recognized the positive functions of co-patent networks. They were willing to provide them with heterogeneous resources and knowledge, forming economies of scale and scope. In the co-patent networks, enterprises, universities, and research institutes established strong collaborative relationships characterized by a many-to-many collaboration mode. The overall connectivity of the network was high, and the core node in the network had a higher degree, playing a leading role. The cost of information search and collaborative transactions among enterprises, universities, and research institutes was low, and the collaborative relationships were highly stable.

The geographical information of the patent applicants is extracted, and the applicants are classified by city and province. Patent applicants located in the same city are recognized as intra-city collaborations, while those in the same province are identified as intra-provincial collaborations. In Table 2, we can see that the number of participating provincial-level administrative regions and cities in the I-U-R co-patent networks of the Chinese rail transit equipment industry has increased year by year across the three stages, reaching 28 provinces during the developmental stage. Compared with the number of collaborative provinces, the number of collaborative cities better reflects the geographical expansion of the I-U-R co-patent networks, increasing by as much as 86%. It is also evident that the average path length of the co-patent networks was 1.513 from 1986 to 2001, 2.746 from 2002 to 2008, and 3.632 from 2009 to 2018. This indicates that the network scale is expanding rapidly, the number of patent applicants is growing quickly, and the transmission efficiency of the I-U-R co-patent networks is decreasing. The network density is declining, and the average path length is increasing. This shows that although the spatial coverage of the co-patent networks is expanding, the degree of closeness among participants is declining. It further indicates that the I-U-R co-patent networks of the Chinese rail transit equipment industry are still in the developmental stage, with significant room for improvement.

To more intuitively observe the geographical changes in I-U-R patent collaboration in the rail transit equipment industry across the three stages, the data are visualized using Power Map in Excel (Version Office 2021, Microsoft Corporation, Redmond, WA, USA). The spatial evolution of the I-U-R co-patent networks appears in Fig. 4. In the germination stage, 20 provincial-level administrative regions and 51 cities participated in the I-U-R co-patent networks, forming a network structure centered on Beijing and Shanghai. With strong economic foundations and concentrated educational resources, Beijing and Shanghai have become the vanguards of rail transit development. They serve as bases for knowledge production and diffusion, promoting co-patent activity in surrounding cities. In addition, the most critical areas in the co-patent networks are the provincial capitals of the northern and eastern regions and their small-scale surrounding areas. At this stage, the economic belts have not yet formed a core city to lead development, but it is evident that the Bohai Economic Circle and the Yangtze River Economic Belt have taken shape.

Fig. 4.

Spatial evolution of the I-U-R patent collaboration.

In the transitional stage, Beijing remains at the core of the I-U-R co-patent networks. From a national perspective, core nodes have begun to increase, forming a multi-core structure centered on Beijing, Tianjin, Shanghai, Hebei, Henan, Sichuan, and Hunan. In particular, the southwestern region centered on Chengdu, Sichuan Province, has gradually evolved from the point distribution of the previous stage into a more connected structure, with its radiation range further expanded.

During the developmental stage, the I-U-R co-patent networks included 28 provincial-level administrative regions and 127 cities, forming a clear multi-core structure. While the Beijing economic circle remained at the core position, the Yangtze River Delta and Central South regions experienced faster development than other regions. Fig. 4 demonstrates that the radiation area of the Yangtze River Delta, centered on Shanghai, has expanded into most of Anhui and Jiangsu provinces. Similarly, the scope of patent collaboration in the central-south region, centered on Hunan, expanded significantly. Compared with the previous stage, the core areas of I-U-R patent collaboration in the rail transit equipment industry grew dramatically during this stage, and inter-regional connections became closer, forming a more integrated network.

By 2018, the I-U-R co-patent networks had formed a structure centered on Beijing, Shanghai, Changsha, and Chengdu, with the provinces more closely linked. Shanghai and Zhejiang became highly integrated, showing strong spatial agglomeration within the Yangtze River Delta. Spatial agglomeration effects also emerged in Wuhan, Changsha, Chengdu, Chongqing, and other cities. However, Guangzhou and Shenzhen in the Pearl River Delta had fewer links with other regions, possibly related to the relatively smaller number of high-level universities and research institutes in Guangdong Province. In southwestern provinces such as Yunnan, Guizhou, and Guangxi, geographical constraints, lower economic development, and poor transportation have contributed to lower spatial agglomeration efficiency in the innovation network. Overall, from a spatial evolution perspective, the I-U-R co-patent networks in the rail transit equipment industry have developed significantly. A basic structure has formed, including the Bohai Economic Circle with Beijing at its core, the Yangtze Delta Economic Belt with Shanghai at its core, and the Central South Economic Circle centered around Changsha (Hunan) and Chengdu (Sichuan). In southwestern regions such as Yunnan, Guizhou, and Guangxi, both intra- and cross-regional collaboration require further strengthening. I-U-R patent collaboration in Xinjiang, Tibet, Inner Mongolia, and other provinces remains in its infancy and requires supportive policies.

From the above analysis, it is clear that the spatial evolution of the co-patent networks in China’s rail transit equipment industry exhibits a degree of imbalance. On the one hand, the formation of a multi-core system is fundamentally a process of element reconfiguration. The dual-core driving model has spread across multiple regions, reflecting the flow of innovation from administrative centers to industrial clusters. However, the weakening of coordination in the Pearl River Delta region indicates that simple economic radiation does not automatically translate into collaborative innovation. A tripartite linkage mechanism that integrates “industry, research, and policy” is therefore needed. On the other hand, regions such as Yunnan, Guizhou, and Guangxi have insufficient agglomeration efficiency. This is due not only to physical isolation caused by geographic barriers but also to the absence of innovation communities like the “system of Chinese Academy of Sciences” in the Yangtze River Delta or the “university-enterprise” alliances in the Pearl River Delta. At the same time, the expansion of the network reveals a paradox. The sharp increase in the number of cooperative cities, coupled with the rising average path length, suggests that the industry’s expansion exhibits “increased quantity but decreased quality”. Most of the new nodes are peripheral cities, and their connections to core cities require passing through intermediate nodes, extending the information transmission path. The decline in network density further confirms the sparsity of connections between nodes, which is directly related to resource dispersion and administrative barriers.

To ensure the accuracy of applicant classification, this study delineates applicant categories based on the following criteria. (1) Enterprises: applicants whose names contain the logo of for-profit organizations, such as companies, groups and limited liability companies, or those verified as industrial and commercial registered enterprises through the National Enterprise Credit Information Publicity System. (2) Universities: applicants whose names include the logo of a higher education institution, such as a university or college, and are officially listed in the national registry of ordinary higher education institutions published by the Ministry of Education. (3) Research institutes: applicants whose names contain the logo of research institutes or other research-oriented institutions, or non-profit R&D institutions affiliated with the national research system. For applicants with ambiguous names or those engaging in cross-border operations (e.g., a technology transfer center in a university), classification is determined by considering the attributes of their supervising bodies and actual business scope. If the core function is promoting technology industrialization, such applicants are classified as enterprises. Disputed applicant classifications undergo a rigorous review and confirmation process by two domain experts to ensure the reliability of the analysis.

In this paper, the degree of nodes and the number of connections are used to examine the status changes of different types of patent applicants during the three stages. The degree of a node refers to the total number of other nodes connected to it, reflecting the node’s importance within the network. A higher degree value indicates a more critical position, a broader source of knowledge, and measures collaborative breadth. The number of connections indicates the frequency of cooperation between one node and other nodes. A higher number of connections suggests more frequent and longer-term collaboration, which serves to measure collaborative depth. To avoid the influence of degree on collaborative depth, the ratio of the number of connections to collaborative degree is used. A breadth-depth matrix is established to classify patent applicants in the network into four types. (1) High-breadth and high-depth (HH) nodes have many collaborative partners and high collaborative strength; these are the core nodes in the network. (2) High-breadth and low-depth (HL) nodes interact widely with other nodes but lack depth, making it difficult to sustain collaboration. These are important but not central nodes. (3) Low-breadth and high-depth (LH) nodes have fewer partners but stronger collaboration intensity and are common nodes in the network. (4) Low-breadth and low-depth (LL) nodes have fewer partners and weak collaboration strength, placing them at the network’s periphery. The criteria for defining the breadth and strength of collaboration are determined by the average values of all network nodes.

The breadth-depth matrix for each stage is shown in Fig. 5. In the germination stage, there were 23 enterprises, 17 research institutes, and three universities classified as HH type, accounting for 32.1% of all participants. These entities occupy core positions in the collaborative network, with broad and frequent collaboration. There were also 43 enterprises, 17 research institutes, and two universities classified as LL type, comprising 46% of participants and playing a minimal role in information exchange. The HH and LL types accounted for a large proportion of the network at this stage.

Fig. 5.

Breadth-depth matrix in each stage.

In the transitional stage, 18 enterprises, one research institute, and one university were classified as HH type, accounting for 20.8% of participants—a decline from the previous stage. Meanwhile, 32 enterprises, nine research institutes, and seven universities belonged to the LL type, comprising 50% of participants, a higher proportion than in the previous stage. The number of research institutes and universities declined, and their roles in the co-patent networks have diminished. Although the number of participants declined slightly, the number of collaborative patents increased slightly. Core nodes began to emerge and concentrate resources, raising the average values for high-breadth and high-depth and marginalizing the edge nodes.

In the developmental stage, there were 67 enterprises, 19 research institutes, and five universities classified as HH type; 87 enterprises, three research institutes, and 21 universities as HL type; 73 enterprises, eight research institutes, and seven universities as LH type; and the remaining 59% of participants were LL type. The number of participants increased rapidly. Enterprises in the collaborative network maintained a strong core position and played a more prominent role. Most universities saw significant growth in collaborative breadth, but collaborative depth remained largely unchanged. This reflects the state’s emphasis on rail transit equipment manufacturing and the importance of enterprises in I-U-R co-patent networks, as they often propose technological requirements and provide funding. Overall, synergy among participants in the I-U-R co-patent networks continues to strengthen.

Based on the above analysis, and from the perspective of technological innovation ecology, we can observe that in the germination stage, a core-periphery structure begins to take shape. HH-type nodes constructed the basic framework for technological innovation through high-frequency collaboration, with patent collaboration intensity more than seven times greater than that of LL-type nodes. This structure reflects the need for resource concentration to achieve technological breakthroughs during the early exploration period. The presence of many LL-type nodes indicates that the industry remains at the stage of technological accumulation, where participants engage mainly in exploratory cooperation. In the transitional stage, resources were reorganized, and the network was restructured. Although the number of HH-type nodes decreased, the number of cooperative patents rose, showing that core nodes improved cooperation efficiency through strategic contraction and resource concentration. The increased proportion of LL-type nodes indicates a reduction in industry entry barriers, allowing many small and medium-sized enterprises to participate in innovation efforts via patent alliances. By the developmental stage, the enterprise-led ecosystem was firmly established. As many as 67 enterprises belonged to the HH type, forming an “industry–university–research institute” triangular structure. At this point, the network displayed small-world characteristics, with core nodes creating technological barriers by controlling key resources.