Exponential Random Graph Model Perspective: Formation and Evolution of a Collaborative Innovation Network in China’s New Energy Vehicle Industry

Abstract

In light of the crucial role of collaborative R&D in advancing technology within the new energy vehicle industry, this study seeks to explore ways to overcome the barriers to technological innovation by establishing an effective collaborative innovation network. Utilizing joint patent-authorized data from China’s new energy vehicles between 2005 and 2019, the collaborative innovation network was developed, and the Exponential Random Graph Model (ERGM) was employed to analyze its formation and evolution mechanisms. The results indicate that the network has undergone significant expansion, closely linked to strong national policy support and the active involvement of innovation participants. The network exhibits effects of expansion, transfer, and closure. External attribute analysis revealed the Matthew effect and geographical compatibility effect and found that organizational compatibility tends to foster complementary cooperation. The findings offer insights into optimizing collaborative innovation networks in the NEVs industry and suggest strategies for policymakers and industry players to promote collaborative innovation.

1. Introduction

Amid escalating global energy and environmental challenges, coupled with the ambitious “dual carbon” targets, new energy vehicles (NEVs) have emerged as a pivotal development trajectory within the clean energy sector, increasingly serving as a vital catalyst for the global automotive industry’s transformation and upgrade. China is playing a significant role in the global new energy vehicle industry. The country supports the industry’s development through supply policies, demand policies, and improvements in the market environment. This includes providing research and development subsidies to manufacturers, offering purchase subsidies and tax reductions to consumers, and enhancing the construction of public charging infrastructure. In this context, China has asserted a significant influence on the global NEVs landscape, accounting for over 60% of worldwide NEVs sales in 2023, while pioneering innovative breakthroughs in cutting-edge domains such as artificial intelligence (AI) and battery manufacturing. Nonetheless, there is significant technological heterogeneity within the NEVs industry [1]; companies currently lack the resources to keep up with rapid technological advancements and handle intense market competition. Although research institutions possess a broad knowledge base and research and development capabilities, they struggle with funding and commercialization challenges during the R&D process. This situation necessitates collaborative innovation between organizations to share resources and complement each other’s strengths [2], thereby expediting the innovation and commercialization trajectory of NEV technologies. Such collaborative efforts are instrumental in advancing the low-carbon economy, underscoring the critical role of synergy in overcoming the barriers to sustainable development within the NEVs sector.

Enterprises, universities, and scientific research institutions, among other diverse entities, forge connections to collaboratively engage in innovation activities, thereby cultivating a sophisticated collaborative innovation network [3]. Freeman, as early as 1991, introduced the concept that an innovation network serves as a foundational mechanism for fostering innovation cooperation between enterprises. This network equips its participants with a plethora of information sources and collaborative paradigms [4]. Within this interconnected framework, various innovation agents re-establish links, facilitating the transmission and dissemination of knowledge and information throughout the network [5]. Through the exchange of ideas and information from multiple perspectives between partners, external new knowledge and technologies are assimilated. This process of integrating novel insights can significantly boost innovation capabilities [6], enhance the precision and quality of research and development efforts, and navigate through the challenges associated with critical core technologies, ultimately catalyzing innovation.

The collaborative innovation network is characterized by its integrative, complex, and uncertain nature. During the cooperation process, the desired collaborative effect is often compromised due to factors such as the network’s structural characteristics and the individual attributes of its nodes. Consequently, a deep understanding of the driving forces behind network formation and a clear elucidation of the mechanisms of action of these factors are crucial for enhancing the synergistic effect. Traditional studies predominantly focus on the network’s topological structure and employ conventional econometric models for regression analysis [7,8]. However, these approaches tend to overlook the intrinsic mechanisms that govern network formation and the interdependent nature of network connections [9]. Moreover, they fail to simultaneously account for the attributes of network nodes and the observable existing connections. The ERGM (Exponential Random Graph Model) is a statistical model used to analyze and explain the structural characteristics of social networks and their forming factors. The ERGM challenges the assumption that network links and edges are independent in traditional regression models, considering the dependency between nodes and edges in the network. Capturing the complex features of network structure is an innovation in network research methods [10]. An (2016) discussed the challenges and methods of ERGM fitting on large networks to provide background and methodological support for ERGM application [11]. Wang et al. (2023) compared the ERGM and ERNM to offer a new perspective on understanding social selection and social influence processes in networks [12]. In practical applications, ERGM has been used to analyze various types of network data, including social, biological, and communication networks. For example, Wang et al. used the ERGM to analyze the evolutionary dynamics of the collaborative innovation network of the Yangtze River Delta urban agglomeration [5].

Existing research has thoroughly explored and synthesized the impact of network evolution structure characteristics and proximity factors on innovation. For instance, Bergek et al. (2008) examined the dynamic changes in the innovation system of the new energy automobile industry [13]. Suo et al. (2024) investigated the spatio-temporal evolution characteristics of the collaborative innovation network in the new energy automobile industry and discovered that the industry’s innovation potential has not been fully realized, indicating significant room for innovation and development [14]. Based on the centrality characteristics of nodes, Liu et al. (2016) discovered that the preferential connection traits of intermediate centrality enhanced innovation performance [15]. According to the theory of structural holes, Burt emphasized that individuals should leverage their network position to achieve a competitive advantage [16,17]. Fang et al. (2023) suggested that nodes with larger degrees possess stronger cooperative abilities and a broader scope of cooperation [18]. Becattini (1990) highlighted the significant role of geographical proximity, specialization, and inter-firm cooperation in enhancing innovation and competitiveness [19], while Cao et al. delved into the effects of proximity mechanisms on collaborative relationships within innovation networks [20]. Similarly, He et al. and Wang et al. have undertaken studies from the perspectives of network hierarchy and model application, focusing on the origins of network formation and its dynamic evolution [21,22]. Su et al. (2022) employed the secondary assignment procedure to examine the evolutionary mechanism of varying proximities within the NEVs collaborative innovation network in the Beijing–Tianjin–Hebei region [23]. Using BYD’s NEVs as a case study, Zhou et al. (2024) identified key factors influencing collaborative innovation [24].

Nonetheless, these studies often concentrate on isolated viewpoints, failing to holistically address the multifaceted influences at play. Given the pivotal role of NEVs in economic growth and scientific–technological advancements, this paper examines the innovative subjects in China’s new energy vehicle sector from 2005 to 2019, constructing a collaborative innovation network and considering the impact of internal and external factors on it. The Exponential Random Graph Model (ERGM) is a key method for exploring the mechanisms of network formation and evolution. Most studies focus on static cross-sectional data, lacking an in-depth exploration of network evolution mechanisms over different periods. Thus, this study, aligned with the evolution of network scale, incorporates the network’s internal structural factors and the external attributes of nodes into the ERGM, providing a comprehensive analysis of each factor’s influence on the formation and evolution of collaborative innovation networks [25]. The contributions of this paper are as follows: (1) In empirical research, it overcomes the limitations of cross-sectional data by dividing the research samples into different periods. It comprehensively analyzes and compares the influence mechanisms of various factors on the formation of the network in each period, revealing the evolution mechanism of the collaborative innovation network based on NEVs. (2) In theoretical research, the analysis of influencing factors and characteristics of the collaborative innovation network offers a reference for enterprises and scientific research institutions in cooperative innovation, providing a theoretical basis for the development of collaborative innovation network research.

2. Theoretical Analysis and Hypotheses

Complex network theory explores the correlation between nodes and the impact of network edges on information transmission and resource flow. It establishes a framework for cooperation, information transfer, and knowledge sharing within collaborative innovation networks and provides a method for analyzing network topology. Considering various factors such as node attributes, network structure, and cooperative relationships, the ERGM method can comprehensively consider the influence of these factors on network formation. The synergistic integration of these two approaches aids a more comprehensive understanding of the formation and influencing factors of collaborative innovation networks. Lusher (2013) categorizes the influencing factors of network generation mechanisms into three groups: network structural factors, actor attributes, and network covariates [26]. In this paper, they are summarized as endogenous structural factors and exogenous attribute factors of nodes, and then comprehensively analyzed.

1.

Endogenous structural factors

The network’s generation relies on the interdependence between edges, with this dependency manifesting as the network structure at the macro level. Thus, the potential endogenous dynamic evolution mechanism of the network can be analyzed and inferred through its characteristics. Structural factors are represented by higher-order structural dependencies. Compared to simple structural statistics, higher-order dependencies offer stronger explanatory power, effectively reducing the model degradation risk associated with simple statistics and enhancing the model’s reliability.

Higher-order dependencies include expansibility, transitivity, and closure. The triangle structure, star structure, two-path structure, and other network expansions mainly manifest as star structures, typically referring to a configuration where a core node is directly connected to several peripheral nodes, which are often not interconnected. The core node usually has a high degree of centrality, holding an important position and influence in the network, and can become a key node for information dissemination. In a collaborative innovation network, the main entity can expand the scale of its self-centered network by continuously building new cooperative relationships, thereby promoting innovation cooperation. The essence of transitivity is a triangular structure, reflecting the intermediary role of nodes. Core enterprises can establish triangular relationships with multiple peripheral enterprises to enhance their innovation ability and market competitiveness. Transitivity is a key factor in forming the closed triangle structure [27], which not only strengthens the stability of cooperative relationships but also contributes to establishing trust, thus promoting close cooperation between nodes [28]. In the innovation network, high transitivity facilitates the flow of information and the transfer of technology. Companies with high transitivity are more likely to establish effective partnerships and thus enhance their ability to innovate. However, over-reliance on third parties for knowledge exchange and information transfer may be risky, as the received information and knowledge may be distorted, potentially reducing the efficiency of innovation. Closure involves adding a connecting edge to an open triangular structure, forming a more stable closed triangular structure. This closed triangle structure enhances robustness, transitivity, and stability while reducing redundant connections in the network. When an innovation agent is embedded in this structure, information can be accessed and transmitted through multiple paths, offering flexibility and efficiency in information flow. In knowledge sharing and innovation, this reduces information acquisition costs and accelerates knowledge dissemination and application. The close connections and frequent interactions between nodes strengthen trust relationships, laying the groundwork for long-term cooperation. Based on this, the following hypothesis is proposed:

H1a: 

The collaborative innovation network of NEVs has an expansionary effect, in which entities with higher expansion (star structure) can more effectively attract and integrate external resources, thus promoting innovation cooperation.

H1b: 

In the evolution of the collaborative innovation network for NEVs, innovation entities with high transmission should avoid forming new cooperative relationships.

H1c: 

The collaborative innovation network of NEVs has a closed effect, conducive to establishing and maintaining stable cooperative relations.

2.

External attributes of the node

The individual and relational attributes of innovation subjects significantly influence the formation of social networks [21]. Individuals with similar attributes tend to exhibit similar behaviors and are more likely to form connections [29]. Typical node attribute effects include the Matthew effect and the homophily effect. The Matthew effect highlights the cumulative advantage in resource allocation, resulting in noticeable polarization; nodes with greater innovation output and broader technical fields are more likely to establish cooperative relationships. Due to their technical advantages, such nodes can quickly absorb new knowledge [30] and are more readily chosen as cooperative partners [31]. Joint patent applications by innovation entities are products of collaborative innovation activities, with the number of patents indicating the interaction frequency and collaborative innovation capability between these entities [32,33]. Innovation entities with more patents possess stronger R&D and knowledge absorption abilities. The technical knowledge of an innovation subject is a crucial indicator of its technical expertise and R&D capability, and the richer the technical knowledge, the easier it is to build cooperative relationships. The assortativity effect describes the tendency of individuals or organizations to form cooperative relationships with those possessing similar attributes. In collaborative innovation, geographical coordination is crucial for fostering cooperation [34], as it influences organizations’ ability to absorb knowledge and integrate technology, thereby impacting the execution of collaborative innovation activities [35]. Geographical proximity reduces the risk of information asymmetry in inter-organizational communication, minimizes knowledge loss during spatial diffusion and transmission [36,37], enhances knowledge spillover and technology integration [38], and thus promotes organizational collaborative innovation. As a medium for knowledge exchange and information transfer between organizations, the degree of technological innovation and knowledge creation is still limited by the complementary knowledge exchange capability between organizations. Organizational alignment refers to the extent to which cooperative relationships are shared within or between organizations in their arrangements. Organizational coordination provides a framework for member communication and coordination, making partnerships based on mutual recognition more effective in innovation cooperation, and promoting the integration of knowledge and information, thereby advancing collaborative innovation activities. However, it is easier to establish partnerships between different types of organizations, such as enterprises and universities or institutes, due to their differences in resources, expertise, and goals. Companies often aim to translate research results into market applications, while universities and research institutions focus on basic research and knowledge creation, and this complementarity fosters cooperation between the two. Based on this, the following hypothesis is proposed:

H2a: 

The collaborative innovation network exhibits the Matthew effect, meaning that stronger innovation abilities and richer technical knowledge facilitate the construction of collaborative innovation relationships.

H2b: 

The collaborative innovation network demonstrates an assortativity effect, in which geographical co-coordination aids in building collaborative innovation relationships, and the complementarity of organization types is crucial for collaborative innovation.

3. Research Design

3.1. Data Sources

NEVs are a prominent area of current research, encompassing core technologies like battery management systems, motor controllers, and vehicle controllers, as well as various technical fields such as energy management, intelligence, and networking. The complexity and technical interactivity across these fields have fostered close collaboration between companies and research institutions. The NEVs discussed in this paper refer to vehicles using non-traditional fuels or new driving technologies, such as electric and hybrid vehicles. Collaborative innovation networks play a crucial role in this process, enabling innovation entities to share knowledge and resources, enhance innovation efficiency, and expedite the commercialization of new technologies. Patents are a significant outcome reflecting cooperation between entities, and patent applications and authorizations not only protect innovation achievements but also illustrate the cooperation model between innovation entities [39]. Therefore, this paper selected China’s new energy vehicle joint patent application data from 2005 to 2022 from the Wisdom Bud Database as a research sample to gain insight into the construction and development of collaborative innovation networks in this field. It takes two–three years for patents to be granted from application to authorization, so this paper focuses on authorized patents from 2005 to 2019 to ensure data integrity and reliability. Enterprises and research institutions involved in R&D (including universities and research institutes) were used as research subjects. After removing duplicate items in the patent data, as well as patents where the innovation subjects were individuals and non-mainland Chinese applicants, a total of 4052 patents were finally authorized, involving 1745 innovation subjects.

Figure 1 illustrates the evolution of the number of innovation entities and authorized patents in the collaborative innovation network of NEVs from 2005 to 2019. Both the count of authorized patents and the number of innovation entities exhibit a consistent upward trajectory, particularly noticeable post-2010 and more prominently after 2015. This growth aligns with the new energy vehicle promotion policy introduced in China in 2014.

We use the first four digits of the IPC to refer to the technical field to which the patent belongs. IPC stands for International Patent Classification, a standard system for classifying patent documents. By using the first four digits of the IPC code, we can accurately identify the technical field of each patent. Figure 2 presents the shifts in the technology fields encompassed by the collaborative innovation network. The expansion of technology fields involved in innovation is consistent, with the cumulative total displaying annual growth. This observation underscores the remarkable collaborative innovation accomplishments in the field of NEVs in China. Therefore, the research subjects are categorized into three time intervals: 2005–2009, 2010–2014, and 2015–2019.

3.2. Research Methods

In this paper, the ERGM was used to explore the formation and evolution of the collaborative innovation network of NEVs. Referring to the research of Steven et al. (2007) [40], the model is set as an exponential function, as shown in Formula (1):

$$\mathrm{Pr}\left(Z|z\right)={\displaystyle \frac{\exp \left\{{\eta }_{i}g\left(z,X\right)\right\}}{k}}$$

(1)

In the above equation, the dependent variable $\mathrm{Pr}\left(Z|z\right)$ represents the probability of network generation; $z$ is the real network structure, $X$ is the node attribute variable of the network, and $g\left(z,X\right)$ is the vector composed of the network structure and node attributes; ${\eta }_i$ represents the standard for judging the influence degree of different statistics on network generation; $k$ represents a normalized constant to guarantee the probability of network generation, $0\le \mathrm{Pr}\left(Z|z\right)\le 1$.

The proposed approach was tested using the Monte Carlo simulation and the MCMC MLE method was used for model estimation. The estimated parameters were continuously optimized until a steady state was reached and the goodness of fit was evaluated using AIC and BIC. Smaller values for these two indicators indicate a closer fit of the model to the observed real network [41]. Goodness-of-fit (GOF) evaluation will serve as an additional method to assist in verifying the model’s validity.

3.3. Variable Definition

Edges, Gwdegree, Gwesp, and Gwdsp were chosen as structural factors, considering various factors that influence network formation and prevent network degradation. Patent (collaboration ability), IPC (technical field), Province (geographical assortativity), and Label (organizational assortativity) were selected as factors influencing network node attributes. Refer to

Table 1. Variable definitions.

Classification	Label	Cutline	Explanation
Structural factors	Edge		There is a link between innovation entities
	Gwdegree		Expansionary effect
	Gwesp		Closure effect
	Gwdsp		Transitive effect
	Patent		The Matthew effect
	IPC
	Province		The assortativity effect
	Label

for details:

Gwdegree, Gwesp, and Gwdsp are higher-order statistics used to describe the complex structure and relationships within a network. These statistics effectively reduce the risk of model degradation caused by simple statistics, enhance model reliability, and more accurately capture the network’s dynamic behavior and structural characteristics. The number of joint patent applications indicates innovation capability; stronger innovation ability facilitates cooperation with other innovative entities. IPC denotes the number of technical fields involved in R&D by innovative subjects, using the first four digits of patent classification numbers to highlight differences across technical fields [33]. Province indicates geographical assortativity, with values assigned to provinces involved in the innovation subject. Organizational assortativity is determined by the type of organization: “E” for enterprises and “U” otherwise. When two nodes are in the same province or belong to the same organization type, the model can capture their compatibility.

4. Empirical Research

4.1. Topology of the Collaborative Innovation Network

Compared to cross-sectional data, mixed cross-sectional data can avoid selectivity bias and generate greater vitality [42]. Therefore, this paper selected the data of joint patent applications for NEVs from 2005–2009, 2010–2014, and 2015–2019 for analysis. In this study, Gephi software was used to draw the network at each stage, where the nodes in the network represent the patent applicants, i.e., the innovation subjects. The connected edges represent the cooperative relationships between different innovation entities, with the size of the node indicating its importance and the thickness of the edge indicating the intimacy of the cooperative relationship, as shown in Figure 3. The overall network topology of each stage is shown in

Table 2. Network topology indicators.

Stages	Network Size	Network Edges	Cooperation Frequency	Network Density	Clustering Coefficient	Average Path Length	Average Degree	Network Diameter
2005–2009	54	42	49	0.029	0.769	1.222	1.556	2
2010–2014	515	651	829	0.005	0.721	3.047	2.528	8
2015–2019	1462	1806	2207	0.002	0.656	4.484	2.471	13

.

(1) Network size and cooperation frequency. The rapid expansion of the network size indicates that the number of innovative entities participating in the field of NEVs is increasing. The rise in cooperation frequency surpasses the growth in the number of connected edges, reflecting that cooperation between some nodes is sustainable and the cooperative relationships are stable.

(2) Network density and structure evolution. Network density refers to the ratio between the existing edges in a network and the potential edges. It reflects the network’s connectivity degree, with a high-density network indicating more direct connections between nodes. The network’s density decreased from 0.029 in the first stage to 0.002 in the third stage, suggesting that the connections are closer and more efficient. The network diameter is the length of the longest shortest path in the network, measuring the closeness of connections between any two nodes. A smaller diameter indicates more efficient information transmission. The average path length increased from 1.222 to 4.484, and the network diameter increased from 2 to 13, highlighting the network’s structural sparsity and aligning with typical real-world network characteristics. Additionally, the network structure evolved from a simple binary structure to a complex core–edge structure, where core nodes may have more resources and stronger connectivity, thus enhancing the network’s overall innovation activities.

(3) The clustering effect and “small world” characteristics. The clustering coefficient measures how well a node’s neighbors are interconnected. It reflects local clustering in networks, where nodes often form tight groups with nearby nodes. During the three stages of collaborative innovation network development, a strong clustering effect shows that network nodes tend to form close cooperation circles locally. This frequent and stable triangular cooperation is vital for the network’s stability and cooperation efficiency. Despite the relatively short average path length, the “small world” nature of the network remains crucial for facilitating information flow, enhancing cooperation, and spreading knowledge.

(4) Breadth of cooperation. The rising trend of network averages indicates that innovative entities in the network generally have at least two partners, which is a positive signal for the healthy expansion of the network. However, the relatively low average also suggests a lack of cooperation breadth, indicating that innovation actors need to further expand their cooperation scope to facilitate a broader exchange of knowledge and resources, thereby enhancing overall innovation capacity and competitiveness.

In summary, although the collaborative innovation network in the field of NEVs is sparse, its structure is becoming increasingly complex, characterized by “small world,” high clustering, and “core–edge” features, consistent with existing research conclusions.

4.2. ERGM Simulation

In this paper, the model parameters were estimated and calculated using the ‘statnet’ and ‘ergm’ packages of R software version 4.3.2 [43]. Three models were established. Model 1 is the zero model, with the independent variable including only the network’s connected edge, serving as the basic model of the research. Building on Model 1, Model 2 incorporates exogenous attribute variables of nodes. Model 3 adds endogenous structural variables to Model 2, making it a comprehensive model that considers both internal and external factors. After repeated attempts and corrections, the fitting results for each stage in Table 2,

Table 3. ERGM fitting results from 2005–2009.

Stage 1	Model 1	Model 2	Model 3
edges	−3.4987 *** (0.1566)	−4.3320 *** (0.5635)	−4.0433 * (2.0083)
nodematch.Label		0.0400 (0.3595)	0.1281 (0.4139)
nodematch.Province		2.2166 *** (0.3227)	1.8364 *** (0.3093)
nodecov.IPC		−0.0850 (0.1078)	−0.1787 (0.1734)
nodecov.Patent		0.2066 (0.1648)	0.4311 (0.2583)
gwdeg			2.1313 (1.1432)
gwesp			2.0419 *** (0.3536)
gwdsp			−1.3281 * (0.5925)
AIC	381.1	345.8	265.4
BIC	386.4	372.2	307.6

Note: ***—p < 0.001, *—p < 0.05.

and

Table 4. ERGM fitting results from 2010–2015.

Stage 2	Model 1	Model 2	Model 3
edges	−5.3098 *** (0.0393)	−6.4164 *** (0.0919)	−8.9449 *** (0.1908)
nodematch.Label		−0.3279 *** (0.0878)	−0.3855 *** (0.1069)
nodematch.Province		2.2432 *** (0.0846)	1.7182 *** (0.0719)
nodecov.IPC		0.0393 *** (0.0026)	0.0246 *** (0.0041)
nodecov.Patent		−0.0021 * (0.0011)	0.0134 *** (0.0037)
gwdeg			3.8605 *** (0.2561)
gwesp			2.6097 *** (0.0963)
gwdsp			−0.0514 *** (0.0084)
AIC	8221	6472	5460
BIC	8230	6521	5539

Note: ***—p < 0.001, *—p < 0.05.

were finally obtained.

(1) As shown in Table 3, Table 4 and

Table 5. ERGM fitting results from 2015–2019.

Stage 3	Model 1	Model 2	Model 3
edges	−6.3807 *** (0.0236)	−7.3604 *** (0.0506)	−9.4695 *** (0.1007)
nodematch.Label		−0.3340 *** (0.0506)	−0.3347 *** (0.0589)
nodematch.Province		2.2134 *** (0.0487)	1.6886 *** (0.0393)
nodecov.IPC		0.0358 *** (0.0009)	0.0394 *** (0.0016)
nodecov.Patent		−0.0014 *** (0.0003)	0.0030 *** (0.0007)
gwdeg			3.1873 *** (0.1345)
gwesp			2.7465 *** (0.0515)
gwdsp			−0.0502 *** (0.0023)
AIC	26,664	22,167	18,702
BIC	26,676	22,227	18,797

Note: ***—p < 0.001

, the edge coefficients in each stage from Model 1 to Model 3 are significantly negative at a 0.1% significance level. This indicates that an existing edge in the network decreases the likelihood of future edge formation, reflecting that the formation and evolution of the collaborative innovation network for NEVs is not random but significantly influenced by the existing network structure.

Next, the fitting results of the variables will be analyzed based on Model 3 in Table 5.

(2) The gwdegree coefficient is 3.1873, significant at the 0.1% level, indicating that in the collaborative innovation network of NEVs, entities with high centrality tend to establish new cooperative relationships and exhibit clear expansibility, thus verifying Hypothesis 1a. Although the effect was not significant initially, it still showed an expanding trend. In the field of NEVs, key resources and technologies are often concentrated upon a few pioneering entities, making them a focus for attracting partners. By continuously building new partnerships, these core players not only consolidate their technological leadership but also form a positive feedback loop, effectively promoting the expansion and strengthening of the entire collaborative innovation network. The geometrically weighted Binary Sharing Partner (gwdsp) and geometrically weighted Edge Sharing Partner (gwesp) coefficients are −0.0502 and 2.7465, respectively, both significant at the 0.1% level, verifying Hypotheses 1b and 1c. Based on existing cooperation, innovation subjects are more inclined to seek cooperation opportunities through existing partners rather than independently seeking new ones. This cooperation model based on existing relationships enhances the stability and trust of the partnership, promoting closer cooperation; the path of information transmission is short and fixed, reducing the risk of information distortion.

(3) The coefficients of the node attribute variables IPC and Patent are 0.0394 and 0.003, respectively, both significant at the 0.1% level, indicating a notable Matthew effect in the network. Specifically, innovation entities with greater technical knowledge and more patents are more likely to establish new partnerships. These agents can gain expertise across multiple technology domains and master core technologies, making other innovative agents in the network more inclined to connect with them. This tendency helps other players reduce the cost of acquiring resources and accelerate technological breakthroughs. Therefore, Hypothesis 2a is verified. This phenomenon shows that in the collaborative innovation network of NEVs, technical knowledge and patent accumulation are key factors for innovation subjects to establish cooperative relations. These resource-rich players occupy a central position in the network and attract more cooperation opportunities, thus further consolidating and expanding their advantages. At the same time, this also suggests that other innovative entities can improve their competitiveness and attractiveness in the network by strengthening technology research and development and patent layout.

(4) AIC and BIC are two commonly used indicators to evaluate a model’s goodness of fit, considering both its complexity and ability to fit data. Table 3, Table 4 and Table 5 show that in the three models across the three stages, the AIC and BIC values decrease successively and significantly. This indicates that from Model 1 to Model 3, the fit degree and explanatory power gradually improve, meaning the network is formed under the combined influence of internal and external factors.

4.3. Evaluation of Goodness of Fit

To assess the model’s applicability, this paper performs a goodness-of-fit test for Model 3 (Figure 4). Four statistics—geodesic distance, edge-sharing partner, binary sharing partner, and degree—are chosen as comparison indicators. By comparing the statistical characteristics of the simulation network with the observation network, a high consistency between the two is observed, demonstrating a good fitting effect. This result confirms the model’s applicability in analyzing real networks.

5. Conclusions and Policy Implications

The formation and evolution of collaborative innovation networks in the field of NEVs are influenced by many factors. This paper used data from joint patent applications for NEVs from 2005 to 2019 to build a collaborative innovation network. Based on the ERGM, this paper comprehensively analyzes the internal and external factors affecting the network’s formation and presents the following research conclusions and implications. The basic conclusions of this study are as follows: (1) The collaborative innovation network has experienced significant expansion and development, and the innovation results are remarkable. The country’s policy support has encouraged more innovation entities to participate in collaborative innovation in the field, driving substantial growth in technology and patents. (2) The formation and evolution of networks are influenced by both internal and external factors. Regarding internal structure factors, existing edges reduce the probability of forming future edges, indicating that the network’s development is a non-random process influenced by existing relationships. The collaborative innovation network has the effects of expansion, transmission, and closure. Regarding the external attributes of nodes, there are the Matthew effect and geographical compatibility effect. Innovative subjects are more inclined to build cooperative relationships with different types of subjects and seek complementarity in knowledge and ability.

The implications of this study are as follows:

(1) Coordinated development of policy incentives and networks. National policy support is a key factor in promoting the development of collaborative innovation networks. It is suggested to encourage more innovative entities to join the network through incentives such as financial subsidies, tax incentives, and research and development grants. At the same time, considering the non-randomness of the formation of the network, it is suggested that innovation entities strengthen the maintenance of existing relationships, and use the transitivity and closure effects of the network to enhance trust and deepen cooperation.

(2) Resource balance and geographic synergy advantage. Innovation entities with a high degree of centrality play a central role in network expansion and should receive priority support to stimulate their leading role. In order to counter the potential concentration of resources arising from the Matthew effect, it is recommended to implement policies to balance the allocation of resources and ensure that emerging and small innovative actors also have equal access to cooperation opportunities. In addition, based on the geographical compatibility effect, it is suggested to promote the establishment of cooperation between innovation entities in geographical proximity and strengthen synergies by building regional innovation clusters.

(3) Complementary cooperation and continuous relationship building. Innovation subjects should actively seek complementary cooperation with different types of subjects to promote cross-field and cross-industry knowledge and technology exchange. This diversified mode of cooperation is essential to energize innovation. At the same time, in order to ensure the sustainability and stability of collaborative innovation, it is recommended that innovation entities invest resources and efforts to cultivate and maintain long-term cooperative relationships, which includes establishing trust mechanisms, optimizing communication channels, and ensuring continuous interaction between partners.

While this paper delves into the factors influencing the formation of collaborative innovation networks, it acknowledges the constraints of its modeling approach. The study is confined to China’s new energy vehicle industry, characterized by distinct industry-specific attributes. There is a need for further investigation across different regions and industries to broaden the understanding of these dynamics. Such expanded research would not only enrich the existing knowledge base but also offer targeted insights for future scholarly endeavors.