Background

As a cutting-edge technology that reduces large-scale CO2 emissions, Carbon Capture, Utilization, and Storage (CCUS) may help address climate change. Thus, CCUS has become a key component of China’s technological protocol to achieve the goal of “carbon dioxide peaking and carbon neutrality”1. CCUS technology separates CO2 from artificial emission sources and air, captures it, and then stores or utilizes it over the long term through resource-based technical means. In conjunction, its effects integrate energy security, economic development, and ecological governance concerns2. The fifth report of the Intergovernmental Panel on Climate Change (IPCC)3 shows that, without taking CCUS technical assumptions into account, the global cost of emission reductions will rise to 138%. The China Status of CO2 Capture, Utilization and Storage (CCUS) 2021 report points out that the emission reduction potential of CCUS technology can basically meet the target demand of the “double-carbon” goals4. However, China’s CCUS technology was implemented late and is, in general, in the industrial demonstration stage. Therefore, there are problems such as long R&D cycles, large investment scales, low overall efficiency, and high security risks, which have been caused by a poor technological foundation. At this stage, technological innovation is a key means to promote the development of CCUS technology5,6,7.

Technological innovation is characterized by high risks, high investments, and high failure rates. Most R&D entities, which are constrained by resources and capabilities, find it difficult to independently develop major technologies. Against a backdrop characterized by open innovation, innovative network embedding has become an effective approach for R&D entities to connect with cutting-edge technologies8. With the dedicated development of innovative cooperative behaviors between R&D entities, the “one-to-one” chain cooperation mode has been transformed into a multi-entity interactive network mode. Innovation collaboration networks are progressively evolving into crucial vehicles for technological innovation. Characterized by an extended technology chain, significant interdisciplinary nature, and substantial initial investments, the innovative development of CCUS cannot be independently accomplished by any single entity. This necessitates a pressing need to establish highly efficient and synergistic innovation collaboration networks to integrate resources, disperse risks, and accelerate both technological breakthroughs and industrialization processes. Existing theories have claimed that innovative cooperation networks can increase the frequency of knowledge sharing between R&D entities, through sharing resources, sharing risks, accelerating innovation, and so forth, thereby lowering R&D costs and improving innovation performance9. Therefore, exploring innovative cooperation networks in the field of CCUS technology in China is significant for achieving key technological breakthroughs and deploying technical strategies.

Existing studies on innovative cooperation networks mainly concentrate on two aspects: evolutionary characteristics and driving factors. In terms of the evolutionary characteristics of innovative cooperation networks, social network analysis methods are mostly adopted. They are used to explore scientific cooperation and innovative networks from the perspective of complex systems. In this regard, various concepts are involved, from network structural characteristics, through network relationships, to dynamic evolution. Zhu10 and Yang11 explored the evolutionary characteristics of innovative cooperation networks based on different industrial cycles from macro and micro perspectives with regard to the technical patents in China’s aviation equipment manufacturing industry and China’s intelligent manufacturing equipment industry, respectively. Yan12, Ding13, and Choe14 analyzed the evolutionary characteristics of industry-university-research innovative cooperation networks in China’s pharmaceutical manufacturing industry, in the ocean energy industry, and with regard to 75 industry-university-research organizations in South Korea, respectively. The latter also introduced structural holes as variables to measure the contributions of an individual’s location in the network to innovative networks.

In terms of the driving factors of innovative cooperation networks, existing studies mostly adopt the Quadratic Assignment Procedure (QAP) method and the exponential random graph model (ERGM) method. Su15 used the QAP method to explore the contributions of industrial adjacency, geographical adjacency, and knowledge adjacency to the development of coordinated innovative networks of new energy vehicles. Liu16 employed the QAP method to explore the factors influencing the structural evolution of knowledge innovative cooperation networks in the Guangdong-Hong Kong-Macao Greater Bay Area. In a complex network, the existing structure affects the emergence of new relationships. However, traditional regression models cannot measure the influence of endogenous network structures. Thus, Fleming adopted ERGM to prove the intermediary effects of “structural hole occupiers” in a patent network, showing that the closed triangle structure in which they participated increased patent citations by 52%17. Ma18 applied ERGM to analyze the evolutionary characteristics and driving factors of technical cooperation networks in the pharmaceutical industry from three perspectives: attribute drive, homogeneity drive, and structure drive. Taking the OLED industry as a case study, Ruan19 conducted an empirical analysis of technical innovative cooperation networks using ERGM in terms of geography, society, technology, organization, and system. Compared with the QAP method, ERGM can take into account the changes in network topology and node attributes, thus proving more advantageous in predicting the formation and evolution of network relationships20.

Existing studies have drawn their summaries and conclusions from the perspectives of CCUS technology and innovative cooperation research. When applied to interpreting innovation collaboration within China’s unique CCUS technology domain, these approaches face significant contextual challenges and theoretical gaps. Most established theories originate from observations of industries characterized by high marketization and rapid technological iteration. Their conclusions may not be directly applicable to strategic sectors like CCUS, which exhibit strong policy-driven nature, high asset specificity, and complex technological coupling. This study takes patent applications in the field of CCUS technology in China as the research object and constructs an undirected innovative cooperation network with different development cycles. First, we perform social network analysis to explore the evolutionary characteristics of the innovative cooperation network of CCUS technology. Second, we add the structural hole effect to the node attribute dimension. Third, we use ERGM to identify the influences of endogenous structure drive, node assortment drive, and node attribute drive on the development of the network. The aim is to promote the cross-regional heterogeneous sharing of the CCUS innovative cooperation network, leverage resource advantages, and improve the quality of innovative cooperation networks.

Theoretical analysis and model construction

As an emerging technology, the complex and open characteristics of CCUS’s collaborative innovation network reflect dual dynamics: innovation entities’ proactive pursuit of collaboration and the cross-boundary integration of innovative knowledge resources. Collaborative innovation networks for emerging technologies not only manifest interactions between entities but also encompass the flow of technological and knowledge resources. Their formation depends on the development of internal structural relationships within the network and is also related to the knowledge attributes of innovation entities21. The self-organizing development within the network manifests as network structures with specific characteristics, becoming an endogenous mechanism influencing network evolution. Innovation entities tend to prefer partners with abundant knowledge resources or similar knowledge attributes when establishing collaborations22. This preference helps reduce both innovation risks and costs. Existing research has identified three primary drivers of collaboration among scientific entities. First, entity attributes (including absorptive capacity, scale, and R&D capability) significantly influence collaboration patterns23,24. Second, relational attributes matter: entities with proximity in organizational, technological, or institutional dimensions find it easier to build trust, enhance knowledge exchange, and achieve technical synergy25. Third, endogenous network structures, particularly how collaborations are embedded within the overall network, affect the formation of new partnerships26.

The Exponential Random Graph Model (ERGM), developed by Pattison D P et al., simultaneously accounts for both endogenous network structures and exogenous factors such as relationships among network actors27. Unlike typical probabilistic models, it operates without requiring a complete training set and is widely applied to study the formation and evolution of networks8. According to ERGM theory, technological collaboration networks are generated through two types of factors: endogenous structural features and relational dynamics among actors in the network28,29. A key advantage of the ERGM is its broad utility across various types of social network analysis, integrating both relational attributes among actors (including node and edge properties) and endogenous structural variables, thereby enabling a comprehensive understanding of the drivers behind network evolution.

The embeddedness characteristics of collaborative innovation networks can influence the further development of collaborative relationships, serving as an endogenous driving force for network formation21. Structural embeddedness essentially refers to the autocorrelation of interdependencies between network edges. Specifically, the addition of new edges is often based on the configuration of other edges30,31. Therefore, structural embeddedness can be used to analyze the driving forces of network generation. This study mainly investigates two endogenous driving forces: the convergence effect and the closure effect. To some extent, the convergence effect describes the R&D entity’s influence within the innovative cooperation network. It is manifested by the local network configuration of a star structure, which is formed by the continuous establishment of cooperative relationships in a certain mode. One example is provided by the “Richman’s Club” phenomenon32. The closure effect describes the closure transitivity of an innovative cooperative relationship, in which a closed triangle structure is formed by adding an edge based on the Type-2 path in the network. The resulting internal cooperative relationship is more stable33.

Relationships among actors in a network encompass both node attributes and edge attributes, which correspond to innovation entity characteristics and collaboration preferences. Common drivers of these relationships include the assortativity effect and the Matthew effect. According to the assortment effect, R&D entities with the same or similar attributes will be more likely to establish cooperative relationships. For example, technological innovation theory holds that similarities in organization, capabilities, location, and system can help both parties establish trust, exchange knowledge, and conduct cooperative innovation behaviors34,35. This study focuses on the geographical assortment effect and the organizational assortment effect. According to the Matthew effect, individuals with stronger R&D capabilities will be more likely to build innovative cooperative relationships. This effect gives rise to the phenomenon that “the strong ones become stronger.” For example, the absorptive capacity theory36 and the technological competition theory37 hold that nodes with stronger R&D capabilities have greater advantages than other nodes in connections. On this basis, this study introduces the structural hole effect. Structural holes refer to gaps in a network in which nodes are directly connected to some nodes but not others. As a result, “holes” appear in the network38. The positions occupied by “bridge” nodes that control the knowledge exchange channels are network structural holes. Burt’s structural hole theory has four indicators. Specifically, restriction degree and hierarchy degree both measure the degree to which actors are restricted in the network; effective scale and efficiency both measure the non-redundant factors of actors39. The structural hole effect manifests itself in two aspects. First, the less the core node is constrained by other nodes, the easier it is to build cooperative relationships with surrounding nodes. Second, the greater a node is constrained by the core node, the less likely it is to establish relationships with other nodes connected to the core node.

Figure 1 shows a conceptual model based on the above theoretical analysis.

Fig. 1
figure 1

Research conceptual model.

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Research design

Sample selection and data sources

The research sample comprises granted patent data from 34 provincial-level administrative regions in China between 1988 and 2021 in the field of CCUS technology. Data were limited to patents that were publicly accessible after application and subsequent grant approval, while excluding rejected or withdrawn applications to ensure the technical validity of collaborative relationships. For the purpose of this study, “the field of CCUS technology” is represented by the nine patent codes under the CCUS section in the International Patent Classification (IPC) Green Inventory issued by the World Intellectual Property Organization (WIPO). The data source is the China Patent Full-text Database (SCPD) of the Chinese National Knowledge Infrastructure (CNKI), and the search query is “classification No. = B01D53/14 or B01D53/22 or B01D53/62 or B65G5/00 or C01B32/50 or E21B41/00 or E21B43/16 or E21F17/16 or F25J3/02”. The data cutoff for this study is set at 2021. Due to a typical 1–3 year lag in the granting of CCUS invention patents in China, patent applications submitted in 2022 had not fully entered the research database by the time of data collection40. The period before 2021 was characterized by relative stability in CCUS technology policy. In contrast, after 2022, intensive policy adjustments occurred, including revisions to the Energy Law and the rollout of dual-carbon strategies. More than 40 policy documents were introduced across various sectors such as energy transition, energy conservation and carbon reduction, industry, urban-rural development, and transportation41. These changes exerted a notable exogenous policy shock on collaboration networks. To isolate the impact of such abrupt policy shifts and focus on endogenous technological evolution, the year 2021 was selected as the cutoff for the observation window. This approach is consistent with established practices in clean energy technology research42,43. This study strictly defines collaborative patents as those jointly applied for by at least two independent legal entities (organizations or individuals). Collaborations between individuals and organizations are considered valid. Applications jointly submitted by multiple departments under the same organization, or by a single applicant (including affiliated entities), were excluded as non-collaborative. After data cleaning, a total of 10,592 patent documents were obtained. Among these, 1,068 were filed through institutional collaboration, involving 725 distinct organizations or individuals.

Research method

ERGM, as a generative probabilistic model, is a statistical tool dedicated to dealing with network relationships and can quantitatively simulate the causes of network relationships. The model incorporates both endogenous variables (internal structure attributes) and exogenous variables (such as node and edge attributes) into network regression, discarding the assumption of independence made in traditional regression. In this way, it explores the factors driving the evolution of network relationships from multiple angles. The general form is as follows:

$$\:Pr\left(Y|y\right)=\frac{1}{k}exp\left\{{\theta\:}_{\alpha\:}^{T}{g}_{a}\left(y\right)+{\theta\:}_{\beta\:}^{T}{g}_{\beta\:}\left(y,x\right)+{\theta\:}_{\gamma\:}^{T}{g}_{\gamma\:}\left(y,z\right)\right\}$$
(1)

where \(\:Pr\left(Y|y\right)\) denotes the probability of occurrence of relationship network \(\:y\) under characteristic conditions; \(\:{g}_{a}\left(y\right)\) denotes network structures that may be formed in the network relationship, such as triangles and stars; \(\:{g}_{\beta\:}\left(y,x\right)\) denotes variables related to network node attributes; \(\:{g}_{\gamma\:}\left(y,z\right)\) denotes variables related to network edge attributes; and \(\:{\theta\:}^{T}\) denotes the parameter to be estimated of each variable, reflecting the degree of influence of each variable on network formation. Finally, \(\:k\) is a normalized constant ensuring that the model conforms to the characteristics of probability distribution.

Variable measurement

CCUS represents a policy-driven technology, where the scale of collaborative patents is directly linked to government resource allocation. Fluctuations in patent numbers thus serve as a critical indicator of technological evolution. To investigate endogenous structural dependence in the generation and evolution of innovative cooperation networks in the field of CCUS technology, this study analyzes endogenous structure drive, node assortment drive, and node attribute drive variables.

Endogenous structure drive variables

In this study, the variable Edges defines the number of edges existing in a network and plays a referential role in the model, being equivalent to the constant term in a regression model. Considering that simple configuration variables are prone to model degradation, this study introduces a geometrically weighted degree distribution term (Gwdegree) and a geometrically weighted edge-sharing partners term (Gwesp), both high-order configuration variables with the same explanatory power, to capture the structural embeddedness effect of innovative cooperation in the field of CCUS. The variable Gwesp represents star structures in a network, where all resource relationships are concentrated at the central node, resulting in “center-edge” unbalanced expansion. The variable Gwdegree represents closed triangle structures in the network, where the node forms a ternary closed community relationship with other nodes, reflecting a trend of transitive closure.

Node assortment drive variables

Node assortment is defined as the influence of the number of edges with the same attributes on network evolution. In this study, the dual dimensions of geography and organization are selected to evaluate assortment effects. Geographical assortment (Area_Homo) is evaluated by indicating the region where each R&D institution is located using the 34 provincial administrative regions in China. Thus, R&D institutions with the same geographical indication have geographical assortment. Organizational assortment (Org_Homo) is evaluated based on the classification of R&D institutions as enterprises, research institutes, higher education institutions, or other organizational types. Thus, R&D institutions of the same organizational type have organizational assortment.

Node attribute drive variables

In this study, R&D capabilities (R$D_cap) and structural holes are selected as node attribute drive variables to evaluate the influence of the individual attributes of nodes on the network. The number of patent applications filed by an R&D institution in the field of CCUS technology, as retrieved from the official China National Intellectual Property Administration (https://www.cnipa.gov.cn/) website, indicates the entity’ s R&D capabilities. That is, the stronger the R&D capabilities of the entity, the more significant the network amplification effect. The structural hole effect is indicated by structural hole hierarchy (SH_hie) and structural hole efficiency (SH_eff). SH_hie, defined as the degree to which restrictions are concentrated on one actor, is used to measure the constraints on a node imposed by the core node in the network. SH_eff is used to measure the non-redundant factors of R&D institutions in an innovative cooperation network and to describe the influence of one node on other related nodes in the network. Thus, influence can be calculated using the following formula:

$$\it \:\text{S}\text{H}\_hie=\frac{\sum\:_{j}\left(\frac{{C}_{ij}}{C/N}\right)ln\left(\frac{{C}_{ij}}{C/N}\right)}{Nln\left(N\right)}$$
(2)
$$\it \:SH\_eff=\frac{\sum\:_{\text{j}}\left(1-{\sum\:}_{q}{,p}_{iq},{m}_{jq}\right)}{\text{n}}, q\ne\:i,j$$
(3)

where j denotes any node having a cooperative relationship with node i; q denotes any third party other than i and j; \(\:{C}_{ij}\) denotes the restriction degree of the node; \(\it \:\text{C}/\text{N}\) denotes the mean restriction degree of each node; \(\it \it \:\text{N}\text{l}\text{n}\left(\text{N}\right)\) denotes the maximum possible sum; \(\it \:{\text{p}}_{\text{i}\text{q}},{\text{m}}_{\text{j}\text{q}}\) denotes the redundant factors between institutions i and j; and n denotes the number of all nodes connected with institution i. Table 1 presents the definitions and graphs of the ERGM variables in this study.

Table 1 Definitions and graphs of ERGM variables.
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Empirical research

Phased network characteristics and evolutionary characteristics of innovation collaboration in china’s CCUS technology field

Phase division of CCUS technological innovation collaboration

Based on the phase division framework of the technological life cycle theory44, and in accordance with the growth rate changes illustrated in Fig. 2 and key policy milestones, collaborative patent activities in China’s CCUS technology are divided into four distinct phases:

  1. (1)

    The Collaboration Emergence Phase (1988–2007) was characterized by a limited number of entities engaging in joint R&D. Due to insufficient knowledge accumulation in the technology domain, patent applications were rare, with an annual average of fewer than five patents. This period primarily involved exploration of technological pathways.

  2. (2)

    The Collaboration Initiation Phase (2008–2011) began when concepts such as “low-carbon economy” and “low-carbon city” entered policy discussions in China. In 2008, the National Development and Reform Commission (NDRC) and the World Wide Fund for Nature (WWF) initiated pilot projects for low-carbon city development. Driven by these policy measures, the number of collaborative patent applications exceeded ten annually, with a notable surge in the growth rate of joint applications, reflecting the breakthrough role of policy in stimulating collaborative innovation.

  3. (3)

    The Collaboration Expansion Phase (2012–2018) was marked by the launch of the national CCUS demonstration project in 201245. The annual average of joint patent applications surpassed 60, indicating that collaboration had become more institutionalized and structured partnerships began to emerge.

  4. (4)

    The Collaboration Maturation Phase (2019–2021) saw the publication of the Green Industry Guidance Catalog (2019 Edition) and China’s announcement of the dual-carbon goals (peaking carbon emissions and achieving carbon neutrality) in 2020. During this phase, the annual average of cross-institutional collaborative patents exceeded 170, demonstrating a growing need for trans-system integration as the technology entered a mature stage.

Fig. 2
figure 2

The Change Curve of the Number of Jointly Applied Patents in the Field of CCUS in China.

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Network characteristics of CCUS technological innovation collaboration stages

As shown in Fig. 3, the Collaboration Emergence Phase (1988–2007) exhibited a fragmented and exploratory network. Few institutions participated in innovation collaborations within the CCUS technology field during this stage, with the largest connected component containing only four nodes. Zhejiang University emerged as a relatively significant research entity in this period. The Collaboration Initiation Phase (2008–2011) began to demonstrate a star-shaped radiation network. More complex collaborative relationships started to form among multiple nodes. Panzhihua Iron & Steel Research Institute (PISI) and China Petroleum & Chemical Corporation were the core nodes of the two important subnetworks during this period. During the Collaboration Expansion Phase (2012–2018), a multi-core structured network took shape. The number of R&D entities continued to grow, accompanied by a noticeable increase in both large nodes and subnetworks within the network. This period saw the formation of a multi-core innovation collaboration structure dominated by large enterprises. The Collaboration Maturation Phase (2019–2021) evolved into a cross-domain synergistic and integrated network. With further expansion of the network scale, the collaboration structure gradually transformed from multiple isolated subnetworks into a cohesive overall network. This network comprised a key subnetwork centered around China Petroleum & Chemical Corporation and Huaneng Clean Energy Research Institute (CERI), along with numerous smaller subnetworks. Throughout the evolutionary process, central state-owned enterprises have consistently maintained control over advanced technologies and research frontiers in this field, playing a leading role in promoting CCUS technology collaboration. During the evolution of the innovative cooperation network, the number of binary small-node cooperation chains also increased sharply, suggesting that the momentum of innovative cooperation in the field of CCUS technology is optimistic and that key subnetworks radiating from new core nodes may be formed in the future.

Fig. 3
figure 3

Evolution of the topology of the CCUS technology innovation cooperation network, 1988–2021.

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Evolutionary characteristics of the innovation collaboration network in the CCUS technology field

COOC software is further used to calculate the network feature indicators of each stage (see Table 2) and explore the evolutionary characteristics of innovative cooperation networks in this field in China, as described in detail below.

(1) Further expansion of network size and diversification of R&D entities: The number of network nodes increased from 30 in the first stage to 430 in the fourth. With the substantial increase in the number of network edges, network size expanded by 14 times, indicating the densification of network connections and the gradual formation of large-scale innovative cooperation in the field of CCUS technology.

(2) Expanded scope of cooperation, reduced overall network density, and intensified local connections: Network density describes the closeness of innovative cooperation between nodes from a macro perspective. To be specific, the network densities of the four stages were 0.0483, 0.0198, 0.0051, and 0.0040, respectively, representing a downward trend. Meanwhile, the number of process nodes surged. In other words, the addition of new nodes in the innovative cooperation network in the field of CCUS technology diluted network density, indicating that the growth rate of cooperative relationships was lower than that of innovation entities and that innovative cooperation was based on the stability of innovation entities. The average clustering coefficient of the network increased from 0.1889 in the first stage to 0.2419 in the fourth, with the formation of local cooperative communities occurring at the micro level, which showed that the innovative cooperation between R&D institutions was strengthened and gradually acquired community characteristics.

(3) Diversified forms of cooperation, open atmosphere, and huge potential for innovative cooperation: As the average degree of the network continued to grow, the number of partners for R&D entities increased, leaving room for improvement in cooperative innovation. Both point degree centrality and betweenness centrality presented a trend of “rising-falling-rising-falling”. With the expansion of network size and the destabilization of connections between individuals, network innovation resources did not continuously converge to a certain node. Instead, network innovation resources in the field of CCUS technology began cycling between the relative focus caused by fierce competition between core R&D institutions and the relative openness of cooperative relationships, placing the innovative cooperation network in a cyclic rising stage.

Table 2 Definitions and graphs of ERGM variables.
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Factors driving the evolution of innovative cooperation networks in the field of CCUS technology in China

The ERGM was estimated using the Statnet package in R language and tested based on the Markov Chain Monte Carlo (MCMC) value. The parametric t-statistic test produced significant results. The goodness-of-fit of the model was evaluated according to the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). The ERGM results of the four stages are shown in Table 3.

In terms of endogenous structures, Edges showed a significant negative influence throughout the period, while the closure effect and the convergence effect were significantly positive. Thus, the evolution of innovative cooperation in the field of CCUS technology was realized in a center-to-edge approach. Only a few R&D institutions participated in cooperative innovation in the first stage, during which the influence of endogenous structure drive factors was not highlighted. Edges manifested significant negative influences in the second, third, and fourth stages, with parameters estimated to be −5.945, −5.679, and − 5.491, respectively, indicating the low density of innovative cooperation networks in the field of CCUS technology in China. Each time a new line (new cooperative relationship) was added to the network, the probability that other node pairs in the network would be connected was less than 6%, and the sparsity effect of unilateral nodes in the network was observed to be strong46. Gwdegree showed a significant positive correlation with the innovative cooperation network during network evolution, together with a high-fitting coefficient, which indicated that the cooperation network tended to form a star structure with “center-edge” distribution and that the convergence effect positively promoted the formation and evolution of the innovative cooperation network. Gwesp showed significant positive correlations from the second to the fourth stage, which meant that the original cooperative relationships between R&D institutions had a positive influence on the selection of future partners and that the presence of a closed triangle structure could promote the formation of a new cooperative relationship.

As regards node assortments, the geographical assortment effect lowered cooperation costs and promoted knowledge spillover, thereby driving organizational assortment to achieve the cross-regional flow of innovative cooperation in the field of CCUS technology. Area_Homo showed a significant positive correlation in each of the four stages, which indicated that geographical assortment lowered the costs of communication between innovation subjects and contributed to knowledge spillovers, serving as a stable driver of cooperative links during the generation and evolution of the innovative cooperative network. Org_Homo showed no significant influence in any of the first three stages, but manifested a significant positive influence in the fourth stage, indicating that the cooperative relationship between similar R&D entities was weak during the preliminary exploration period in the field of CCUS technology (that is, enterprises were more inclined to cooperate with universities or research institutes). With the progress of CCUS technology, more parent-subsidiary/headquarters-branch innovative cooperation gradually emerged in the innovative cooperation network, such as the innovative cooperation between China Petroleum & Chemical Corporation and its branches as well as that between Nanjing CLP Panda Tablet Display Technology Co., Ltd. and Nanjing CEC Panda LCD Technology Co., Ltd. Such enterprises can communicate and provide feedback in a timely manner, achieving free knowledge transfer and spillover and promoting the fluid development of innovative cooperation networks.

With respect to node attributes, the Matthew effect of R&D capabilities gradually disappeared after its initial appearance in the mid-term. Similarly, structural hole hierarchy tended to weaken, which strengthened the influence of structural hole efficiency. R$D_cap showed no significant influence in the first stage, manifested a significant positive correlation in the second stage, and exhibited significant negative correlations in the third and fourth stages. The Matthew effect in the second stage indicated that the stronger the R&D capabilities of an R&D entity, the larger the number of associated R&D institutions. In the third and fourth stages, the Matthew effect failed. The reason may be that, as CCUS technology became relatively mature, entities with strong R&D capabilities exhibited technological lock-in based on technological monopoly, which hindered the flow of knowledge and consequently restricted the development of innovative cooperation networks. SH_hie showed a significant negative correlation in each stage except for the first. This result suggests that, when an individual R&D entity is in a passive position in a subnetwork and is greatly restricted by the core R&D institutions, the possibility of it establishing cooperative relationships with other enterprises will be lower, which will further hinder the development of innovative cooperation networks. SH_eff showed significant negative correlations in the third and fourth stages, suggesting that the core R&D institutions in a subnetwork are a monopoly having no direct connections with other enterprises, which to some extent inhibits the further evolution of cooperative networks.

Table 3 ERGM model fitting results.
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Goodness-of-fit test

The robustness of the model was tested by the optimal goodness-of-fit test, and the indicator “edge_wise shared partners” was selected as the comparative indicator to validate the capacity of the simulation model to emulate the real network. The goodness-of-fit test results of the model are shown in Fig. 4, in which the black line represents the statistical characteristics of the real network and the gray line and the box plot depict the network characteristics of the simulation model. It can be seen that there was no significant difference in statistical results between the four-stage network evolution simulation model and the real network, suggesting that ERGM can produce stable estimation results and capture the key aspects of generating innovative cooperation networks in the field of CCUS technology in China.

Fig. 4
figure 4

Model fit goodness of fit analysis.

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Discussion

This study systematically analyzes the evolutionary trajectory and intrinsic driving mechanisms of innovation collaboration networks in China’s CCUS technology. Empirical results reveal that the evolution of these networks exhibits distinct phase-specific characteristics and is driven by multi-layered factors.

Structural and evolutionary features of china’s CCUS innovation collaboration network

China’s CCUS innovation collaboration network has undergone a complete evolutionary process, transitioning from a fragmented exploratory structure to a star-shaped radiation pattern, then to a multi-core organized framework, and finally toward a cross-domain synergistic and integrated architecture. This progression is reflected not only in the substantial expansion of network size (number of nodes and edges), but more significantly in the structural transformation of network quality. The CCUS innovation collaboration network in China is characterized by a continuous decline in overall network density alongside a steady increase in the average clustering coefficient. The ongoing influx of new participants has diluted the global connectivity of the network, indicating both an expansion of collaborative scope and greater diversity of entities involved. Meanwhile, collaboration intensity within local clusters has strengthened, resulting in the formation of several tightly connected and highly efficient research groups. This finding contrasts sharply with patterns observed in industries such as biomedicine and photovoltaics, where network scale and average clustering coefficient typically rise simultaneously47,48. Unlike innovation networks driven primarily by market forces, the development of CCUS technology relies heavily on national strategic planning49. Since the introduction of China’s National Energy Technology Major Demonstration Project Management Measures in 2012, diverse entities including central state-owned enterprises and research institutes have rapidly entered the field. However, policy-driven innovation collaboration is characterized by targeted assignment, prioritizing closed-loop cooperation within key demonstration projects rather than fostering random connections across the entire network50. While this approach enhances local clustering, it also restrains the increase in global network density. Furthermore, CCUS requires tight coordination across capture, transportation, and storage stages, exhibiting strong technological coupling and significant geographical lock-in effects (e.g., immovable storage sites)51. These constraints encourage the formation of stable triadic collaborations shaped by both technical and geographic factors, driving up the clustering coefficient while limiting extensive cross-technology and cross-regional connections.

Results indicate that, unlike market-driven sectors where small and medium-sized innovative enterprises operate with agility and flexible collaborations, central state-owned enterprises hold an overwhelmingly dominant position in the CCUS field. Although policies encourage collaboration, central state-owned enterprises prioritize technology confidentiality, safety accountability, and supply chain control. They prefer forming deep partnerships within their internal branches and subsidiaries or with long-term stable partners over open network-wide collaboration. This behavioral pattern further exacerbates the distinctive network morphology characterized by high clustering coefficients and suppressed density growth. The unique interplay of strong policy intervention, high technological coupling, and concentrated market structure in the CCUS field makes it impossible to directly apply standard network evolution models from general high-tech industries to CCUS innovation collaboration networks.

Driving effects of endogenous network structures on evolution of china’s CCUS innovation collaboration network

In terms of driving factors, this study reveals that endogenous network structures serve as a core force shaping the formation of CCUS innovation collaboration networks. Results from the ERGM indicate that star-shaped structures and closed triads consistently exert significant positive driving effects throughout the evolutionary process. Star-shaped structures reflect network expansibility and a core-periphery architecture, enabling central nodes to access more resources52. This aligns with the “preferential attachment” mechanism proposed by Barabási et al.53, which suggests that new nodes tend to connect to already well-connected core nodes in the network, leading to a “rich-get-richer” Matthew Effect. This phenomenon corroborates the observation that, during the early and middle stages of CCUS technology development, core institutions were typically large central state-owned enterprises or top universities with substantial resources. Leveraging their strong financial capacity, policy support, and technological advantages, they naturally became the preferred partners for various innovation entities, thereby driving the formation and consolidation of a star-shaped radiation network.

Closed triads reflect network transitivity and facilitate information exchange among collaborating organizations54. Coleman’s closure theory argues that closed triadic relationships foster cooperation and enhance relational robustness between nodes through established trust, shared norms, and effective social sanctions55. Stable triadic relationships based on mutual trust and reciprocity help initiate and consolidate new collaborative ties, facilitating the evolution of the network from a simple “core-periphery” star model to a complex, multi-tiered “core-semi-core” structured pattern. This constitutes a key micro-level mechanism through which the CCUS innovation collaboration network deepens and develops. Core actors within star-shaped structures provide stability as organizers for the formation of closed triads, while the widespread presence of such triads enhances the overall stability and collaborative efficiency of the star-shaped network. Together, they help mitigate the high levels of technological and market uncertainty.

Driving effects of node assortativity on the evolution of china’s CCUS innovation collaboration network

The assortative selection mechanism among nodes explains how partner preference influences the formation of innovation collaboration networks in the CCUS field. ERGM results show that geographical adjacency consistently promotes collaboration throughout the entire evolution of the network, which aligns closely with findings from other studies8. This highlights the fundamental role of geographic proximity in reducing communication costs, facilitating tacit knowledge spillover, and enhancing regulatory coordination. Notably, this facilitating effect does not diminish as the network matures. One possible explanation lies in the immovable nature of CCUS storage sites, which creates a strong region-locking effect51. CCUS innovation heavily depends on physical infrastructure: carbon capture sources such as power plants and steel mills are fixed in location, pipeline infrastructure involves massive investment and path dependency, and geological storage sites are constrained by strict geological conditions56. Such strong geographical and technological coupling makes proximity essential for on-site debugging, equipment maintenance, and risk sharing. As a result, the economic and technical benefits of geographical proximity continue to outweigh its costs, making it a stable screening mechanism for innovation collaboration.

In contrast, the effect of organizational assortment was not significant during the first three phases of network evolution and only became positively significant in the Collaboration Maturation Phase. This suggests that in the early technology exploration and demonstration stages, heterogeneous industry-university-research partnerships were the dominant model for breaking through technical bottlenecks. As the technology moved toward scaling and industrialization, collaboration between homogeneous organizations such as parent-subsidiary companies and supply chain partners became increasingly prevalent and important. Such collaborations help reduce transaction costs, share infrastructure, and mitigate market risks. Such collaborations help reduce transaction costs, share infrastructure, and mitigate market risks. In the early development of CCUS technology, the government often directly coordinated and allocated critical resources since the technology was still emerging and immature57. Policy aimed to rapidly integrate capabilities in basic research (universities and research institutes) and engineering application (central state-owned enterprises), thus intentionally fostering heterogeneous organizational collaboration58. At this stage, collaboration between similar types of organizations was limited due to functional overlap and redundant knowledge bases. As the technology entered the scaling and industrial phase, collaboration goals shifted toward improving efficiency, reducing transaction costs, and controlling the industrial chain. The advantages of homogeneous collaboration became prominent. Central state-owned enterprises, along with their subsidiaries and supply chain partners, could greatly simplify negotiation processes, unify technical standards, and enable seamless internal knowledge flow. All are core needs for operational efficiency and supply chain security. Meanwhile, university-university and institute-institute collaborations arose from the need to deeply explore fundamental scientific questions, leading to the formation of tighter academic communities focused on common research challenges.

Driving effects of node attributes on the evolution of china’s CCUS innovation collaboration network

The influence of R&D capability shifted from facilitative in early stages to inhibitory in later phases. This observed failure of the Matthew Effect contradicts findings from traditional innovation network studies, yet accurately reflects the unique nature of CCUS as a strategic high-tech field. This result diverges from Ahuja’s classical proposition that innovation network resources continuously concentrate toward core nodes55. The evolutionary trajectory of the CCUS innovation collaboration network corroborates this observation. In the initial phase, central state-owned enterprises capitalized on their policy and resource advantages to rapidly emerge as core actors. Notably, during Phases 3 and 4, despite a substantial surge in the number of R&D entities, the centralization of the degree distribution did not intensify. Instead, a trend toward multi-polarization and increased network density emerged, signifying a shift toward decentralization. This shift may be attributed to the specific industrial stage of CCUS technology. As the technology transitioned from lab-scale R&D and limited policy pilots to large-scale commercial demonstration and deployment, the complexity of innovation increased exponentially59. Mature CCUS projects require seamless coordination across the entire industrial chain, a task beyond the capacity of any single entity. The technical requirements themselves compelled deep cross-sectoral and cross-organizational collaboration. This full-chain coupling objectively counteracted the Matthew Effect in the innovation network. Furthermore, subsequent policies such as the 13th Five-Year Plan for Energy Technology Innovation (2017) intentionally promoted diverse innovation consortia to avoid technological lock-in by individual firms, facilitate technology diffusion, and reduce costs60. These policy measures actively weakened the Matthew Effect shaped by earlier monolithic policy interventions.

ERGM results further confirm that structural holes played an inhibitory rather than a facilitative role in this network. Core actors occupying structural hole positions did not serve as active knowledge brokers as predicted by Burt’s theory17. Instead, motivated by concerns over core technology protection and maintaining competitive advantage, they partially restricted cross-group information flow. This collaboration paradox, common in high-tech barrier fields where entities both need and fear collaboration, constitutes another key micro-mechanism underlying the failure of the Matthew Effect.In the CCUS domain, central state-owned enterprises (e.g., oil and power companies) occupying structural holes prioritize national energy security and emission reduction targets over maximizing innovation output through knowledge brokerage. Thus, they focus more on internal integration than external bridging. Their structural hole positions hinder rather than facilitate cross-sector knowledge integration, effectively acting as structural barriers. Therefore, the conditional failure of the Matthew Effect in the evolution of the CCUS network does not indicate a stagnant stable phase of collaboration. Rather, it signifies a transition from a resource monopoly-based elementary form to a deeply complex structure driven by technological needs and policy guidance.

This research is not without limitations. This study constructs an innovation collaboration network based on granted patent data, which effectively ensures the authenticity of collaborative relationships and the innovativeness of technological outcomes. However, it must be acknowledged that granted patent data inherently suffers from time lag. Although China’s patent examination efficiency is relatively high globally, with the average grant cycle for invention patents shortened to approximately 15 months, a delay remains unavoidable. The granted patent data up to 2021 used in this study likely reflect collaborative decisions and innovation activities formed around 2020. This implies that while the study accurately captures the evolutionary characteristics of the collaboration network driven by China’s CCUS technology demonstration projects from the end of the 12th Five-Year Plan period through the 13th Five-Year Plan period, it may not fully encompass the most recent collaborative dynamics emerging after the comprehensive introduction of the dual-carbon goals. Future research could incorporate patent application data to construct a more real-time and dynamic collaboration network, thereby capturing network changes in response to the latest policy impacts. This study acknowledges that patent count has limitations in representing innovation quality. Metrics such as citations and claims were not included, which may lead to an underestimation of high-quality non-collaborative innovations. Furthermore, variations in individual contributions within collaborative patents have not been disentangled. Follow-up studies will seek specialized database access to enable more granular analysis.

Based on the above conclusions, the following policy implications are proposed:

Macro Policy Level (National/Ministries):

  1. 1.

    Given the high technological coupling and geographical lock-in effects, it is recommended to formulate differentiated regional CCUS development policies. Priority should be given to key regions (e.g., oil fields, industrial clusters) for deploying integrated demonstration projects, so as to align innovation resources with geographic constraints.

  2. 2.

    In response to the structural characteristics of the network under policy intervention, optimize the allocation of scientific and technological resources. While continuing to support targeted major demonstration projects, establish open competitive funding mechanisms to encourage market-selected, cross-regional collaborations beyond top-down planning, thereby balancing local clustering and global connectivity.

  3. 3.

    To address high market concentration and its inhibitory effect on collaboration, strengthen innovation governance. Develop guidelines to promote intellectual property sharing and data flow in the CCUS field, and explore the establishment of fair, reasonable, and non-discriminatory licensing mechanisms for core patents to prevent technological lock-in and market barriers.

  4. 4.

    Establish effective platforms for innovation collaboration and knowledge sharing. Examples include organizing regular high-level forums and establishing a national CCUS technology innovation alliance. These initiatives will help achieve cross-organizational and cross-regional sharing of heterogeneous innovation resources and improve the quality of the CCUS innovation collaboration network.

Mesoscopic Organizational Level (Industrial Alliances, Industry Associations, Key Central SOEs):

  1. 5.

    Leveraging the key role of closed triadic structures, key central SOEs or industry alliances should take the lead in forming substantive innovation consortia or patent pools that cover the entire chain of capture, transport, and storage. Clearly define member responsibilities and profit-sharing mechanisms to stabilize collaboration expectations and reduce transaction costs.

  2. 6.

    In light of the emerging trend of organizational homophily, industry associations should develop technical standards, interface specifications, and collaboration frameworks for the CCUS field. This will reduce coordination friction among heterogeneous organizations while providing platforms and support for efficiency-driven collaboration among homogeneous organizations (e.g., upstream and downstream enterprises in the supply chain).

  3. 7.

    To mitigate the inhibitory effect of structural holes, leading central SOEs are encouraged to initiate industry-wide CCUS technology information sharing platforms or pilot testing bases. While protecting core intellectual property, these platforms can disseminate technology needs and challenges in a targeted manner to facilitate better matching between knowledge and demand across a broader network.

Micro-Entity Level (Enterprises, Universities, Research Institutes):

  1. 8.

    Innovation entities should adjust their collaboration strategies according to the stage of network evolution. Universities and research institutes should actively engage in policy-driven industry-academia-research collaboration in early stages, and strengthen inter-institutional (e.g., university-to-university) collaboration in basic research to address common scientific challenges in later stages.

  2. 9.

    Enterprises, especially SMEs, should proactively embed themselves in triadic collaboration structures or innovation consortia led by core entities. This can serve as an important channel for accessing resources, learning technologies, and mitigating risks.

  3. 10.

    Leading enterprises should reassess their knowledge management and collaboration strategies to balance technology protection and collaborative innovation. They should recognize that excessive isolation within a complex technological system may ultimately hinder overall technology diffusion and cost reduction, thereby affecting their own long-term interests.

Conclusions

This study examines the evolutionary characteristics and driving mechanisms of innovation collaboration networks in China’s CCUS technology based on patent cooperation data from 1988 to 2021 using the Exponential Random Graph Model (ERGM). The main conclusions are as follows:

First, China’s CCUS innovation collaboration network demonstrates a clear four-stage evolutionary pathway. It evolved from a fragmented exploration network in the technology emergence phase, to a star-shaped radiation network centered around central state-owned enterprises during the policy initiation phase, then to a multi-core structured network in the demonstration and promotion phase, and finally advanced to a cross-domain synergistic integration network in the industrialization phase. This trajectory reflects not only the expansion in network scale and complexity, but more profoundly, the strategic shift in national policy from technological exploration to large-scale deployment. This evolution is the inevitable outcome of combined effects of policy intervention and increasing technological maturity.

Second, the network evolution is driven by multidimensional factors whose influence varies across development stages. Among endogenous structural effects, star-shaped and closed triadic structures consistently serve as core engines facilitating collaboration, indicating that CCUS innovation requires both resource integration by central actors and stable, trust-based local cooperation. Geographical adjacency continues to exert a stable influence due to the geographically locked nature of infrastructure. Organizational homophily becomes significant only in later stages, marking a shift in collaboration logic from policy-induced heterogeneous complementarity (e.g., industry-university-research partnerships) toward efficiency-driven homogeneous collaboration aimed at reducing transaction costs. The role of R&D capability has shifted from facilitation to inhibition, leading to the failure of the “Matthew Effect”. The structural hole effect plays an inhibitory role in this network. These patterns indicate that innovation collaboration in CCUS has evolved from a resource monopoly-based elementary form into a deeply complex structure shaped by technological needs and policy guidance.