Evolution Characteristics of Advanced Nonferrous Metal Industry Patent Cooperation Network in China from the Perspective of Multilayer Network

,


Introduction
Te advanced nonferrous metal industry is one of the strategic emerging industries. Developing an advanced nonferrous metal industry not only helps to promote the adjustment of China's current economic structure and the upgrading of industrial structures but also deeply afects the efectiveness of building an innovative country in China. In recent years, the Chinese government has given great policy support to the advanced nonferrous metal industry. China's advanced nonferrous metal industry has made rapid development and great progress, but there is still a big gap compared with international giants in the core technology feld of the industry.
Te patent is an important means of technological innovation and achievement transmission and exchange, and it is also an important index to judge the degree of technological innovation. Patents have an important impact on the development and technological breakthroughs of related industries. Patent innovation is the driving force of technological development, which is mainly refected in optimizing patent layout, promoting technological innovation, and realizing industrial applications. Te development of the modern manufacturing industry cannot be separated from cooperative innovation, and the need for cooperative innovation in the advanced nonferrous metal industry is more prominent. Patent cooperation is an important form of in cooperative innovation, which can provide important innovation power for the development of enterprises. By studying the patent innovation network, we can understand the development trend of technological innovation, the layout characteristics, and the evolution laws of patents in China's advanced nonferrous metal industry. Te innovation and development status of advanced nonferrous metals can be scientifcally analyzed and reasonable suggestions can be put forward.
In recent years, more and more nonferrous metal manufacturing enterprises have cooperated with universities and research institutes in R & D and have jointly applied for patents on the background of emerging and cross-integrated new technologies. Tey spontaneously form a patent cooperation network, which can realize resource sharing and complementary advantages. Tis kind of patent cooperation network can greatly reduce the innovation cost and risk and improve the technological innovation ability of an industry. However, at present, the exploration and utilization of patent cooperation networks in China's nonferrous metal manufacturing industry are far from enough, and the innovation and aggregation efect of patent cooperation networks have not been fully exerted. Tus, exploring, utilizing, and optimizing patent cooperation networks to improve industrial technological innovation ability has become an important way for China's advanced nonferrous metal industry to shorten the technological gap between China and international oligarchs and break the technological blockade. With the development of China's advanced nonferrous metal industry, the innovation network of China's advanced nonferrous metal industry, including the knowledge network and cooperation network, has changed signifcantly and become more complex. So, what are the evolution characteristics of the patent cooperation networks and knowledge networks in China's advanced nonferrous metal industry? In the evolution process of a cooperative network of advanced nonferrous metals, which enterprises and research institutions are the key nodes to grasp the general direction of technology and how do their composition structures change? What are the distribution of technology felds and the evolution law of technology hot felds in China's advanced nonferrous metal industry? Tese are the problems worth studying. Te purpose of this study is to reveal the evolution law of its structural characteristics by constructing the innovation network of China's advanced nonferrous metal industry and to provide suggestions for optimizing the innovation network and strengthening technological innovation. Wang et al. pointed out that enterprise innovation is double embedded in the knowledge network composed of knowledge elements and the social network formed by the cooperative relationships of R & D personnel, and these two networks are decoupled [1]. Te process of combining knowledge elements is the production process of innovation behavior [2], and all knowledge elements are connected in the process of combination, forming a knowledge network [3]. Innovation is actually the interaction process of the innovation subject's knowledge base and the combination mode, and the structural characteristics of the knowledge network represent the combination potential of core knowledge felds [4], which in turn becomes an important factor afecting the innovation performance of enterprises.

Research on Multilayer Innovation Network.
From the perspective of social attributes of innovation activities, enterprises embedded in cooperative networks can provide favorable resources for enterprise innovation. Te innovative behavior of enterprises needs to be realized through the process of expanding and deepening the specifc social network [5]. It is found that enterprises in diferent positions in the network have diferent degrees of control over resources and information. Cooperative network structure and relationship characteristics will have a certain impact on cooperative innovation behavior and performance, resulting in nonequilibrium behavior of innovation subjects [6,7] and diferences in innovation performance [8]. In fact, the innovation activities of enterprises are multidimensional. Te knowledge network and cooperation network in which R & D personnel are located have their own unique operational characteristics, which will have diferent impacts on innovation activities. At present, most of the research on the evolution characteristics of innovation cooperation is based on patent data to analyze its evolution characteristics or patterns from a single network level.

Research on the Evolution of Innovation Network.
In terms of innovation network evolution, existing scholars mainly conduct research from three aspects. First, focus on the cooperative relationship between universities and research institutes, and explore the evolution of cooperative networks at diferent stages through the cooperative publication of papers and works. For example, Balconi et al. [9] analyzed the role of university professors in the Italian inventor patent cooperation network; Lissoni [10] found that universities occupy a core position in the patent cooperation network and have a stable cooperative relationship with other types of inventors; Li et al. [11] found that comprehensive universities, science and engineering universities, and energy-based enterprises occupy the core position in the school-enterprise patent cooperation network. Te second is to study the evolution of the innovation network of strategic emerging technology industries, involving information foundations, intelligent manufacturing, biomedicine, and other industries. For example, Zhang et al. [12] from the software service industry, Cao et al. [13] from the new energy automobile industry, Li et al. [14] from the satellite and application industry, and Chen et al. [15] from the chip industry, respectively, confrmed this point. Tese research felds belong to national strategic emerging industries. Te research on these strategic emerging industries is helpful in improving the comprehensive innovation level of China. But unfortunately, these studies have not involved the advanced nonferrous metal industry. Te third is to study the structure and evolution of the regional patent cooperation network. For example, Ejermo and Karlsson [16] believed that geographic distance is a key factor afecting patent cooperation networks, and there is generally a phenomenon of intraregional aggregation in patent cooperation networks. Pan et al. [17] studied the patent cooperation networks in 31 provinces of China and found that geographical distance would have an impact on the linkage of patent cooperation networks. However, other scholars put forward diferent views. For example, Wilhelmsson [18] found that cities with denser populations and more diverse industrial structures tended to have lower levels of patent cooperation; Zheng et al. [19] constructed the cross-city patent cooperation network of Fujian, Xiamen, and Quanzhou, measured the order of network evolution by using the concept of "entropy," and found that the cross-city cooperation network showed an obvious entropy increase in the evolution process.

Research on the Innovation Network of the Nonferrous
Metals Industry. Te advanced nonferrous metal industry is a national strategic leading industry and an important part of new materials. Its innovation ability is crucial to the transformation and development of downstream industries such as aerospace, rail transit, electronic information, and automobiles to the high end of the industrial value chain, so it is worth studying. Concerning the research of the advanced nonferrous metal industry, some scholars study the path of industrial development and innovation. Tian [20] proposed to strengthen the innovation capacity building of the industry, strengthen the knowledge alliance and technology alliance, and realize the integration of technology and management. Choose the path of independent innovation, enhance competitiveness by participating in international market resources, and improve the efciency of the nonferrous metal industry. Lin et al. [21] combined the exploratory single case study method and studied the path of both exploratory innovation and utilization innovation in the process transformation of typical research institutes in the rare metal industry. It is found that the engineering center has become the key link in the transformation from exploratory innovation to utilization innovation. Research on the nonferrous metals innovation network. Zhou et al. [22] combined chaos theory to expound on the chaotic characteristics of the innovation network of nonferrous metal industry clusters. Too strong or too weak aggregation capability level of integrated units is not conducive to the development of a nonferrous metal cluster innovation network. In the development process of a cluster innovation network, it is necessary to adjust the evolution speed of the cluster innovation network by the strength of its aggregation ability. It is proposed that nonferrous metal cluster enterprises can be divided into four stages: generation, growth, maturity, and decline in the life cycle of the cluster innovation network. Te above research on the advanced nonferrous metal industry provides a useful reference for this study.
"Triple Helix" innovation theory is an innovation theory established by Etzkowitz and Leydesdorf in 1995 [23]. Te "Triple Helix" theory borrows the concept of biology and puts forwards that all three parties can be the main body of innovation, and that the three parties cooperate and interact closely in innovation. At present, the "Triple Helix" innovation theory has been widely used in academic circles to evaluate the collaborative interaction and dynamic evolution of universities, industries, and governments (including scientifc research institutions) [24]. Many scholars have introduced the "Triple Helix" theory into the innovation network research of industry, education, and research [25,26].
Terefore, based on the "Triple Helix" theory, enterprises, universities, and research institutes can be regarded as three types of innovation subjects, with the support of the government and other relevant institutions, and carry out innovation cooperation activities based on a clear division of functions. In this paper, the "Triple Helix" theory is used for reference, and the "Triple Helix" theory is introduced into the research framework of China's advanced nonferrous metal innovation network.
To sum up, the existing research on the evolution of innovation networks has provided a solid foundation and benefcial enlightenment for this study. However, there are few kinds of research on the combination of advanced nonferrous metals and innovation networks. Moreover, in the feld of advanced nonferrous metals, scholars mostly start from a static perspective. Comprehensive, systematic, and dynamic research on the patent status and patent cooperation network of the industry needs to be deepened.
Terefore, based on the data of patent cooperation applications of the advanced nonferrous metal industry, this study uses the social network analysis method and Gephi network visualization to analyze the current situation of the nonferrous metal industry in China. Te patent cooperation network and knowledge network are constructed from the perspective of the multilayer network, analyzed from the dimensions of the patentee, knowledge element, and geographical distribution, and reveal the structural characteristics and evolution laws of patent cooperation in the advanced nonferrous metal industry from multiple dimensions. It provides a reference for optimizing the patent cooperation network of the advanced nonferrous metal industry, enhancing its technological innovation, and formulating an industrial development strategy.

Research Design
3.1. Research Methodology. Tis paper adopts research methods such as patent bibliometrics, social network analysis, and data visualization. It uses the social network analysis software and its visualization functions such as Gephi and Python to construct the topological structure diagram of patent cooperation and the heat map of patent technology theme evolution in China's advanced nonferrous metal industry. Also, analyze the network structure index, network structure evolution, and technology topic evolution. Te indicators for measuring the patent cooperation network of advanced nonferrous metal industry mainly include the following: (1) Network size, that is, the number of nodes in the network, refects the size of the network. Te larger the value, the larger the network scale.

Mathematical Problems in Engineering
(2) Te number of network edges, that is, the total number of connections produced by cooperation among network nodes, refects the network structure relationship. Te larger the value, the more complex the network structure. (3) Te average path length is the number of edges in the shortest path between any two nodes i and j in the network. d ij is the distance between nodes, and the average of all the distances between nodes is the average path length of the network, which refects the average distance between two nodes in the network (Watts and Strogatz collective dynamics of "small world" networks [J]. Nature, 1998, 393 (6684): 440-442). Te larger the value, the sparser the network, and the lower the transmission performance and efciency of the corresponding network. Te calculation formula is (4) Te average clustering coefcient, which is a measure of the density of nodes in the network, refects the average value of the clustering coefcients of all nodes in the network. Te larger the value, the easier it is for adjacent nodes to establish cooperative relations. Te calculation formula is l i refers to the actual number of edges between all nodes connected to node i.
where the number of nodes is n and the actual number of edges is l, which refects the closeness of the network relationship. Te larger the value, the closer the network structure and the closer the relationship between network members. (6) Network diameter is the maximum distance between any two nodes in the network. Te larger the value, the sparser the network, and the lower the transmission performance and efciency of the corresponding network. Te calculation formula is where i and j represent any two nodes. According to this, the patent search expression of the advanced nonferrous metal industry is determined. Te document points out that the technologies covered by the advanced nonferrous metal industry include high-precision copper, pipe, rod, and wire profles; high-precision copper and tubes, rods, and linear materials; aerospace highstrength aluminum alloy forgings; high-strength and highconductivity copper materials; electrolytic copper foil, rolled copper foil, electronic copper, medical titanium alloy, metal fber porous materials, porous titanium and titanium alloy, foam copper, aluminum, nickel, nonferrous metal fber porous materials, etc. Second, according to the patent search expression, patent data are retrieved through the PatSnap patent database, and 1018491 original patent data are obtained and downloaded. Tird, invention patents contain a higher knowledge level of inventors and more value, and are more representative than utility model and appearance patents. Terefore, this study only selects invention applications and authorizes invention patents. Te remaining 259579 patents were obtained. Finally, screened patents with more than 2 original patent holders and then continued to exclude patents containing natural-person applicants. A total of 34116 cooperative invention patents in the advanced nonferrous metals industry were obtained as the data basis of this study. Since there is at least an 18-month time lag from patent application to publication, and invention patents tend to take longer from application to publication, the data set in this study is selected up to 2020 as a reference. Because the patent application data for the advanced nonferrous metal industry frst appeared in 2002, the scope of this study is from 2002 to 2020. From Figure 1, it can be seen that the number of joint patent applications for advanced nonferrous metals in China is increasing year by year, and the technological development of an industry will be directly afected by various policies issued by China. Tis study divides the period of joint patent applications into four development stages  Te "13th Five-Year Plan" for the development of the nonferrous metals industry, promulgated by the Ministry of Industry and Information Technology, outlined eight major tasks, including implementing an innovation drive, accelerating industrial restructuring, vigorously developing high-end materials, promoting green sustainable development, improving resource supply capacity, promoting deep integration of the two industries, actively expanding application felds, and deepening international cooperation. Te nonferrous metals industry entered a new stage of development after the Fifth Plenary Session of the 18th CPC Central Committee. At this stage, it changed from rapid development to highquality development, and the number of patents increased as a whole. (4) 2017-2020 is a period of stable growth or a growth bottleneck period. At this stage, although the number of cooperative patent applications still maintains high-intensity cooperation, the growth rate is slow, far from the rapid development of the previous stage. Tis may be related to technological bottlenecks and lagging economic development during the epidemic.

Sample Selection and Data
According to the above analysis, based on the patent data of the cooperative application, this paper explores the evolution characteristics of the cooperative patent in the advanced nonferrous metal industry from three aspects: the type of original patentee, the region where the original patentee is located, and the technical subject areas involved in the cooperative patent application. Te aim is to maintain a stable level of technological innovation for enterprises in the industry during the normalization of the epidemic situation, thus promoting the core competitiveness of enterprises.

Analysis of the Characteristics of the Overall Industrial
Cooperation Network. According to the sample patent data, the patent cooperation network of China's nonferrous metal industry from 2002 to 2020 was constructed by using Gephi0.9.2 software, as shown in Figure 2. Te cooperative patentees are divided according to the year and imported into Gephi 0.9.2 software in the form of point relationships and edge relationship, respectively. In the diagram, nodes represent types of principals that cooperate with each other. Te nodes are divided into four types, which replace enterprises, universities, research institutes, and natural peoples with diferent colors. Te size of a node represents the number of links between the node and other nodes, that is, the cooperation strength of the node. Te connection between nodes represents the cooperative relationship, and the thickness of the connection represents the frequency of cooperation between linked nodes. Te thicker the connection, the more frequent the cooperation between nodes in this research period. Generally, the larger the node value, the larger the degree value of the node, and the wider the cooperation range; the thicker the connecting edge, the greater the cooperation frequency between adjacent nodes, that is, the more stable the cooperative relationship between adjacent nodes. As shown in Figure 2, the patent cooperation network of China's advanced nonferrous metal industry is Mathematical Problems in Engineering disconnected as a whole. Some nodes occupy the core position in the network, forming a larger subnet and several small subnets. Te topological structure indicators of patent cooperation in China's advanced nonferrous metal industry from 2002 to 2020 are shown in Table 1. It can be seen that many nodes in the network diagram have not yet formed direct connections; the degree of patent cooperation is not sufcient; and the network vitality is insufcient. Most patent applicants have little cooperation and weak connections, and some key applicants act as intermediaries to form a tie to transmit information and connect with other nodes.
Centrality analysis is a key tool to measure the importance of network nodes. Tis study selects two indexes, degree centrality and betweenness centrality, to explore the important nodes in the patent cooperation network of China's advanced nonferrous metal industry from 2002 to 2020. Te top ten sample invention patent applicants with degree centrality and betweenness centrality are shown in Table 2. Applicants with a strong degree of centrality have a higher position in the network, and they have more subjects to cooperate with, which leads to cooperative relations and makes the network closer. Applicants with a strong betweenness centrality have a strong ability to infuence the whole network through cooperation. Some applicants show high status in both centralities, such as State Grid Corp. and Tsinghua University, which rank at the forefront in both centralities; that is, they have higher status in the network and greater infuence on the whole network. Te four evolution analysis charts show the following:

Analysis of Four-Stage Evolution Characteristics of Co
(1) Over time, the intensity of cooperation has gradually increased. In the frst two stages, there is mainly small-scale cooperation. For example, two or three enterprises cooperate and do not form a complex cooperation network; in the latter two stages, there   are a large number of small-scale centralized cooperative relationships with certain nodes as the core of cooperation. Tis shows that enterprises fnd the limitations of their technology and knowledge in the development process and begin to try to fnd a more stable cooperative relationship. Tis relationship can not only help enterprises to open up new technical felds and enhance their technical breadth and depth but also share the uncertainty and risk of technological innovation in the cooperation network. Tis will greatly reduce the loss of interest that enterprises need to bear due to innovation failure.
(2) Te evolution of research subjects is more in line with the trend of integration of industry-university-research. Colleges and universities have more patent knowledge and rich theoretical resources, but there is no way to transform patented technology well without product demand and fnancial strength. Enterprises have the economic strength to bring patented technology to the ground, but a lack of knowledge support from patent developers leads to the lack of patented technology. Te full combination of industry-university-research is helpful to realize the collaborative transformation process from patent knowledge to product proft. We can see from Figures 3 to 6 that in the initial stage, there is more cooperation between natural persons and enterprises. However, over time, more and more cooperative relations have been formed, with universities as the "stamens" and various types of enterprises as the "petals." Tis relationship can promote the fow and transformation of knowledge and technology, thus enhancing the success of invention patents in enterprises and the efciency of patent transformation in colleges and universities.
To further analyze the structural changes of the patent cooperation network of advanced nonferrous metals, the structure index of the advanced nonferrous metal patent cooperation network is measured by using the social network analysis method. Te change in topological structure characteristics is shown in Table 3.
Te network nodes refect the network scale. As can be seen from Table 3, the scale of the patent cooperation network in China's advanced nonferrous metal industry is building up. Te network scale values show that the value of network nodes in stage 1 is 275, that in stage 2 is 1025, that in stage 3 is 2088, and that in stage 4 is 2567. From stage 1 to stage 4, the number of network edges has the same trend as that of network nodes, but the change speed of network edge number is more elastic than that of network scale. Tis can be refected by graph density, which decreases gradually with the change of stages, which shows that the cooperation relationship and cooperation times between network nodes are increasing.
Te average clustering coefcient refects the close relationship between the whole network. Te clustering coefcients of the four stages are much higher than the network density of the same stage, which shows that the establishment of an invention patent cooperation relationship in China's advanced nonferrous metal industry is not a random choice. Tere is preferred connectivity, and a stable cooperative relationship is gradually formed. Te network diameter and average path length are also rising, which shows that the cooperation network of the Chinese advanced nonferrous metal industry is becoming more and more sparse. Te increase of network nodes in the network makes the distance between nodes far away, which leads to the decline of network transmission performance and efciency of network nodes. Tis shows that although there are more and more subjects participating in cooperation in this feld in China, there is still a large cooperation space among innovative subjects. Generally speaking, the four stages of the evolution of the network have the characteristics of a high clustering coefcient and a small average path distance, showing a distinct small-world efect. Tis is conducive to the sharing of resources and information in the network and facilitates the exchange and cooperation between applicants.

Evolution Analysis of Important Nodes.
From the analysis of cooperative networks, it can be seen that the networks in each stage are comparable. Select two indexes, degree centrality and betweenness centrality, to analyze the Mathematical Problems in Engineering top ten nodes of the two indexes in each stage. It can refect the importance of refecting nodes and analyze the changing characteristics of important nodes in each stage. As shown in Table 4, from the point of view of degree centrality, the most active applicants are enterprises, universities, and scientifc research institutions, which form a relatively stable cooperation mode of "industry-universityresearch." From the point of view of centrality value, from the initial company as the main core to the later university as the core, the weight of universities is getting bigger and bigger. From 2002 to 2007, there was more patent cooperation related to the petrochemical industry, which made Sinopec and its research institutes rank 1 and 2, respectively, and the proportion of enterprises, universities, and scientifc research institutions was equal; from 2008 to 2011, the composition structure of patent applicants is similar to that of the frst stage, and enterprises still occupy an important position. However, it can be seen that Zhejiang University and Tsinghua University have gradually become the subcore nodes of the network, indicating that universities have    According to each stage of betweenness centrality, it can be seen that the composition structure of applicants is still dominated by enterprises, universities, and research institutes, and the value of betweenness centrality gradually increases in diferent stages. Te infuence of the third and fourth stages is more obvious, and the control power of the network is stronger. From 2002 to 2007, enterprise applicants accounted for half, which had strong control over the network, followed by universities, which showed relatively weak infuence; from 2008 to 2011, similar to the previous A24 stage, the applicants with more patent cooperation are still enterprises, and most of them are concentrated in companies in the felds of petroleum, chemical industry, and natural gas. Also, the betweenness centrality value increases, which shows that it has stronger control power than the frst stage in the network; from 2012 to 2016, there are a large number of college applicants, occupying strong network control, but enterprises still have the strongest leading patent cooperation ability; from 2017 to 2020, the number of applicants from colleges and universities has increased in both the number and the intensity of control, which can efectively infuence patent cooperation. It can be seen that the ranking structure of the betweenness centrality and the degree centrality of the network is diferent, and the universities have increased the ranking of the two types of centralities. It refects that colleges and universities are playing an increasingly important role in the network and have gradually acquired strong control power, which can efectively infuence patent cooperation. Some applicants have a position before the exam in both types of centralities, such as China Petrochemical Corporation, Tsinghua University, and China National Petroleum Corporation. It shows that these members play an important intermediary role in contacting other members, building a "bridge" for cooperation among other members, and grasping the general direction of technical cooperation.

Evolution Characteristics of Cooperative Patent Application Technology Field.
In order to have a deeper understanding of the felds involved in patented technology and the R & D intensity invested in each feld in the advanced nonferrous metal industry, Python is used to draw the thermal map of patented technology theme evolution and Gephi0.9.2 is used to draw the patented technology cooccurrence map. We can visually analyze the depth and cooccurrence of technology. Figures 7-10 represent technology-intensive felds, technology-tentative areas, and technology-developmental areas, respectively. In the fgures, the horizontal axis represents the felds where patented technologies are distributed; the vertical axis represents the passage of years; and the color progressive bars on the right represent the number of patented technologies from less to more. In the heat map, we can see the development process of technical felds vertically, and we can see the development and changes of various technical felds with the change of years horizontally. From Figure 7, we can see that the technology-intensive distribution areas of the advanced nonferrous metal industry are B01, B21, B22, B23, C01, C07, C09, C22, C23, and H01. Te overall total amount is more than 800. Te top three in total are B01 (general physical or chemical methods or devices), H01 (basic electrical components), and C01 (inorganic chemistry), with 7001 times, 6444 times, and 5176 times, respectively. It can be seen from the fgure that the evolution of various technical felds shows a trend from shallow to deep, and these technical felds are the main research felds of the advanced nonferrous metal industry. Figures 8 and 9 show the evolution characteristics of technical topics in diferent felds at the frequency of 0-10. From the ordinate point of view, this part of the feld spans a wider range, with a total of 72 categories, but the total number is only 840 times, which belongs to a wide range but a small number of tentative technical felds. Tis feld is divided into two types of technologies with diferent characteristics. One is research that advances with time and keeps continuity, and the research intensity increases year by year, such as C30 (crystal growth), E21 (drilling of soil or rock; mining), G06 (calculation; reckoning or counting), etc. Te patented technologies in these felds are likely to grow into patented technologies in developmental felds and auxiliary intensive technology felds through continuous cooperation and development; the other is that it occasionally appears in the progress of time, forming intermittent research. Also, the total amount is very small, for example, C05 (fertilizer; fertilizer manufacturing), C06 (dynamite; matches), A23 (food or food products not included in other categories; and their handling), etc. Te actual efect of patented technology inventions in these felds is not great, or it is difcult to research and develop, and the benefts are small, so this kind of technology does not have good research value. Figure 10 shows the technical felds in the frequency range of 0-80, and the number is about one-tenth of the technology-intensive felds, which play an auxiliary role in patents in the intensive felds. Te number is about 8 times that of the tentative feld, which belongs to the feld with higher research value and signifcance. Similar to the tentative feld, there are two types of technologies in this feld. One is a technology that may become an intensive technology feld in the future, such as C25 (electrolytic or electrophoretic processes; equipment used). Tis kind of technology shows the phenomenon of continuous research with time. Te research intensity is more than that of previous years, and it also invests more in research than other technologies. Tere is a great research gap, but it should have its own research value and signifcance. Enterprises, universities, and research institutes can increase research on this part of technology. Te other is an experimental development technique that shows signs of disappearing as it matures over time, with a few studies appearing early on, such as H04 (electrical communication technology). Or there is the phenomenon of staged technology research and development, such as B32(layered products). Tis kind of technology does not have strategic support for the innovation and development of enterprises. Terefore, enterprise should reduce their research and development investment in this kind of technology.
From the above analysis, we can see that technological innovation institutions should keep continuous research in intensive technology felds to lay the foundation of innovation competitiveness. Enterprises that master the core competitive advantages of the industry can have good basic development abilities in the advanced nonferrous metal industry. In addition, the innovation subject can also separate some innovation resources, cooperate with enterprises, universities, and research institutes with heterogeneous resources, and then seek the blue ocean feld of technology in the feld of technology development and tentative felds. Good development research in this feld can provide stable technical assistance advantages for enterprises and even occupy the leading resources in the future development of technical felds, providing a high-quality guarantee for their innovation competitiveness.

Analysis of Four-Stage Evolution Characteristics of
Knowledge Networks. Trough the analysis of the abovementioned patent categories, we can see which categories the advanced nonferrous metal industry should conduct indepth research. Within each category, the success and availability of patent research and development can be enhanced by studying the cooperative research and development of patent subcategories. Tis paper is based on the subclass data of the IPC classifcation number of a cooperative patent application. Te Gephi 0.9.2 is used to construct the IPC co-occurrence network diagram of patented technology to analyze the characteristics and evolution law of the knowledge network. Figures 11-14 show the co-occurrence evolution process of IPC classifcation numbers in four stages, and Table 5 shows the co-occurrence topological index of cooperative patented technologies in the advanced nonferrous metal industry. Te node in the network represents a subclass of the IPC classifcation number, and the larger the node, the more times the IPC appears; the connection represents a co-occurrence of two classifcation numbers, and the thicker the connection, the more co-occurrence frequency of nodes at both ends of the connection, which shows that the two technologies are more closely related.
With the evolution process diagram and the co-occurrence topological indicators shown in Table 5, it can be analyzed as follows: (1) Te network scale is increasing gradually, from 112 nodes at the beginning to 325 nodes, which shows that the cooperative patents of the advanced nonferrous metals industry contain more and more knowledge elements. It can also be seen from the growth of network connections and the average degree that the frequency of co-occurrence between technologies has also increased by a greater margin. It shows that the intensity of technological co-occurrence is getting bigger and bigger, and patents gather more and more technical cooperation. Tis requires enterprises to seek more partners with heterogeneous resources for patent technology cooperation. (2) From the network diameter and graph density, we can see that the technology co-occurrence network is getting closer and closer. With the increasing number and complexity of network scale and network connections, the network diameter decreases step by step, and the graph density increases and stabilizes gradually, which shows that the technology is characterized by overall dispersion and local tightness. More research on IPC technology subcategories included in intensive technology felds is conducive to the promotion of core competitiveness.
(3) From the average clustering coefcient and average path length, it can be seen that the four stages have the characteristics of a high average clustering coefcient, low average path length, strong network cohesion, and small-world efect. Tere are relatively close technologies. R & D institutions should identify these technologies and cooperate in research, and cooperate to develop more comprehensive patents, thereby enhancing their innovation ability and core competitiveness.

Conclusion
Taking the advanced nonferrous metal industry as an example, this study constructs the invention patent cooperation network, the heat map of patent technology theme evolution, and the patent technology IPC co-occurrence network of the advanced nonferrous metal industry in China from the perspective of cooperation network and knowledge network from 2002 to 2020. Furthermore, we deeply study the structural characteristics and evolution law of the  invention patent network in the advanced nonferrous metal industry and draw the following conclusions and give relevant suggestions.

Crucial Findings.
(1) Te scale of patent cooperation networks in China's advanced nonferrous metal industry is expanding day by day. Te network density is increasing, the network cohesion is strong, and the small-world efect is obvious. It shows the characteristics of overall dispersion and local tightness, and there are few "bridges" between groups, so the network still has great room for development. Te "Triple Helix" feature of the cooperation network is gradually obvious. In the long-term formal and informal cooperation and exchanges, universities, enterprises, and scientifc research institutes have crossed, closely cooperated, and interacted with each other, and the cooperative relationship has become more stable. Te evolution of knowledge networks over time shows the characteristics of technological dynamic changes.
(2) Patent applicants such as China Petrochemical Corporation, Tsinghua University, China National Petroleum Corporation, Zhejiang University, Baoshan Iron and Steel Co., Ltd., and Shanghai Jiaotong University are important nodes of the network. Tese nodes have more contact with other nodes, play an intermediary role, are the "bridge" for cooperation among other subjects, and grasp the general direction of technical cooperation. Terefore, these core nodes should be the key breakthrough points to guide and adjust the cooperation behavior of important nodes; with time, the structure of key nodes that play a leading role has changed from the initial enterprise-led to university-led. (3) Te total number of technology categories involved in the advanced nonferrous metal industry is increasing, and the depth is also gradually increasing. Diferent types of technology felds are presented, including technology-intensive felds, tentative technology felds, and technology development felds, which are characterized by high intensity, wide range, and steady progress.

Policy Implications.
To speed up the cultivation of China's advanced nonferrous metal industry, realize the optimal allocation of innovative resources, and improve international competitiveness, this paper puts forward the following theoretical and practical enlightenment.
(1) Te government should strengthen and guide the cooperative relationship of the "Triple Helix" subjects to promote the stability and development of the innovation network among industries, universities, and research. Te government should introduce relevant policies to promote the breakthrough of the core technology of China's advanced nonferrous metal industry, guided by industrial demand and aimed at tackling key problems with new technologies. Encourage innovative organizations to focus on the core common technologies of the industry to carry out joint research and achieve breakthroughs in the core technologies of the industry with the strong support of the government's science and technology support plan. First of all, the government should set up an incentive mechanism to actively guide research institutions such as universities and research institutes to realize the transformation of patented technology through cooperation with enterprises. Second, the government should establish a dynamic management and evaluation system for industry-university-research cooperation projects, constantly adjust the deployment of industry-universityresearch cooperation projects, and strengthen the tracking and implementation of policies. Finally, the government should improve the intellectual property system and build a long-term protection mechanism for intellectual property rights. (2) In the stage of knowledge innovation, universities have created a large number of scientifc research achievements through collaborative innovation with governments, enterprises, and research institutions. However, most of them exist in the form of papers or patents and do not transform knowledge into capital, which leads to the waste of technological innovation. Terefore, universities should give full play to their advantages in the process of knowledge innovation and extend this advantage to the feld of technological innovation to realize the capitalization of knowledge. In addition, universities and research institutions should focus on the core common technologies of industrial development to fundamentally solve the "two skins" problem of the current science and technology economy. Because they have overlapping functions in scientifc research and personnel training, they can break the original organizational boundaries and develop synergistically through the deep integration of scientifc and technological resources by integrating resources such as science, technology, and talents with universities and scientifc research institutions to promote the deep integration of basic research and applied research personnel training, which can realize the superposition of high-quality resources and complementary advantages, thus driving the sustainable development of regional economies and societies. (3) Strengthen the dominant position of enterprises in technological innovation; support enterprises to enhance their independent innovation ability; and establish and improve the enterprise-led collaborative innovation mechanism of industries, universities and research. Enterprises, as the main battlefeld and the realizing party of scientifc and technological achievements, can accelerate the process of knowledge capitalization and technology industrialization through collaborative innovation. However, most Chinese enterprises pay insufcient attention to basic research, which leads to the weak dominant position of enterprises in the innovation network, and their lack of scientifc and technological innovation ability leads to loose cooperative relations, which has become an important factor restricting the development of China's "Triple Helix" collaborative innovation system. Enterprises can enhance their innovation abilities, at the same time, they can carry out technical cooperation with other enterprises to promote the formation and implementation of patent alliances to enhance their innovation advantages. On the other hand, it can cooperate with university research institutions to realize the transformation and docking of resources and provide strong support for technological innovation and achievement transformation. (4) In practice, the government should guide advanced nonferrous metal enterprises to increase investment in basic research of core technologies in the industry through leveraged means such as fnancial subsidies and interest subsidies. Encourage enterprises to improve their scientifc research ability by building laboratories or R & D centers jointly with university research institutes.
Based on macropolicy support, the government can also build innovation carriers to participate in collaborative innovation. For example, the establishment of new industry research institutes and technology incubators. Te new industry research institute is an innovative platform for deep integration of industry, education, and research, which is jointly sponsored by key universities and research institutions of key enterprises in the industry under the guidance of the government to carry out collaborative innovation and core technology breakthroughs and tackle key problems. Te new industry research institute pays attention to the interconnection of basic research and applied research to realize the efective connection of "basic research-technological tackling-technical application-successful industrialization." Te technology incubator is one of the carriers of science and technology innovation services and the training base of innovative and entrepreneurial talents. Among them, the government provides infrastructure such as sites, as well as preferential policies, such as seed funds and taxes. A technology incubator helps to improve the conversion rate of scientifc and technological achievements and reduce the risks and costs of start-up enterprises. Trough these methods, it is benefcial to solve the dilemma of obstacles in knowledge transfer across organizations caused by the mismatch of knowledge and ability between advanced nonferrous metal enterprises and universities and research institutes in China, and fundamentally solve the phenomenon of "two skins" between science and technology and the economy.

Data Availability
Te data used for this study are available upon request.

Conflicts of Interest
Te authors declare that there are no conficts of interest.