Abstract
Combined with the basic properties of the cluster innovation network, with the cluster innovation network, which can be composed of different universities that have knowledge potential difference as the research object, the knowledge transfer process is divided into four stages: knowledge externalization, knowledge sharing, knowledge innovation, and knowledge internalization, and the article constructs a knowledge transfer process model through introducing explicit knowledge and tacit knowledge conversion effect mechanism. According to the theory of complex adaptive system, the principle of network connection oriented the knowledge potential difference and the characteristic of the explicit knowledge and tacit knowledge within universities. We research the knowledge transfer process of universities using the system simulation method and focus on the evolution mechanism of the cluster innovation network’s knowledge level at knowledge externalization and knowledge sharing stage. It further reveals the basic topology structure and dynamic evolution law of universities cluster innovation network. We find that both knowledge externalization efficiency and knowledge learning ability have positive correlation with the general knowledge level of network. The evident small-world network characteristic emerges during the dynamic evolution of universities cluster innovation network. Meanwhile, there exists a coupling evolution between the knowledge level of universities and the topology structure of the cluster innovation network.
1. Introduction
In order to enhance the comprehensive strength and international competitiveness of higher education, China proposed the goal of “Double First-Rate” construction with world-class universities and world-class disciplines from a strategic perspective in 2015. Strengthening the capacity for independent innovation and further increasing the iconic innovation achievements with significant influence at home and abroad have become a crucial way to achieve the goal of “Double First-Rate.” Studies have shown that industrial clusters can positively enhance knowledge dissemination and innovation performance [1, 2]; integrating resources through network relationships can improve innovation performance [3]. Therefore, universities within the cluster innovation network through cooperation can obtain important innovation resources to stimulate innovation vitality and improve their level of knowledge.
In the era of knowledge-based economy, as the environment changes and the complexity of innovation deepens, it is difficult for individual innovation to meet innovative demands. At this time, cooperative innovation under network conditions is becoming more and more popular [4]. Meanwhile, the innovation process shows characteristics of complex knowledge network [5]. Thus, the knowledge network connected by knowledge subjects such as universities, enterprises, and scientific research institutions has become the core platform of innovation activities. Knowledge subjects integrate resources and cooperate deeply through establishing formal and informal relationships to acquire and share knowledge and information resources embedded in their internal and external networks, and ultimately achieve the purpose of creating new knowledge [6]. With the implementation of the innovation-driven strategy, the cluster innovation network has become a new model and mechanism for dealing with innovation. Strong cluster collaboration can enhance innovation capability and allow organizations to achieve their goal that could not be achieved alone [7]. As an important carrier of knowledge flow, the cluster innovation network is a self-organizing emergence in which internal and external innovation subjects of the cluster innovation network adapt to the complexity of innovation [8]. The partner selection behavior of subjects influences the evolution of the innovation network structure [9]. Network structure is a crucial factor which influences the knowledge transfer and innovation performance [10–12]. Therefore, there is a complex relationship between the knowledge transfer and the network structure in the innovation network and many studies have discussed this superficially and deeply.
Many studies showed the surface relationships between knowledge transfer and network structure: IM Taplin [13] studied network structure and knowledge transfer in cluster evolution using the methods of qualitative analysis; Fritsch M et al. [14] focused on knowledge transfer in a sample of 16 German regional innovation networks with almost 300 firms and research organizations involved and found that strong ties are more beneficial for knowledge exchange than weak ties through the case study; Kim and Park [15] constructed the knowledge diffusion process of R&D network to investigate the impact of network structure on the performance of knowledge diffusion; the results show that the small-world network is the most efficient and equitable structure toward effective knowledge diffusion. In addition, many scholars were aware of the complex network and adaptive system characteristics of multi-agent cluster cooperative networks. They analyzed the deep-rooted mechanism of knowledge transfer process and dynamic evolution law in the innovation network using modern multi-intelligent simulation methods; B He and G Song [16] established the differential dynamic model of tacit knowledge transfer efficiency and made example simulation to research how cluster network structure feature influences tacit knowledge transfer process; Wang [17] constructed the knowledge transfer diffusion process model of the cluster innovation cooperation network and analyzed the impact of individual motivation on knowledge transfer and diffusion performance using the intelligent simulation method; MA Xuejun et al. [18] built the industry alliances knowledge transfer network model with the quantitative analysis of the simulation example from a complex network perspective.
Although most studies have analyzed the relationships between knowledge transfer and network structure among enterprises within cluster innovation network from various aspects, studies on the factors affecting knowledge transfer and network evolution process in universities-oriented cluster networks are scarce. In addition, a large majority of researches take the abstract and general knowledge as the research object; they do not divide the research object into explicit and tacit knowledge and neglect the transformation influence mechanism of explicit and tacit knowledge in the process of knowledge transfer. Moreover, the above lack quantitative researches on each phase of knowledge transfer.
Therefore, based on the previous researches on knowledge network and knowledge transfer process, this study establishes the model of knowledge transfer process of universities from the perspective of the cluster innovation network and explores quantitatively conversion influence mechanism of explicit and tacit knowledge from the attribute dimension of knowledge (explicit and tacit knowledge) using complex adaptive system theory and system simulation method. Additionally, this paper focuses on the relationship between the mechanism of partner selection based on the knowledge potential difference of knowledge subjects, knowledge level, and the cluster innovation network structure in the knowledge sharing stage. Moreover, the basic topology structure and dynamic evolution law of universities innovation network can be revealed.
2. Theoretical Framework
After the concept of knowledge transfer was first proposed by Teece [19] in 1977, many scholars at home and abroad have proposed different knowledge transfer models through researching and exploring. The most representative is the SECI model presented by Nonaka and Takeuchi [20]. They first combine the knowledge attribute dimension (explicit and tacit knowledge) with knowledge transfer and propose the organizational knowledge creation spiral which divide knowledge transfer into socialization, externalization, combination, and internalization. The nature of this model is spiral structure in the process of self-transformation and mutual transformation of explicit and tacit knowledge.
At the same time, the cluster innovation network has gradually become an important platform and support for knowledge transfer and knowledge innovation among the various knowledge subjects in the cluster. Industrial cluster networks are the context of knowledge transfer between different subjects [21], so the essence of the cluster innovation network with universal characteristics of the obvious knowledge network is the knowledge network. The network structure can present complex evolutionary dynamics when knowledge transfer is within the innovation network. Meanwhile, some studies have shown that the innovation results formed by knowledge transfer in the cluster network are often larger than the results of the individual innovation [22–24]. Thus, the knowledge transfer within the cluster innovation network is a key link of cluster innovation activities. It is an important factor of the competitiveness of cluster firms, innovation, and development of industrial clusters [21]. In the whole process of transfer, the knowledge subjects in the network not only enhance knowledge levels, but also change the breadth and depth of knowledge stock [25] (knowledge potential difference) through learning, transformation, and accumulation of explicit and implicit knowledge. Marjolein CJ [26] points out that knowledge transfer behaviors are difficult to occur when knowledge potential differences of diverse subjects are too large or too small. Therefore, the changed knowledge potential differences can in turn affect cooperation relationships among subjects, thus leading to the evolution of the cluster innovation network and its topology [27], and the cluster innovation network has a significant small-world phenomenon in the process of dynamic evolution.
In the cluster innovation network, the process of knowledge transfer between subjects is not only an exchange of knowledge, but also a knowledge innovation and its spiral growth. However, knowledge transfer, knowledge innovation, and knowledge growth are closely related to the characteristics of innovation subjects. Compared with firms, universities, as a special knowledge-intensive organization, have more comprehensive knowledge, more diverse levels, and more prospective research fields. Universities have large pieces of explicit knowledge, as academic results, research data, and so on; they, especially, have formed massive tacit knowledge over a long period of time, such as campus culture, training methods, research methods, and thinking patterns of scholars or students [28]. Overall, it is generally considered that universities have unique characteristics of explicit and tacit knowledge: their tacit knowledge is a lot richer than explicit knowledge and they have low level of externalization of tacit knowledge.
This paper draws on the SECI model and combines the network connection principle of knowledge potential difference with the unique explicit and tacit knowledge characteristics of universities to establish the four-stage model of knowledge transfer from the perspective of universities’ cluster innovation network (Figure 1).
Knowledge externalization is the first stage of knowledge transfer, which is realized within knowledge subjects. It mainly converts noncoding tacit knowledge into the explicit knowledge expressed by words, graphs, formulas, and so on through coding and simulation. This stage plays a vital role in the process of knowledge transfer. Meanwhile, it is imperative to make tacit knowledge externalize before knowledge sharing stage [29], because knowledge sharing requires the necessary communication and mutual cooperation among knowledge subjects, but tacit knowledge with highly tacitness and its characteristics make it hard to be shared. The externalization of tacit knowledge can promote knowledge flow and improve knowledge transfer performance [30].
In the stage of knowledge sharing, this study assumes that only explicit knowledge can be exchanged between knowledge subjects based on the characteristics of tacit knowledge, such as tacitness, contingency, and difficulty to circulate. After the first stage of tacit knowledge externalization, it has eliminated obstacles that tacit knowledge is difficult to flow to a certain extent. When the knowledge potential difference is within appropriate range, the knowledge subjects (universities) in the network establish a learning cooperation relationship to exchange and learn explicit knowledge. As knowledge exchange constantly goes deeper, both the knowledge levels and the knowledge similarity of subjects are getting higher and higher. According to Marjolein CJ [26], if the innovation subjects’ knowledge levels are too similar or too different than each other, the cooperation will be unnecessary in the innovation cluster. At this time, the knowledge gaps between each other are getting smaller or wider until cooperation conditions are not met. In order to break through the current network and further enhance the level of knowledge, some knowledge subjects will seek new partners, which will further arouse continuous evolution of the cluster innovation network. At the same time, there will be a small-world phenomenon in process of evolution: highly clustered and small characteristic path length [31].
As the third stage of knowledge transfer, the major task of knowledge innovation is that each subject analyzes the knowledge learned from the knowledge sharing stage and interacts with its own the existing knowledge. The result of different knowledge interaction can lead to knowledge innovation [20]. Knowledge innovation is based on knowledge sharing; the new knowledge learned by various knowledge subjects will have an impact on the explicit knowledge and tacit knowledge they had before. So at this stage, explicit knowledge and tacit knowledge will innovate, thereby changing the overall level and stock of knowledge.
Knowledge internalization, as the last stage, is not only a value transformation and formation stage of the knowledge transfer process, but also a knowledge promotion and application stage. It can be regarded as the reverse behavior of externalization of tacit knowledge in form: implicitization of explicit knowledge on the basis of innovation. In this stage, knowledge subjects absorb and digest explicit knowledge and internalize it into a higher level of tacit knowledge to achieve mastery and sublimation of knowledge.
3. Model Construction
3.1. Introduction to the Model
According to Valk [32] and Hermans F [33] et al., the cluster innovation network consists of nodes, which represent knowledge subjects (universities), and links, which represent the relationships of knowledge exchange and cooperation between universities. This research assumes that the number of knowledge subjects (nodes) in the cluster innovation network is and the initial network is connectionless. Based on Pareto principle, 80% of the nodes represent universities with common level of knowledge and the remaining 20% represent universities with higher level of knowledge. The knowledge of node is divided into knowledge dimensions () and each dimension is composed of explicit knowledge and tacit knowledge according to the different attributes of knowledge.
It is assumed that nodes within the cluster innovation network have different levels of knowledge at the initial time; and of the high-level universities take random values in the range of [0.8,1], and and of the general-level universities take random values in the range of [0.4,0.8). In the whole process of knowledge transfer, we separately take the average levels of explicit and tacit knowledge within 10 dimensions to simulate (as and ).
As a special learning organization, universities’ core competitiveness lies in tacit knowledge. Compared with explicit knowledge, universities have a relatively large proportion of tacit knowledge. Therefore, we assume that the overall knowledge level of node is : the weight of explicit knowledge is and the weight of tacit knowledge is .
The average knowledge level of the cluster innovation network as a whole is
3.2. The Simulation Model of Knowledge Transfer Process
3.2.1. Knowledge Externalization
In the process of externalization, the externalization efficiency of node at time is defined as ; of each university in the cluster innovation network at time is equal in order to simplify the model. Specifically, tacit knowledge cannot be completely externalized because of the characteristics of universities’ knowledge. This research assumes that the externalization efficiency is within the scope . Meanwhile, with the continuous externalization of knowledge, will decrease to a stable limit value according to the following formula (5).
is the externalization factor and different externalization factors () correspond to different externalization efficiencies (). The larger is, the lower externalization efficiency is. On account of universities with lower degree of tacit knowledge’s externalization, the range of value for is [0.7,1]. The value of adjustment coefficient is set to through previous multiple tests and experiments.
In this stage, the levels of explicit and tacit knowledge and the externalization efficiency of node at time have a combined effect in explicit knowledge level of node at the next moment . Therefore, the tacit knowledge externalization of node is expressed as follows:
3.2.2. Knowledge Sharing
The stage of knowledge sharing is mainly the exchange of explicit knowledge among subjects according to the principle of network connection based on knowledge potential differences. Some studies point out that only knowledge potential difference among innovation subjects in a reasonable range is an important driving force for knowledge transfer [34]. According to Huang Weiqiang [9], the cooperation and exchange between two knowledge subjects in the cluster should ensure that the comprehensive knowledge gap is within a suitable range. This paper uses Euclidean distance to express the comprehensive knowledge potential difference between node and at time .
We propose and , respectively, representing the lower limit and upper limit of the comprehensive knowledge potential difference. The knowledge potential differences of the cooperative universities must meet the upper and lower limits:
This study assumes that initial network is connectionless; that is, all nodes are independent of each other. Select a node from nodes and calculate the comprehensive knowledge potential difference between node and the other node in turn (). Additionally, we suppose that the set of node where meet the upper and lower limits is . At this time, the cooperative relationships between node and nodes in the set will be established, connecting node and nodes in the set to communicate and learn explicit knowledge. In addition, the set of nodes where explicit knowledge level of a node in the set is greater than node is . In the set , we define the node whose explicit knowledge level is the highest as , as shown in formula (9). The explicit knowledge level of node can achieve ultimate level after exchanging explicit knowledge with node follows the learning rule.
The explicit knowledge level of the node at time is associated with the learning ability of node , the comprehensive knowledge potential difference between node and node at time , and explicit knowledge levels of node and at time . Therefore, on the premise of these assumptions, when subjects exchange and learn knowledge, the learning function of node over time is defined as follows according to Huangweiqiang’s research [9]:
In formula (11), is the comprehensive knowledge potential difference between and at time , indicates the explicit knowledge level of node at time , and is the learning ability of node .
This paper assumes that the knowledge level of knowledge receiver is less than that of knowledge sender. With the knowledge exchange, the explicit knowledge level of the receiver can be improved to a certain extent, but the maximum will not exceed the sender’s level. At the same time, the level of explicit knowledge of the sender remains constant. When the nodes that meet the principle of network connection based on knowledge potential difference establish cooperative learning relationships, the knowledge levels of these nodes are improved, and the overall knowledge level of the cluster network is gradually improved. Meanwhile, the comprehensive knowledge potential between nodes changes, which will prompt them to break off the previous cooperative relationships and seek new partners to continue to learn and improve the level of knowledge. Thus, at this time, we disconnect all network relationships in order for it to restore the connectionless network. Then repeat the above operation until the comprehensive knowledge potential difference of all nodes in the cluster innovation network cannot meet the principle of connection, and knowledge learning and exchange between nodes stop. The knowledge level of each node in cluster innovation network gradually converges, and the average knowledge level of the entire network tends to be stable.
3.2.3. Knowledge Innovation
The explicit knowledge learned has a subtle influence on the original explicit and tacit knowledge through knowledge exchange and sharing. Therefore, explicit and tacit knowledge will, respectively, innovate at this stage. This study supposes that the innovation ability of node has a trend of diminishing marginal returns over time, and the explicit/tacit knowledge level of node at time is affected by explicit/tacit knowledge level and innovation ability of node at time . According to Li Jinhua [35], the rule of explicit and tacit knowledge innovation of node is as follows:
is the innovation factor of node . Based on the knowledge characteristics of the university and previous multiple tests and simulation, this paper sets equal to 4. refers to the sum of observation periods of the first two stages of knowledge transfer (the knowledge externalization and knowledge sharing).
3.2.4. Knowledge Internalization
After knowledge innovation, the university could continuously integrate and accumulate new explicit knowledge and apply it to the daily learning practice of teachers and students, thereby enhancing the core competence of insiders and internalizing explicit knowledge into noncoding tacit resource to improve the independent innovation ability of universities.
In this stage, the tacit and explicit knowledge level of node and the internalization efficiency at time can affect the tacit knowledge level of node at time . Therefore, the rule of internalization is as follows:
refers to the knowledge internalization efficiency of node at time . In order to simplify the model, this paper assumes that the knowledge internalization efficiency of each node in the cluster innovation network has the same value at time , and they take values within the range of . In addition, with the continuous internalization of knowledge, could decrease to a stable limit value according to the following formula (15).
is an internalization factor that affects the efficiency of knowledge internalization. is a moderator. Based on the knowledge characteristics of universities and previous multiple tests and simulation, we assume and the range of value for is . refers to the sum of observation periods of the first three stages of knowledge transfer (the stage of knowledge externalization, sharing, and innovation).
3.3. Network Topology Statistics
Nowadays, many networks are becoming more and more complex. In order to expose the internal characteristics of these complex networks in detail, many scholars have proposed descriptive statistical indicators such as degree, degree distribution, clustering coefficient, and path length to reflect the network characteristics.
(1) Degree and Degree Distribution. The degree of node is the number of other individuals connected with node in the network. Degree distribution refers to the distribution of degrees of all nodes in the entire network, recorded as .
(2) Average Clustering Coefficient. Clustering coefficient, a local feature of the network, reflects the clustering characteristics of the entire network. The degree of node is , that is, in the network the number of other nodes that have cooperative relationships with is . There are at most edges in these nodes. The number of cooperation relationships between nodes is ; that is, the number of edges that actually exists is . At this time, the clustering coefficient of node is :
The average clustering coefficient of the entire network is recorded as , as shown in formula (17) ( is the number of network nodes):
(3) Average Path Length. The minimum number of edges connecting arbitrary two nodes and in the entire network is the path length of these two nodes, recorded as , and the average value of all in the network is the average path length, recorded as :
The average path length reflects the connectivity of the entire network. It is an important measurable index to describe the cooperation between the cross-cohesive subgroups. The more “cross-distance” connections, the more “shortcuts” of the network, and the network’s average shortest path will be greatly reduced.
(4) Small World. According to some researches, many networks in the real world have small-world property; that is, the network has a high clustering coefficient and a short average path length. Davis et al. [36] compared the parameter index of the actual network with the parameter index of the random network with the same number of nodes and the number of links and proposed the small-world entropy, denoted as .
If the average shortest path of the actual network and the random network are approximately equal and the clustering coefficient of the actual network is greater than the random network, the actual network has small-world property. In other words, when the small-world entropy is significantly greater than 1, we can judge that the actual network shows the small-world phenomenon.
4. Simulation Results
According to the above model, this paper quantitatively analyzes the mechanism of knowledge transfer in universities and how the cluster innovation network affects knowledge level using the numerical simulation method to further reveal the basic topology structure and dynamic evolution discipline of the cluster innovation network. The knowledge sharing stage emphasizes cooperative partner selection mechanisms and interactive learning mechanisms of different knowledge subjects, and this stage is also the key to the evolution of innovation network. At the same time, because of the paper’s space limit, we only select the simulation process and results of knowledge externalization and knowledge sharing.
This study assumes that the innovation network is connectionless at initial moment, and there are 100 nodes in the network (). According to Baum J A C [37], the network’s initial average knowledge level within knowledge sharing phase is different from initial average knowledge level of the literature [37], so this paper appropriately adjusts the range of the knowledge potential difference based on the research in the literature [37], and we take , through multiple tests.
The results of previous multiple tests and simulation show that the knowledge level of knowledge externalization and knowledge sharing stage could converge over a period of time. Therefore, we suppose that the total observation time of the first two stages of knowledge transfer is and the observation durations of the first two stages of knowledge transfer are , , respectively. In order to eliminate single-shot errors as much as possible and reflect the evolutionary trend more scientifically, the simulation operation is repeated 20 times for each set of the parameters, and the final result is taken as the average of 20 simulation results.
4.1. Change Mechanisms of Network’s Average Knowledge Level in Knowledge Externalization and Knowledge Sharing Stage
4.1.1. The Impact of Externalization Efficiency on the Network’s Average Knowledge Level
Knowledge externalization is the initial stage of knowledge transfer within universities. According to the model, the externalization efficiency is affected by the externalization factor . Therefore, the relationships between the externalization factor and the average knowledge level of the cluster innovation network can reflect the impacts of the externalization efficiency on the network’s average knowledge level. Meanwhile, due to the assumptions of the first stage and lower degree of tacit knowledge’s externalization of universities, this paper supposes through previous multiple tests with 20 independent simulation operations, respectively, corresponding to three different externalization efficiencies . Figure 2 shows that the larger the externalization factor , the lower the knowledge externalization efficiency . At this time, the average knowledge level of the innovation network tends to converge prematurely, and the convergence value of knowledge level is lower. Overall, the externalization efficiency shows negative relation with the convergent speed of network average knowledge level, but is positively associated with the final convergence knowledge level.
4.1.2. The Impact of Learning Ability on the Average Knowledge Level of Network
With each university finishing externalization of tacit knowledge, the overall knowledge level of the innovation network can increase, and the second stage of knowledge sharing will begin after the first stage’s knowledge level is stable and convergent.
In the process of knowledge sharing, the learning abilities of knowledge subjects are affected by many factors. Knowledge sharing is based on knowledge externalization in this paper; therefore, the average knowledge level of network in the final moment of knowledge externalization phase could affect the initial average knowledge level of knowledge sharing phase, thus impacting knowledge learning ability. In order to eliminate the contingency of research results, this study divides network’s average knowledge level at initial moment of knowledge sharing stage into two sets of data for simulation according to externalization factor ; that is, we explore the impact of different learning abilities on network’ average knowledge level when and to determine whether the two sets of results match.
When externalization factor , the network’s average knowledge level at the initial moment of knowledge sharing stage is around 0.7. We assume learning ability to analyze the evolving trend of the average knowledge level of innovation network under these four different learning abilities (Figure 3). It can be found that the knowledge levels of universities with different learning abilities show an increasing trend and converge to stable values, respectively, over time in Figure 3. When the learning ability is weak (), the network’s average knowledge level converges the slowest. When the learning ability is strong (), the network’s average knowledge level converges the fastest. The learning ability has a positive relationship with the convergence rate of the network’s average knowledge level; that is, the stronger the learning ability, the faster the convergence rate. In particular, there is not any purely positive correlation between the learning ability and the final convergence value of network’s average knowledge level. When , the larger the learning ability , the higher the final convergence level. But the convergence level when is less than that when and , which is around 0.721.
Figure 4 reveals the evolving trend of the average knowledge level of the cluster innovation network while and . The network’s average knowledge level at the initial moment of knowledge sharing stage is around 0.696. We can find that the trend shown in Figure 4 is consistent with that in Figure 3. With time, the average knowledge levels of network with five different learning abilities show an increasing trend and converge to stable values, respectively, in Figure 4. The relationship between learning ability and average knowledge level of network is as follows: the learning ability is positively associated with the convergence speed of the network’s average knowledge level. Additionally, the learning ability has a positive correlation with the final convergence value of network’s average knowledge level when . However, the convergence level when is less than that when ; at this moment, there is no positive relationship between the learning ability and the final convergence level.
The two sets of simulation results above show the same phenomenon: the average knowledge levels of the cluster innovation network under different learning abilities increase progressively with time and finally converge to steady values separately. It illustrates that knowledge sharing and learning enhance knowledge level and promote knowledge transfer performance. However, there is a gradual convergence of the knowledge levels of some universities in the cluster innovation network and other universities’ knowledge levels have wider gap. At this time, the knowledge potential differences between each other are hard to meet the principle of network connection, so the cooperative relationships between universities cannot be established and the overall knowledge level of the innovation network reaches a saturated state.
In addition, Figures 3 and 4 show that the learning ability is positively correlated with the convergence speed of the innovation network’s average knowledge level. On the contrary, the relationship between the learning ability and the final convergence value of the network’s average knowledge level is not positive. Only when the learning ability is within a limited range, the larger the learning ability , the greater the final knowledge convergence level of the cluster innovation network. If the learning ability exceeds a certain value, the final convergence value of the network’s average knowledge level drops off with the increase of the learning ability. This is because when knowledge subjects have stronger learning ability, they are satisfied with achieving the higher knowledge level quickly and lack motivation for learning new knowledge. On account of the emergence of “negative emotions,” knowledge subjects will not effectively learn new knowledge even with the continuous evolution of the innovation network, so the average knowledge level of the innovation network reaches convergence.
4.2. Basic Topology of the Cluster Innovation Network
In the whole process of knowledge transfer, only did the knowledge sharing stage occur between different universities, and the other stages are internal activities of the university.
In particular, in the stage of knowledge sharing, the nodes establish learning cooperative relationships based on the principle of network connection-oriented knowledge potential difference over time. The knowledge levels of subjects and the cooperation relationships are constantly interacting, and cooperation relationships and network structures are constantly and intricately changing before the network’s average knowledge level converges. In addition, according to the conclusions of Section 4.1, the knowledge learning ability is positively correlated with the final convergence value of network’s average knowledge level only when is within a certain range. If exceeds this range, knowledge subjects should find another way to improve knowledge level. Therefore, in order to explore how the learning ability and knowledge level affect network topology and make the conclusions bring realistic significance, this paper only discusses the dynamic evolution law of network basic topology when learning ability is within the appropriate range in the stage of knowledge sharing.
Table 1 shows the network topology parameters under different learning abilities in the earlier period () and the later period () of knowledge sharing stage when externalization factor and learning ability . The data in Table 1 are the average of 20 simulation operations independently performed.
Table 1 describes that the small world quotient (RSW) of each learning ability is greater than 1 at time , which indicates that the actual network shows the small-world phenomenon: . However, the small-world quotients under different at time are less than those at time . We can deduce that the average clustering coefficient is small and the average path length is large in the later period of knowledge sharing stage. The innovation network gradually becomes sparse, and the network’s small-world property weakens.
Table 1 is only a partial discussion of the network topology of the prenetwork and postnetwork in knowledge sharing stage. In order to explore network evolution rule more systematically and comprehensively, Figures 5, 6, and 7, respectively, depict the changes of the average path length, the average clustering coefficient, and small-world quotient of the innovation network when externalization factor and learning ability . To eliminate the influences of some uncertain factors and reveal the trend of each parameter more accurately, the data in Figures 5, 6, and 7 are the results of 20 moving averages of original data.
The commonalities of the network evolution trends under different values are as follows:
Figure 5 reveals that, with the evolution of the network in the process of knowledge sharing, the trends of the average path length of the innovation network under different learning abilities are approximately the same; the average path length increases to the first small peak at the beginning and decreases slightly soon after. Then the average path length continuously increases over time until it is stable at a higher level. Figures 6 and 7 show that, in the earlier period of knowledge sharing, the average clustering coefficients and the small-world quotients of different learning abilities present consistently the inverse evolution of the left-biased distribution, which increases firstly and then decreases. In the later period they have stabilized at lower levels, respectively.
We can combine Figures 5, 6, and 7 to explore the specific evolution of the university innovation network in the knowledge sharing phase from a global perspective:
(I) The First Period. In the early evolution, the average path length increases in a shorter period, but the path length at this time was at a lower level relative to other moments. Meanwhile, the average clustering coefficient and the small-world quotient both show the trend of rapidly rising to the peak and then decreasing. In addition, the clustering coefficient’s level at the early period is higher than other moments, and the small-world quotient is greater than 1. These illustrate that, in the early stage, there are a large number of universities with cooperative relationships in the cluster innovation network, and the network has a relatively high degree of clustering. Although a minority of key “remote-cooperations” turn into “adjacent-cooperations” gradually, which makes the average path length of the network increase slightly, the overall level of average path length is still relatively short. Therefore, the innovation network presents the particularly obvious small-world property during this period.
(II) The Second Period. The average path length begins to show a small amplitude short-term decline after the initial small-range rise. Meanwhile, the average clustering coefficient and the small-world quotient are still in the trend of decline. During this period, the network has a relatively high degree of clustering and a short average path length, and the small-world quotient is still significantly larger than 1. From the perspective of the shorter average path length and the higher average clustering coefficient, in this period, the number of “adjacent-cooperations” in the network reduces slightly, and the number of “remote-cooperations” has a small increase, which could lead to a decrease in the average path length and an increase in the degree of clustering. The network shows the significant small-world phenomenon.
(III) The Third Period. At this period, the average path length of the network begins to rise, but the increase velocity in the later stage is getting smaller and smaller. On the contrary, the average clustering coefficient and the small-world quotient decrease, and the rate of decline in the later stage is slower and slower. At the same time, small-world quotient gradually becomes less than 1 in the process of decline. These show that the number of “remote-cooperations” and “adjacent-cooperations” decreases in varying degrees. In addition, the degree of network clustering reduces, and the compactness of cooperation relationships between universities is relatively weak. Overall, the long average path length and the low average clustering coefficient indicate that the efficiency of knowledge dissemination in the cluster network is greatly reduced, and the small-world network is gradually disrupted.
In summary, in the knowledge sharing stage, with the continuous learning of universities, the innovation network is constantly evolving and shows a significant small-world phenomenon in the process of evolution.
4.3. Collaborative Evolution of Knowledge Level and Innovation Network Structure
Universities, important subjects of innovation network, decide whether to conduct learning cooperation relationships between each other according to the knowledge potential difference principle. In the knowledge sharing stage, the knowledge levels of subjects can affect the comprehensive knowledge potential differences, further influencing the cooperative decision-making processes and the evolution of the innovation network structure. Meanwhile, cooperation relationships and network structure change, which in turn affect the knowledge growth performance and the average knowledge level of the network.
It can be found from Figures 3, 5, 6, and 7 that the rising period of the average knowledge level of the innovation network is the period that small-world property of the network is significant, and the period when the average knowledge level of the network tends to be stable is the period when the small-world network gradually begins to collapse.
When the network with a relatively high clustering coefficient and small characteristic path length shows the conspicuous small-world phenomenon, the cluster innovation network cooperation is highly clustered relatively and the network distance is short. At this moment, knowledge and information transmission have high efficiency to achieve high performance of knowledge sharing. It is helpful to knowledge learning, which can further improve the average knowledge level of the network. When the small-world property begins to be inconspicuous or even gradually disintegrating, the average path length increases and the average clustering coefficient decreases. At this time, the number of “adjacent-cooperations” is more than the number of “remote-cooperations.” The network is gradually sparse. It is not conducive to knowledge learning and sharing, and the information transmission is less efficient, which could result in the average knowledge level of the network not ascend.
Conversely, the level of knowledge also affects the network topology. In the early period of knowledge sharing, the explicit knowledge levels of universities in the network are relatively low, so they have a strong desire to improve their knowledge level. At the same time, because the comprehensive knowledge potential differences of most universities meet the conditions of cooperation, they have a strong connectivity base to establish cooperative relationships. These connections make the innovation network with the small-world property: a short average path length and a high average clustering coefficient.
After a period of knowledge learning and sharing, knowledge levels of many universities are gradually improved and converge to a stable condition. At this time, the knowledge potential differences between each other are too big or too small to meet the conditions for cooperation. The dissemination of knowledge is hindered, which can aggravate the collapse of the small-world network.
Overall, there is a coevolutionary relationship between the knowledge level of university and the innovation network structure in the stage of knowledge sharing.
5. Conclusion
In order to promote the construction of “Double First-Rate,” strengthening the innovation cooperation of universities is an important way to improve the abilities of independent innovation. This requires constant knowledge interaction and transfer between universities in the cluster innovation network, and these processes could promote the continuous evolution of the network. This paper combines the attribute dimension of knowledge (explicit and tacit knowledge), the principle of network connection based on knowledge potential difference and knowledge transfer process to establish a four-stage knowledge transfer model within universities cluster innovation network, and depicts the conversion influence mechanism of explicit and tacit knowledge and the internal mechanism of knowledge transfer quantitatively using the system simulation method to further explore the basic topology and dynamic evolution rules of the cluster innovation network in the knowledge sharing phase. The study draws the following conclusions:
(1) In the stage of knowledge sharing, each university establishes the cooperative relationship based on the principle of network connection-oriented knowledge potential difference for knowledge learning. The network structure evolves constantly with the change of cooperative relationships. In addition, the innovation network shows a significant small-world property in the dynamic evolution process. In the early period of knowledge sharing, the network has a short average path length and a relatively high degree of clustering; meanwhile, the small-world quotient is significantly larger than 1. Therefore, the innovation network shows the obvious small-world phenomenon. After a period of interaction and learning, the cooperation relationships of knowledge subjects become very sparse, and the number of “remote-cooperations” is gradually reduced. At this moment, the small-world quotient of the network with a long average path length and a low average clustering coefficient is less than 1. The small-world network begins to gradually collapse.
(2) There is a coevolutionary relationship between the knowledge level of university and the innovation network: in the knowledge sharing stage, many universities improve the levels of explicit knowledge through learning and cooperation and then improve their overall knowledge levels. At this time, the knowledge gaps between some universities will be widened or narrowed, which affects the choices of partners and the evolution of the innovation network. Meanwhile, the network evolution can change the path length and clustering coefficient of the network. The short average path length and high average clustering coefficient appeared in the evolution enhancing the compactness of network cooperation, which greatly improves the efficiency of knowledge transfer and learning, and further affecting the average knowledge level of the network.
(3) In the knowledge externalization stage, there are certain correlations between the externalization efficiency and the average knowledge level of the innovation network: The network’s average knowledge level increases at first and then converges to a stable value in the process of externalization of tacit knowledge. Meanwhile, the knowledge externalization efficiency is negatively correlated with the convergence speed of the network’s average knowledge level and positively associated with the final convergence value. Therefore, universities should improve the efficiency of knowledge externalization through reducing the externalization factor appropriately, thus improving the average knowledge level of the innovation network. For example, in the stage of knowledge externalization, under the premise of not infringing on intellectual property, university researchers can perfect the process of knowledge coding and establish corresponding knowledge databases actively to distill the experience and knowledge accumulated in the ordinary practice process into a clear knowledge mapping structure and so on for the exchange and sharing of knowledge in the next stage.
(4) In the knowledge sharing stage, the average knowledge levels of the network under different learning abilities show a similar trend, increase, and after a certain period of time converge to a stable value. In addition, the learning ability has a positive relationship with the convergence speed of the network’s average knowledge level. Specifically, only when the learning ability is within a certain range, it is positively correlated with the final convergence value of the network’s average knowledge level. If this range exceeded, this positive relationship does not exist.
Therefore, while universities improve their learning abilities actively, they should pay attention to the fact that when the learning ability is raised to a certain level, the knowledge agents lack motivation to learn new knowledge for what they think that their levels are high enough, because they reach the higher knowledge level relatively quickly. The average knowledge level of the cluster innovation network reaches a saturated state. At this moment, universities should seek other new partners outside the cluster actively to continue establishing cooperative relationships.
Data Availability
The simulation data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This research was funded by Projects of the National Social Science Foundation of China (Grant no. 18BGL020) and the Master’s Creativity and Innovation Seed Fund Project of Northwestern Polytechnical University (Grant no. ZZ2018200).