Evaluating tacit knowledge diffusion with algebra matrix algorithm based social networks

https://doi.org/10.1016/j.amc.2022.127125Get rights and content

Highlights

  • Algebra matrix method integrates the structural factor and the state information of social networks.

  • Monte Carlo simulation experiments verify the effectiveness of the algebra matrix evaluation.

  • The evaluation deviations of diffusion threshold are shown best performance comparing with three popular mean field methods.

  • The weighted average strategy is proposed as applications.

Abstract

Tacit knowledge is the knowledge existing in human brain which is not easy to be recorded or quantified, and often is learned in the face-to-face interactions. The tacit knowledge diffusion depends on the decision-making of tacit knowledge owners, and the expression of explicit knowledge carriers. However, the comprehensive influence of the tacit knowledge owners, explicit knowledge carriers and the relations of them were not attracted enough attention. In this paper, an algebra matrix method is used to integrate the multidimensional information of network structures and the nodes’ states. By the algebra matrix method, the diffusion threshold of the tacit knowledge is calculated, which is called algebra matrix evaluation. This evaluation method is proven to be effective by comparing with Monte Carlo simulations on three types of artificial networks and five reals. With applications of the algebra matrix evaluation, we construct a co-author network according the data of the academic papers from 1980 to 2017 on Aminer platform, and define states of tacit knowledge owners and the explicit knowledge carriers by the scholar’s career lengths and the paper’s cited quantities respectively. It is found that the thresholds of tacit knowledge diffusion are decreasing with the expansions of the scale of the largest connected components, whether tacit knowledge diffuses in the co-author networks or in the largest connected components. And with the evolution of cumulative co-author network, the diffusion thresholds of tacit knowledge in the largest connected component decrease in ladder-like with unequal steps. Furthermore, it is find ignoring the state factor will lead to the deviation in the evaluation of tacit knowledge diffusion thresholds, which is 16.33% in the largest connected components and 45.07% in the whole network.

Introduction

Knowledge diffusion improves the efficiency of knowledge applications and innovations in the whole society [1], [2]. Knowledge are divided into explicit knowledge and tacit knowledge, where explicit knowledge is the knowledge with public features [3] easily identified and coded [4], while tacit knowledge is embedded in the organizational system leading difficult to be explained, transferred or coded [3], [5]. Studies have shown that tacit knowledge is very important in terms of knowledge reserves [6], knowledge value [7] and knowledge function [8], [9] etc. Therefore, a reasonable understanding of tacit knowledge diffusion will not only help to improve organizational efficiency [10], but also help to improve organizational performance [11], thereby promoting the production of technological innovation [12].

Because the path of tacit knowledge diffusion is not clear and the carriers of tacit knowledge are various, it is difficult to evaluate the difficulty of tacit knowledge diffusion. How to use the interaction between disseminators to quantify the evaluation of tacit knowledge diffusion has become a challenging work [13], [14]. The interaction between disseminators makes the tacit knowledge diffusion the result of human subjective consciousness [15]. Because of the interaction of disseminators, social network analysis can be an effective method to quantify the difficulty of tacit knowledge by calculating the threshold of tacit knowledge diffusion in social networks [13], [16], [17]. Scholars introduced random theory into the dynamic model to evaluate the diffusion threshold of tacit knowledge through numerical simulation [18]. The process of tacit knowledge diffusion is similar to the process of epidemic spread [19], so two common dynamic models of epidemic spread were modified to evaluate the diffusion of tacit knowledge, which are susceptible-infected-susceptible (SIS) model [17], [19] and susceptible-infected-removed (SIR) model [20]. On this basis, a variety of dynamic models of tacit knowledge diffusion were proposed, including ‘potential knowledge recipients’-‘potential knowledge diffusion individuals’-‘knowledge diffusion individuals’-‘knowledge immunes’ (SEIR) knowledge diffusion model [21], susceptible-infected-hesitation (SIH) knowledge diffusion model [22] and so on. Although these dynamic models based on dynamic differential equations can effectively evaluate the diffusion of tacit knowledge, there are some common problems: (1) The results of dynamic simulation are random, which needs to waste a lot of computational power to simulate many times; (2) The simulation results are greatly affected by the initial parameter setting; (3) Due to the limitation of parameter setting and process iteration, the dynamic model is difficult to fully apply the real data.

How to integrate the real information of tacit knowledge and evaluate its diffusion threshold independently of subjective parameters, which may be a meaningful research idea. In real tacit knowledge diffusion, the three most important components are diffusion paths [16], [23], tacit knowledge owners [15], [24] and explicit knowledge carriers [25], [26]. Although the diffusion path of tacit knowledge is not easy to be observed directly, the structure of social networks provides manifestation of the possible paths [13], [21], [27]. In the social network with the possible diffusion path as edges and individuals as nodes, nodes play the role of knowledge base and filter [28]. The embeddedness of diffusion individuals and their own attributes will affect the knowledge diffusion [29]. What’s more, explicit knowledge and tacit knowledge are constantly transformed through the spiral flow relationship (socialization, externalization, combination and internalization) [25]. Tacit knowledge will also be revealed with the explicit knowledge carrier. In conclusion, when evaluating the diffusion threshold of tacit knowledge, in addition to the possible diffusion path, the self attributes of tacit knowledge owners and explicit knowledge carriers should not be ignored.

Therefore, this paper proposes a evaluation method based on algebra matrix to evaluate the diffusion threshold of tacit knowledge, which is called algebra matrix evaluation. In the evaluation, the algebra matrix is used to integrate the multi-dimensional information of structure and state, and the self-consistent equation is further used to describe the micro process of tacit knowledge diffusion. The contributions in this work can be summarized in five aspects: (1) The algebra matrix method is used to integrate the tacit knowledge’s multi-dimensional information including the structural factor of social network and the state information; (2) The weighted average strategy is proposed to expand the applicability of the algebra matrix evaluation; (3) A Monte Carlo simulation experiment based on the real situation are designed to verify the effectiveness of the algebra matrix evaluation; (4) Combined with the paper data from 1980 to 2017 provided by Aminer platform, the impact of large-scale components on the diffusion of tacit knowledge is analyzed; (5) Compared with three common mean field dynamics methods, the evaluation deviations for diffusion threshold are estimated in the largest connected component and the whole network, respectively.

The rest of this paper is organized as follows: In Section 2, the algebra matrix method is used to integrate the social network structure, the states of tacit knowledge owners and the states of explicit knowledge carriers. In Section 3, based on the micro process of tacit knowledge diffusion, the algebra matrix evaluation is proposed to evaluate the diffusion threshold, and compared with Monte Carlo simulation based on real situation to verify its effectiveness. In Section 5, using the data of papers from 1980 to 2017 provided by Aminer platform, we define the state information of tacit knowledge owners and explicit knowledge carriers by the academic career length and the cited amount of papers respectively, and analyze the tacit knowledge diffusion in the real network. Finally, in Section 6, discussion and conclusion on this work is presented, and future works are also discussed.

Section snippets

The algebra matrix

Tacit knowledge diffusion is regarded as a social interaction process between the sharers and the receivers [30], [31], which mainly includes diffusion paths [16], tacit knowledge owners [24] and explicit knowledge carriers [26]. In this section, the algebra matrix method is used to integrate and quantify these multi-dimensional information of tacit knowledge diffusion.

Evaluating tacit knowledge diffusion

In the previous section, the multi-dimensional information about network structure and node state is integrated by algebra matrix method. In this section, we focus on the giant knowledge diffusion component (simply mark it as giant component) formed in the process of tacit knowledge diffusion based on these integrated information, and evaluate the diffusion threshold of tacit knowledge, of which the evaluation process is called algebra matrix evaluation. Finally, the effectiveness of the

Effectiveness analysis of the algebra matrix evaluation

In this section, we design a Monte Carlo simulation experiment to verify the effectiveness of the algebra matrix evaluation with four types of networks, random, scale-free, small world and real social networks.

Applications of the algebra matrix evaluation

The previous section shows the effectiveness of algebra matrix evaluation. So, we apply this evaluation method to find out the tacit knowledge diffusion on co-author networks. Generally, co-authorship of scholars is considered as an important bridge of tacit knowledge diffusion [23], so the co-author network is certainly looked as a proper path of the knowledge flow [21], [27]. By the co-author network, scholars are looked as the tacit knowledge owners, and academic papers are regarded as the

Discussion and conclusions

The explicit knowledge and the tacit knowledge constitute the complete knowledge system. However, the explicit knowledge is easy to encode [3], so it can be found by the text content of publications [4]. The tacit knowledge is often embedded in the organization, which is difficult to quantify [5]. The tacit knowledge owner is the decision maker in the process of tacit knowledge diffusion [15], and the explicit knowledge carrier is an important part of tacit knowledge manifestation [25].

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    This work is supported partly by National Natural Science Foundation of China(No.72171136).

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