Measuring knowledge diffusion efficiency in R&D networks

Knowledge Management Research & Practice

ISSN: 1477-8238 (Print) 1477-8246 (Online) Journal homepage: http://www.tandfonline.com/loi/tkmr20

Measuring knowledge diffusion efficiency in R&D networks Su Jiafu, Yang Yu & Yang Tao To cite this article: Su Jiafu, Yang Yu & Yang Tao (2018): Measuring knowledge diffusion efficiency in R&D networks, Knowledge Management Research & Practice To link to this article: https://doi.org/10.1080/14778238.2018.1435186

Published online: 20 Feb 2018.

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Knowledge Management Research & Practice, 2018 https://doi.org/10.1080/14778238.2018.1435186

ORIGINAL ARTICLE

Measuring knowledge diffusion efficiency in R&D networks Su Jiafua, Yang Yub and Yang Taoc a

Chongqing Key Laboratory of Electronic Commerce & Supply Chain System, Chongqing Technology and Business University, Chongqing, China; bThe State Key Lab of Mechanical Transmission, Chongqing University, Chongqing, China; cSchool of Management, Chongqing Technology and Business University, Chongqing, China

ABSTRACT

This paper investigates the issue of measuring knowledge diffusion efficiency in R&D network based on the weighted network method. For the reality of R&D networks, we integrate the node and tie weights to build a weighted R&D network model. On the basis of the weighted R&D network, the multiple factors of knowledge diffusion efficiency are analyzed, and then a novel measurement method is proposed by comprehensively embodying these factors. Furthermore, an extended application of the measurement method is proposed to identify the important members of R&D network. An example of weighted Braess network and a real-world case are employed to illustrate the applicability and effectiveness of the proposed method. Results show that the proposed measurement method can more efficiently and accurately measure the knowledge diffusion efficiency of R&D networks than the traditional methods, and its application can effectively identify the important members with great influence on knowledge diffusion.

1. Introduction In the face of fierce market competition environment, firms attach increasing importance to the knowledge complementary advantages of R&D, especially for the industries with fast knowledge and technology update (Bunduchi, 2013). R&D networks allow firms to combine the knowledge, skills, and physical assets needed for innovation to get the synergy (Awate, Larsen, & Mudambi, 2015). To this end, R&D networks should serve as conduits through which knowledge and information can spread smoothly among different collaborative actors. R&D network is essentially a social network which can connect collaboration actors on the level of individual, group, and organisation (Santoro, Borges, & Rezende, 2006). The real-world R&D networks are typically asymmetric and heterogeneous featuring that the actors have different characteristics, and the links among actors are always with different strength (Abu Ata & Dragan, 2016; Luo, Du, Liu, Xuan, & Wang, 2015). R&D is a knowledge-intensive activity covering the process of knowledge discovery, knowledge diffusion, knowledge application, and knowledge creation (Cummings & Teng, 2003). In the context of R&D networks, knowledge diffusion is a key link which can stimulate the new knowledge creation and contribute to the innovation (Lin & Li, 2010), and it is an important issue for the effective knowledge management of R&D networks.

CONTACT  Yang Yu 

[email protected]

© Operational Research Society 2018

ARTICLE HISTORY

Received 28 March 2017 Revised 15 January 2018 Accepted 29 January 2018 KEYWORDS

R&D network; knowledge diffusion; weighted network; efficiency of knowledge diffusion; member importance

Knowledge diffusion has been studied in a broad range of research directions, e.g., the key factors affecting knowledge diffusion (Cummings & Teng, 2003; Joia & Lemos, 2010), the methods to facilitate knowledge diffusion (Jeon, Kim, & Koh, 2011; Wu & Zhu, 2012) and the approaches to model the knowledge diffusion process (Yang, Hu, & Liu, 2015; Zhuang, Chen, & Feng, 2011). Although the importance of knowledge diffusion in relation to organisational performance has been extensively illustrated in various organisations, we have seen a very few formal operationalised researches on the knowledge diffusion efficiency. The existing researches mostly focused on the qualitative analysis of knowledge diffusion efficiency (Plonka, Sharp, Linden, & Dittrich, 2014; Zhang, Xie, & Lin, 2011), whereas the systematic and quantitative researches on measuring knowledge diffusion efficiency are least studied. The purpose of this study is to develop a systematic and quantitative method to measure the knowledge diffusion efficiency in R&D networks. Effective knowledge management of R&D networks calls for a comprehensive understanding of the factors of knowledge diffusion, and a practical method to measure knowledge diffusion efficiency. This work can help firms to improve the quality of decision-making in management of R&D networks. To do this, this paper will build a weighted network model which can better reflect the real R&D networks, and

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then on its basis propose a new measurement method for knowledge diffusion efficiency in R&D networks. This study aims to make the following contributions to this area of exploration: it investigates and clarifies the connections and relationships between various factors and knowledge diffusion efficiency in the context of R&D network. Moreover, from a systemic perspective, it proposes a new measurement method for knowledge diffusion efficiency in R&D networks, which can fill up the gaps of the previous studies. The remainder of the paper is organised as follows. Section 2 briefly reviews and discusses the related works. The weighted R&D network model is built in Section 3. Section 4 proposes the method to evaluate knowledge diffusion efficiency based on the weighted R&D network, and then verifies its feasibility and advantage by a classical network case. Section 5 applies the proposed measurement method to a real case. Finally, the conclusions of this paper are outlined in Section 6.

2.  Related works 2.1.  The factors of knowledge diffusion efficiency With the rapid development of Internet and information technology, knowledge diffusion can provide more and deeper mutual knowledge learning and cooperation among individuals, organisations and their networks. Although knowledge diffusion is helpful to improve the organisational performance, it is still facing barriers of impeding the effective knowledge diffusion across networks. Gilmour (2003) stated that knowledge diffusion and sharing was prone to failure in the process of collaborations, because people tended to guard or selectively share their knowledge. Haldin Herrgard (2000) pointed that the main obstacles to sharing tacit knowledge were linked with the unconsciousness of the tacit knowledge and the difficulty to express it. On the other hand, many researchers have investigated the successful factors of knowledge diffusion, such as the knowledge characteristics (Kang, Rhee, & Kang, 2010; Zhou & Li, 2012), the actor’s knowledge collaboration capability (Mu, Tang, & MacLachlan, 2010; Tang, Mu, & MacLachlan, 2010), the relationship strength among actors (Hansen, 1999; Todo, Matous, & Inoue, 2016), and the distance between actors (Binz, Truffer, & Coenen, 2014; Wang & Zhang, 2010a). Considering knowledge diffusion in R&D networks, a concerned research issue comes to the fore, that is, the connections and relationships between network properties and knowledge diffusion efficiency. Hansen (1999) addressed the effect of tie strength between people on knowledge transfer, and he found that strong ties could promote the transfer of complex knowledge. Reagans and McEvily’s (2003) research indicated that both the network cohesion and social range could promote knowledge diffusion in informal networks. Following

the above researches, Tian, Di, and Yao (2011) studied the relationship between the distribution of tie weights and network efficiency in the weighted networks, and found that the exponential distribution of tie weight could more significantly improve the network efficiency. Wang and Zhang (2013) stated that the efficiency of knowledge flow in the informal networks was very sensitive to the distribution of tie strength. The works on the relationships between network properties and knowledge diffusion inspire us that in the knowledge management, organisations can strengthen and promote knowledge diffusion by adjusting the network properties such as collaboration tie strength and knowledge collaboration willing. However, the researches on network properties mainly focus on the micro level of networks to investigate knowledge diffusion, which prevent us from a systematic and comprehensive understanding of knowledge diffusion in the context of networks. Besides the network properties, the network structure can also greatly affect knowledge diffusion efficiency. Cowan and Jonard (2004) compared the knowledge diffusion efficiency in different types of network structures. Their research results shown that the knowledge diffusion efficiency was optimal in the small-world networks. Regarding the knowledge diffusion process with knowledge innovation, Lin and Li (2010) investigated how the knowledge diffusion and growth was affected by network structures, and they indicated that the optimal knowledge transfer performance was obtained in scale-free networks. Wang, Guo, Yang, and Liu (2015) built an improved knowledge diffusion hyper-network model, and the simulation results shown the knowledge diffusion in hyper-network model was much faster than the traditional network models. The above works provide a theoretical basis to set and reform the R&D networks topology for better knowledge diffusion efficiency. However, the measurement of knowledge diffusion efficiency has been little studied seriously in the above researches. Although these researches use some indexes to measure the knowledge diffusion speed and average knowledge level, the above indexes just reflect the macro-state of knowledge diffusion in networks at a particular moment, which cannot be competent to comprehensively measure knowledge diffusion efficiency in real networks. 2.2.  The measurement of knowledge diffusion efficiency In practice, the measurement of knowledge diffusion efficiency of R&D networks plays a vital role for the effective decision and management of R&D networks (Wang & Zhang, 2010a). There are a few attempts to measuring the knowledge diffusion efficiency in some areas. Among them, in order to investigate the efficiency

KNOWLEDGE MANAGEMENT RESEARCH & PRACTICE 

of knowledge spillover, CaniŠls (2000) built a spatial knowledge spillovers honeycomb model by introducing the “learning by doing” effect into the research of regional knowledge spillover. Form the view of knowledge collaboration, König, Battiston, Napoletano, and Schweitzer (2012) developed a model to measure the efficiency and stability of R&D networks, and implied the efficient network for knowledge spillover was asymmetric and had a nested structure. Based on the smallworld network, Latora and Marchiori (2001) proposed a mathematical efficiency model to measure how well information propagated over the networks. Aiming at Co-citation networks, Liu and Rousseau (2010) introduced two notions of field diffusion breadth and field diffusion intensity to measure efficiency of knowledge diffusion by publications and citations. In the areas of regional innovation networks, organisational networks, and citation networks, the above researches all made positive attempts to propose specific methods or metrics for measuring information or knowledge diffusion efficiency theoretically and practically. Nevertheless, these works mainly studied the issue of measuring knowledge diffusion efficiency in homogeneous and unweighted networks, which means that there is no difference among the different nodes and ties in specific networks. Obviously, it does not correspond to the reality of R&D networks. For the real R&D network, researches have shown that it is with the significant heterogeneity among its nodes and ties (König et al., 2012; Savin & Egbetokun, 2013). In addition, the heterogeneity of nodes and the ties among nodes greatly influences the properties of R&D network, especially the knowledge exchange in network (Kim & Park, 2009; Liao & Yang, 2013; Reagans & McEvily, 2003). Therefore, in order to better reflect the reality, the R&D networks ought to be treated as weighted networks when studying the issue of measuring knowledge diffusion efficiency. Motivated by the above considerations, we will build a weighted R&D network model in this paper, and on its basis propose a new measurement method for the knowledge diffusion efficiency. Thus, this paper will take an approach to shed some light on the measurement of knowledge diffusion efficiency in R&D networks, which will provide managers with a decision support for knowledge management.

3.  The weighted R&D network model As stated above, in order to better reflect the real R&D networks, this paper aims to build a weighted R&D network model to investigate the issue of measuring knowledge diffusion efficiency. Reagans and McEvily (2003), Liao and Yang (2013), and Wang et al. (2015) indicated that not only the network structure, but also the properties of nodes and ties all had great influence on the performance of knowledge diffusion in networks. Back to the scenario of R&D network, its nodes

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are R&D members, and the ties are collaboration relationships among members. In this paper, the properties of nodes associated with knowledge diffusion are summarised as the individual knowledge collaboration level. Meanwhile, the properties of ties boil down to the collaboration relationship strength. The weighted R&D network model is built as the following procedures. 3.1.  The basic R&D network model The basic R&D network model is represented as RDN = (P, E). Where P = {p1 , p2 , ⋯ , pn } is the nodes set of R&D network members, and E = {eij = (pi , pj )|𝜃(pi , pj ) = 1;pi , pj ∈ P} is the ties set of collaboration relationships among members. θ(pi, pj) = 1 if member pi has collaboration relationship with pj, else θ(pi, pj) = 0. 3.2.  The method to determine node weights In R&D networks, the node weight is used to represent the individual knowledge collaboration level of each member. During the process of knowledge diffusion, the individual knowledge collaboration level reflects a member’s potential and ability to exchange and share knowledge for a R&D project or task. The individual knowledge collaboration level is the important driving factor for knowledge diffusion, which determines the efficiency and quality of knowledge diffusion to some degree (Cummings & Teng, 2003; Mu et al., 2010). For the individual knowledge collaboration level, if R&D members do not have adequate ability to transfer knowledge, the performance of knowledge diffusion will be hindered (Tang et al., 2010). Specially, when members cannot precisely communicate and exchange the knowledge they want to transfer, the knowledge will probably be distorted or lost. On the other hand, in order to diffuse knowledge effectively, the member on the each side of knowledge transfer ought to have sufficient knowledge stock and overlapping knowledge, which can help them to better span different knowledge areas and make more efficient collaborative efforts on knowledge work (Mu et al., 2010; Reagans & McEvily, 2003). Moreover, the knowledge sharing willingness also plays a vital role for the successful knowledge diffusion. Members cannot exchange and share their knowledge effectively, if they are short of enough motivation, initiative, and immersion for knowledge diffusion (Huang, Yang, Jin, et al., 2013). In short, to achieve high knowledge diffusion efficiency, the knowledge transfer capability, knowledge stock, and knowledge sharing willingness are all necessary aspects of individual knowledge collaboration level. Based on the above analysis, the individual knowledge collaboration level is further subdivided into the knowledge transfer capability (R1), individual knowledge stock (R2), and knowledge sharing willingness (R3).

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According to the subdivided factors, a decision matrix is used to evaluate and quantify the individual knowledge collaboration level. Specifically, T = [tig ]n×3 denotes the decision matrix, where tig is the evaluation information of member pi concerning criterion Rg, g = 1, 2, 3. The criterion Rg could be either subjective or objective. If Rg is a subjective criterion, for simplicity, its value could be given by decision-makers’ direct assessment or Delphi method. In addition, if Rg is an objective criterion, its value could be obtained based on the statistic data or other objective data source. Considering the commensurability among different criteria, the normalisation is necessary to deal with this problem. According to the principle of reliability, intuitiveness and simplicity, this paper applies the approach proposed by Yoon and Hwang (1995) as the normalisation method. In this method, the element of T = [tig ]n×3 could be normalised into a corresponding element of matrix T � = [tig� ]n×3 using the following formulas: �

tig =

tgmax −tig tgmax −tgmin

g = 1, 2, 3,

tig� =

for cost criteria.

(1)

tig −tgmin tgmax −tgmin

g = 1, 2, 3,

for benefit criteria.

where tgmax = max{tig |i = 1, 2, ⋯ , n }, tgmin = min

{

(2)

tig |i = 1, 2, ⋯ , n

}

.

Suppose that the weight of criterion Rg is wg, ∑3 g=1 wg = 1, g = 1, 2, 3. To determine the weights, the analytic hierarchy process (AHP) is one of the most widely used multiple criteria decision-making approach. In practice, AHP is a systematic and easy operation method to assign the weights of a set of criteria, which has received a wide attention by the researchers and practitioners (Vaidya & Kumar, 2006). Hence, AHP is applied to determine wg in this work. Then, through the simple additive weighting method, the individual knowledge collaboration level Ai, that is, the node weight, can be expressed as

∑ 3

w(pi ) = Ai =

wg ⋅ tig� , g = 1, 2, 3

(3)

g=1

3.3.  The method to determine tie weights The tie weight is used to represent the collaboration relationship strength among R&D members. The collaboration relationship strength reflects the closeness engagement of the collaboration relationship among members. The higher collaboration relationship strength makes members more willing to exchange and sharing knowledge (Li, Yang, Yu, Bao, & Xie, 2014). The closer organisational cooperation and personal relationship encourage members to invest more time and effort on

knowledge diffusion. In R&D networks, the collaborations among members inherently contain two kinds of relationship. One is the formal collaboration relationship generated from the organisational relationship among members based on R&D project or task, and the other one is the informal collaboration relationship which is produced from the social relationship and personal communication among members (Li et al., 2014; Liao, Ye, & Wu, 2011). It should be noted that the formal and informal collaboration relationship are not separated from each other in a collaboration tie, and they are in the status of intergrowth and coexistence (Allen, James, & Gamlen, 2007; Liao et al., 2011). In other words, the formal collaboration relationship is often accompanied by the informal relationship among members, and vice versa. Based on the above analysis, we attempt to obtain the collaboration relationship strength from the view of formal and informal collaboration relationships. In the practice of R&D, The formal collaboration relationship typically occurs and accumulates in members’ project or task collaboration (Liao et al., 2011). Feng, Jiang, Fan, and Fu (2010) stated that in R&D teams, people favoured the members with whom they had successful collaboration experience before. Kaihara and Fujii (2008), and Gulati (1998) also shared the same conclusion by empirical study. The above researches manifest that the project collaboration experience is helpful to improve the formal relationship among members. Therefore, we assume that members who have cooperated more R&D projects together will have better collaboration relationship than those who have cooperated less. In order to obtain the formal relationship strength, we add together the strengths of ties derived from the projects that are cooperated by a particular pair of members. Thus, the weight Fwij, which denotes the formal collaboration relationship strength between members pi and pj, can be expressed as (Newman, 2001):

Fwij =

∑ 𝛿ik 𝛿jk k

Nk − 1

(4)

where 𝛿ik =1, if member pi is a participant of project k, otherwise 𝛿ik = 0. Nk denotes the quantity of participants of project k. We explicitly do not consider the projects with single-participant (Their inclusion would make Fwij wrongly defined in Equation (4)). This method is further illustrated by a simple example in Figure 1. The calculated value of Fwij may not be within [0,1]. Hence, Fwij should be normalised using the following formula:

Fwij� =

Fwij max(Fwij )

(5)

On the other hand, the informal collaborative relationship is mainly produced in the social relationship and personal communication among members, which

KNOWLEDGE MANAGEMENT RESEARCH & PRACTICE 

1

1

2

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Synthesising the value of formal and informal collaboration relationship strength, the collaboration relationship strength Sij among pi and pj, that is, the tie weight, can be obtained by:

3

w(pi pj ) = Sij = 𝜇 × Fwij� + 𝜈 × Iwij� 1/2

+

1/3

+

1/2 = 4/3

Figure 1. Members A and B have cooperated three projects that are labelled 1, 2 and 3. The three projects, respectively, contain 2, 3 and 2 members. The tie between A and B accrues weights 1/2, 1/3 and 1/2 from the three projects, for a total weight of 4/3.

is always concomitant with the formal collaboration relationship in a same tie (Li et al., 2014). According to the social network theory, betweenness centrality is the common index to measure individual social relationship influence (Zhou, Jin, Zhang, et al., 2016). Specifically, betweenness centrality reflects the significance of node’s location in whole network and the influence of node on information flow (Magaia, Francisco, Pereira, & Correia,, 2015). In the R&D network, the informal collaboration relationship among members is always accompanied with information exchange. Based on the above analysis, betweenness centrality is appropriate to measure the individual social relationship influence in the context of R&D network, and we define it as the informal collaboration relationship influence of R&D member in this paper. Based on the social network theory, the informal collaboration relationship influence of member pi can be expressed as:

Bi =

∑ 𝜓st (i) 𝜓st s≠i≠t

(6)

where ψst denotes the quantity of shortest paths between members ps and pt, and 𝜓st (i) denotes the quantity of shortest paths between ps and pt which walk through pi. Barrat, Barthelemy, Pastor-Satorras, and Vespignani (2004) and Karsai, Juhász, and Iglói (2006) found that the tie weight had a positive correlation with the influence of nodes at each end of the tie. The relationship can be expressed as wij = (ki kj )𝜃, where ki and kj denote the influence of nodes, and θ is a parameter of specific network. According the above researches, the informal collaboration relationship strength Iwij can be obtained by: √ Iwij = Bi ⋅ B j (7) The value of Iwij may not be within [0,1], thus Iwij should be normalised by the following formula:

Iwij� =

Iwij max(Iwij )

(8)

(9)

where μ and ν are, respectively, the weights of formal and informal collaborative relationship strength, and μ + ν = 1. 3.4.  The weighted R&D network model Finally, integrating the node and tie weight into the basic R&D network model, the weighted R&D network model (WRDN) can be expressed as:

WRDN = (P, E, w(pi ), w(pi pj ))

(10)

4.  The measurement method of knowledge diffusion efficiency In the complex network theory, the path length is an important parameter to depict the network topology structure. As suggested by the researches on relationship between the path length and knowledge diffusion (Reagans & McEvily, 2003; Singh, 2005), the performance of knowledge diffusion decreases with the increasing of the path length. Motivated by this conclusion, Liu, Zhang, Chan, et al. (2009), and Wang and Zhang (2010b) introduced the path length as an index to measure knowledge diffusion efficiency in unweighted network. However, in unweighted network, the path length is incompetent to measure the knowledge diffusion efficiency. Specifically, the situation when pairs of nodes have same path length faces the dilemma that equal path length cannot distinguish the difference of knowledge diffusion efficiency between these pairs of nodes. The reason why the path length fails to measure knowledge diffusion efficiency mainly lies in that the nodes and ties are homogeneous in unweighted network, and the path lengths will easily slip into homogeneity. In contrast, the weighted path length can markedly overcome the above dilemma of the unweighted path length, and its relationship with knowledge diffusion has more practical significance. Therefore, based on the weighted R&D network model, the weighted path length will be introduced firstly. Additionally, the properties of node and tie both have significant influence on the knowledge diffusion efficiency, specifically the individual knowledge collaboration level and collaboration relationship strength (Reagans & McEvily, 2003; Wang & Zhang, 2013), which should get due and adequate attention. Finally, comprehensively considering the multiple factors of the node and tie weights and the weighted path length, a new knowledge diffusion efficiency measurement method for R&D network will be proposed in this research.

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4.1.  The weighted path length In the context of unweighted network, the path length among two nodes is defined as the number of ties on the shortest path of the two nodes. The path length implies the distance and cost of knowledge exchange among members. There is a negative correlation between the path length and knowledge diffusion among members. Recently, because of the more reality, the weighted network has received more and more attentions by researchers (Liao & Yang, 2013; McAssey & Bijma, 2015; Tian et al., 2011). The path length in weighted networks has also got wide and deep investigations (Dijkstra, 1959; Opsahl, Agneessens, & Skvoretz, 2010). Dijkstra (1959) proposed an effective algorithm that could get the paths with least resistance, which could be applied to the networks whose tie weights represented costs of transmission. In Dijkstra’s work, the weights are dissimilarity weights, and the bigger weights represent the farther relationship between two nodes. Conversely, the weights in weighted R&D networks are similarity weights, which means that the bigger the weight is, the closer the relationship between two nodes is. Hence, the weights need to be reversed before applying Dijkstra’s algorithm to obtain the shortest paths in R&D networks. Here, we introduce Newman’s (2001) improvement of Dijkstra’s algorithm to identify the weighted path length dw(i,j) between pi and pj.

⎞ ⎛ ⎟ ⎜ 1 1 d (i, j) = min ⎜ � � +⋅⋅⋅+ � � ⎟ (11) ⎜ w pi ph w ph pj ⎟ ⎠ ⎝ w

where ph denotes the mid-nodes between pi and pj. The average path length is defined as the average value of the path length between any two nodes in network. In unweighted network, the average path length can be obtained by the following formula:

L=

∑ ( ) 2 d i, j N(N + 1) i≠j

(12)

where N is the number of nodes in network, and d(i, j) is the shortest path between pi and pj. Then, we can further get the weighted average path length by the following equation:

Lw =

∑ w( ) 2 d i, j N(N + 1) i≠j

(13)

4.2.  The knowledge transfer effect between two nodes The nodes and ties are the core elements of network, and knowledge basically transfer through the ties between the nodes at each end. Therefore, the investigation of knowledge transfer effect between two nodes is the

important foundation for the research on knowledge diffusion efficiency of the whole network. Knowledge transfer effect is defined as the degree of change of members’ knowledge status, stock, and level that is caused by knowledge exchange and transfer among members. As analysed above, the individual knowledge collaboration level is an important aspect that can improve the performance of knowledge exchange and transfer in R&D networks (Huang et al., 2013; Mu et al., 2010). Similarly, the collaboration relationship strength has a positive relationship with knowledge transfer and sharing (Hansen, 1999; Wang & Zhang, 2013). The path length reflects the cost for knowledge transfer among member, which has a negative relationship with knowledge transfer among members (Hansen, 1999). CaniŠls (2000) developed a knowledge spillover honeycomb model to measure the knowledge spillover effect among actors, which has been extensively used in the regional knowledge management. CaniŠls’ model did well to explain the influence of knowledge stock, knowledge learning ability, knowledge distance and knowledge stock gap on knowledge spillover, and could effectively measure the knowledge spillover effect. Considering the similarity in connotation with knowledge transfer, knowledge spillover is sometimes studied as the equivalent with knowledge transfer. Hence, we borrow from CaniŠls’ knowledge spillover model and its modified models (Zhang, 2016; Zhu & Han, 2008) to obtain the knowledge transfer effect using the following formula: ) ( Ai Aj ⋅ Sij (14) Tij = w d (i, j) + 1 where Tij denotes the knowledge transfer effect coefficient between member pi and pj. According to the Equation (14), the value of Tij is within [0,1]. A larger value of Tij (near 1) implies higher knowledge transfer effect between pi and pj, whereas a lower value (near 0) is the opposite. 4.3.  Measuring knowledge diffusion efficiency in the whole R&D network Knowledge diffusion efficiency reflects the speed and quality status of knowledge exchange and diffusion in the whole R&D network. To measure the knowledge diffusion efficiency in R&D network, the efficiency of network will be firstly introduced in this work. The efficiency of network is proposed by Latora and Marchiori (2001) to measure the efficiency of information exchange in networks. This model can well depict the relationship between network structure and information exchange efficiency in unweighted networks. The model can be described as: in a network RDN, the information exchange efficiency eij between node i and j can be expressed as the reciprocal of their distance dij, that is, eij = d1 . Then, averaging the information exchange ij

KNOWLEDGE MANAGEMENT RESEARCH & PRACTICE 

efficiency of all pairs of nodes in network, the efficiency of network E can be obtained by the following formula: ∑ 1 ∑ eij d i≠j∈RDN i≠j∈RDN ij (15) = E= N(N − 1) N(N − 1) Based on Latora and Marchiori’s work, Baggio and Cooper (2010), Vragović, Louis, and Díaz Guilera (2005) applied the efficiency of network to measure the knowledge and information diffusion efficiency in real networks. Nevertheless, this method is proposed aiming at the unweighted networks, which is not appropriate to the weighted networks. To address this issue, Tian et al. (2011), and Li et al. (2014) tried to modify the efficiency of network to apply for the weighted networks, and they mainly used the tie weight to revise the path length. It should be noted that these modifications can only reflect the influence of tie weight, e.g., line load, communication frequency and knowledge flow resistance, on network efficiency. As for the knowledge diffusion efficiency in R&D networks, it is affected by multiple factors of the path length, node weight and tie weight (Reagans & McEvily, 2003; Wang & Zhang, 2013). The above efforts, which only considered tie weights, are obviously hard to reflect the real and accurate knowledge diffusion mechanism and process. Motivated by this consideration, this paper introduces the knowledge transfer effect coefficient to modify the efficiency of network to measure the knowledge diffusion efficiency in weighted R&D networks. Specifically, the knowledge transfer effect coefficient Tij is used to replace the information exchange efficiency eij between two nodes in model of the efficiency of network. Then, the new measurement metric, that is, the efficiency of knowledge diffusion, can be expressed as: ∑ ∑ eij Tij i≠j∈WRDN i≠j∈WRDN (16) = EKD = N(N − 1) N(N − 1) where EKD denotes the efficiency of knowledge diffusion of the whole R&D network. The new metric of efficiency of knowledge diffusion comprehensively integrate the factors of the path length and network size, individual knowledge collaboration level and collaboration relationship strength. Therefore, it will be used as the main metric to measure the knowledge diffusion efficiency in R&D networks. 4.4.  The application of the metric of the efficiency of knowledge diffusion In the management of R&D networks, identification and ranking the important members is a key issue, which is helpful for managers to implement the targeted member management. Based on the metric of efficiency of knowledge diffusion, an extended application is further proposed to locate and rank the important R&D network

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members. In this method, the importance of a R&D network member, pi ∈ WRDN , is obtained according to the relative drop of efficiency of knowledge diffusion by removing pi from the R&D network (Li et al., 2014; Nagurney & Qiang, 2008). Then, the importance value I(pi ) of member pi can be obtained by the following formula:

) ( ΔEKD EKD(WRDN) − EKD WRDN − pi (17) I(pi ) = = EKD EKD(WRDN) where WRDN – pi is the resulting network, when pi is removed from WRDN. This method can identify the important members with significant influence on the efficiency of knowledge diffusion in R&D networks. In practice, for the stability and effectiveness of R&D networks, it has great practical significance to find and manage these important members with great impact on knowledge diffusion. 4.5.  The comparison between efficiency of knowledge diffusion and efficiency of network on Braess network As mentioned above, we insist that the efficiency of knowledge diffusion is more competent for the weighted networks than the efficiency of network, because the former is a systematic measure that embodies multiple factors of knowledge diffusion efficiency. For the verification purpose, a contrast test is executed to compare the two measurement methods as well as their applications on identifying and ranking of important members based on an example of weighted coupled Braess network, which has seven nodes and 10 ties (Figure 2). Firstly, let us calculate the two measures. The efficiency of knowledge diffusion is 0.126, whereas the efficiency of network is 0.694. The importance and the ranking of the nodes are, respectively, given in Table 1. It is easy to see that the efficiency of knowledge diffusion and efficiency of network show quite different results, regarding the importance rankings of the nodes in the weighted coupled Braess network. Strikingly, the importance values and rankings of nodes 2, 3, 5 and 6 are same, and cannot be further distinguished by the efficiency of network, as well as the nodes 4 and 7. It is due to the shortcoming that the efficiency of network solely depends on the unweighted path length and reflects the general structural importance of nodes. Conversely, the efficiency of knowledge diffusion measure and rank the importance of nodes with specific and differentiated importance, because it integrates the multiple factors of weighted path length, individual knowledge collaboration level and collaboration relationship strength among members, which can comprehensively reflect the real status of knowledge diffusion in R&D network. The different results of the two measures explicitly explain that the multiple factors do matter the knowledge diffusion

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Figure 2. A weighted Braess network. Table 1. Importance and the ranking of the nodes in the weighted coupled Braess network.

Node 1 2 3 4 5 6 7

Importance value from the efficiency of knowledge diffusion 0.779 0.513 0.476 0.310 0.425 0.503 0.335

Importance ranking from the efficiency of knowledge diffusion 1 2 4 7 5 3 6

efficiency, and an appropriate and competent knowledge diffusion efficiency measurement method for weighted networks should comprehensively integrate these factors.

5.  Case study In this section, a real case is presented to illustrate the proposed weighted R&D network model and the measurement method of knowledge diffusion efficiency. Table 2. The weight criteria for weighted R&D networks of XM. Node weight

Criteria Individual knowledge stock (R1) Knowledge sharing willingness (R2) Knowledge transfer capability (R3)

Quantification Linear combinations of work experience and Knowledge Database contribution Expert assessment Total number of problems solved by cooperating with other members

5.1.  Case background XM is an innovative technology company in China, which concentrates on the areas of intelligent hardware and electronic productions. It is very successful in the R&D of smartphones and other intelligent products. To obtain more competitive edge, XM strongly support employees to build project-based R&D networks. In practice, the measurement of knowledge diffusion efficiency is a very concerned issue of XM, so that the R&D network can be appropriately and effectively managed.

Importance value from the efficiency of network 0.795 0.326 0.326 0.360 0.326 0.326 0.360

Importance ranking from the efficiency of network 1 3 3 2 3 3 2

The case study was conducted at four larger R&D teams of XM, which focused on developing software for smartphones and had a total of 162 members at that time. We selected these four R&D teams because each of these teams could be regarded as a complete R&D network itself, which could be responsible for most knowledge management activities concerned the software development projects or tasks. Therefore, much of the knowledge diffusion among members was considered to occur in these teams. In addition, the author’s academic group has a stable practice and research collaboration with the software development department of XM, which is helpful to gather necessary data. Information for building the R&D networks of the four teams was collected by the survey that was executed among the team members. Specifically, the egocentric technique was applied to find the important knowledge contacts of each member. In doing so, the members needed to answer the question who were the important partners of knowledge exchange in their R&D activities. The respondent could nominate up to four contacts in answering the question. Using the collected information, the R&D networks of the four teams could be built. In order to effectively carry out the knowledge collaboration works, XM has set up a well-performing knowledge collaboration system (KCS). According to the resource integrated in KCS, the node weight criteria proposed in this paper were classified into subjective and objective criteria based on the characteristic of criteria (Table 2). Thereinto R2 was classified as subjective criterion, and its values were given by expert evaluation with a nine-point Likert scale, ranging from the very bad to

KNOWLEDGE MANAGEMENT RESEARCH & PRACTICE 

very good. R1 and R3 were categorised as objective criteria whose values were obtained by the data in KCS. It should be noted that in order to assure the reliability of expert evaluation on R2, the experts mainly considered the items of personal feature, interpersonal trust, team culture and knowledge heterogeneity to evaluate the knowledge sharing willingness (Huang et al., 2013; Li, Zhu, & Lai, 2010). On the other hand, for the tie weight, the cooperated project information for formal collaboration could be extracted by the KCS, and the informal collaboration relationship strength is depending on the network structure information. Then, the node and tie weights of the four networks were obtained by the methods proposed in Section 3, and the weighted R&D network models could be generated by the UCINET (Figure 3). 5.2.  The knowledge diffusion efficiency of R&D networks Based on the weighted R&D networks of the four teams, we computed their weighted average path length and the efficiency of knowledge diffusion. For the comparison purpose, the corresponding unweighted networks of the four teams were measured by the unweighted metrics: the average path length and the efficiency of network. Furthermore, a user vote (UV) method was used to compare the weighted and unweighted measures. We set up the questionnaires to obtain the following information: (1) the reachability with other members; (2) the closeness degree with other members; and (3) the difficulty of the knowledge exchange and sharing in the team. The results of UV method implied the members’ subjective cognition on knowledge diffusion in R&D networks that could reveal the knowledge diffusion status of networks to some degree. For a higher reliability,

Figure 3. The weighted R&D networks of the four teams.

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the questionnaires were sent in anonymous way to the members through email. The survey had a high response rate of 92% (149/162), and the returned surveys were analysed to get the UV results. The comparison results of different measures are shown in Table 3. The results of the unweighted and weighted average path length and efficiency of network are same, that is, Team1>Team2>Team4>Team3. The results conform with the research that in unweighted network the global efficiency of network is the approximate of the reciprocal of length path (Latora & Marchiori, 2003; Tian et al., 2011). However, the result of efficiency of knowledge diffusion is Team3>Team2>Team4>Team1, which is quite different with the above three metrics, but fully consistent with the UV result. The efficiency of knowledge diffusion comprehensively integrates the path length, individual knowledge collaboration level and collaboration relationship strength, and they can be subjectively perceived by the members who are involved in the R&D networks. On the other hand, the researches of Huang (2009), and Srivastava, Bartol, and Locke (2006) shown that there was a positive relationship between knowledge diffusion efficiency and team performance. Hence, we utilised the knowledge collaboration database information and interview the managers to evaluate knowledge collaboration performance of the four teams, which was made as the practical evidence to compare the above metrics. After our investigation, the team performance Table 3. The comparison results of the four networks. TeamMetrics Average path length Weighted average path length Efficiency of network Efficiency of knowledge diffusion UV method

Team 1 3.11 4.29

Team 2 3.24 4.56

Team 3 3.75 5.58

Team 4 3.31 4.67

0.63 0.11

0.49 0.23

0.43 0.31

0.55 0.15

3.54

4.07

4.57

3.71

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Table 4. The Top 10 important members in Team 1. Member p9 p3 p4 p8 p5 p18 p25 p13 p14 p10

Importance value 0.1206 0.1163 0.1030 0.0900 0.0870 0.0719 0.0700 0.0668 0.0661 0.0648

Importance ranking 1 2 3 4 5 6 7 8 9 10

result is also Team3>Team2>Team4>Team1, which is consistent with the result of the efficiency of knowledge diffusion. Sum up, the efficiency of knowledge diffusion can more accurately and effectively measure knowledge diffusion efficiency than the other three metrics. Therefore, the efficiency of knowledge diffusion should be used as the main metric to measure knowledge diffusion efficiency in R&D networks. 5.3.  Locating important members using the efficiency of knowledge diffusion In this section, the application of the efficiency of knowledge diffusion is used to identify and rank the important members in R&D networks. Taking Team 1 as the example, the importance and ranking result of its members is listed in Table 4. The top 10 important members are analysed to illustrate the method. In this case, the members in set of {p9 , p3 , p4 , p8 , p5 , p18 , p25 , p13 , p14 , p10 } were obtained as the Top 10 important members using the application of efficiency of knowledge diffusion, and the result implied these members had significant influence on knowledge diffusion efficiency in Team 1. The theory of Belbin team roles (Belbin, 2012) was introduced to help us to demonstrate the role and importance of these members in team. Among them, p9 and p3 were both with a high knowledge collaboration level and a relatively high volume of collaboration relationship with other members. According to the theory of Belbin team roles, the two members probably played as “Shaper” and “Coordinator” in Team 1. By further surveying, we got that they were the project leaders of Team 1 that taken charge of the project promotion and resource coordination. p8 and p5 had a high volume of collaboration relationships and a relatively high knowledge collaboration level. They possibly played the role of “Resource Investigator”. In reality, they were very skilled in listening and digging other team members’ knowledge and idea, and they had good relationships with others. p13 and p14 had a relatively high knowledge collaboration level, especially the aspect of knowledge stock, while they had less relationships with other member. With these characteristics, they likely played the role of “Specialist” in Team 1. We got that they were the experts in software system development, who concentrate on their knowledge domains and mainly

cooperate with other “Specialist” members. In addition, the other unmentioned members all could be analysed by the theory of Belbin team roles. Note that, the theory of Belbin team roles is just used to help us to better understand and analyse the importance of members in their teams, which does not mean that some types of roles are necessarily more important than others. On the contrary, we insist that all these roles play important role for the effective running of teams. Based on the above analysis, this example verifies that this method can effectively locate and rank the important members which have great influence on the knowledge diffusion efficiency.

6. Conclusion The measurement of knowledge diffusion efficiency is an imperative issue, because only when knowledge diffusion efficiency can be quantifiably measured can the knowledge diffusion activities and process be effectively managed. However, measuring the knowledge diffusion efficiency within R&D networks is a complex decision since multiple factors should be considered. To address this issue, this paper proposed a new measurement method for knowledge diffusion efficiency based on the weighted R&D network model. In this method, the main factors of knowledge diffusion i.e., the path length, individual knowledge collaboration level and collaboration relationship strength were comprehensively considered to propose the main measure of efficiency of knowledge diffusion. Based on the efficiency of knowledge diffusion, an extended application was further developed to identify and rank the important members with great influence on the knowledge diffusion efficiency in R&D networks. The proposed method was illustrated in the real case of XM, and shown its reliability and validity. The results implied that for the real weighted R&D networks, the new measure proposed in this study, that is, the efficiency of knowledge diffusion, could provide more effective and realistic measurement of knowledge diffusion efficiency than the traditional unweighted metrics and methods. For decision-makers of R&D networks, this research can support them to make effective decisions and strategies to improve the knowledge diffusion efficiency and KM performance. Firstly, decision-makers can achieve a reasonable and quantitative measurement of the real status of knowledge diffusion efficiency. The research results indicate the factors, i.e., R&D network structure and properties, knowledge sharing willingness and ability, and knowledge collaboration relationship, all have great influence on knowledge diffusion efficiency, which should be paid much attention by decision-makers and managers. In addition, through the application of the efficiency of knowledge diffusion, the new measure can assist to identify and rank the important members with great influence and importance on knowledge diffusion

KNOWLEDGE MANAGEMENT RESEARCH & PRACTICE 

efficiency. Such identification and ranking is very helpful in the case of the systematic and targeted management of members, as well as when to encourage the important members to exert their advantages to improve the knowledge diffusion efficiency in R&D networks. While this study can improve our understanding of knowledge diffusion efficiency in the context of R&D network, its limitations should be also recognised. First, this study partly relies on some subjective data to build the weighted R&D network model, which spend much effort and time to do the survey and collect data. Future research will apply more objective criteria and data, which could improve the efficiency and quality of this work. Second, the creation of new knowledge is neglected in this research. During the knowledge diffusion process, it is always with the new knowledge creation. Therefore, the introduction of knowledge creation into present work may deserve future research. Third, the expandability of this research does not get enough discussion. In the future work, we intend to extent the proposed methods to other collaborative networks, e.g., regional innovation network, scientific cooperation network, enterprise alliance network, and provide decision-makers and policy makers the universal and valuable insights for collaborative networks’ knowledge management.

Disclosure statement No potential conflict of interest was reported by the authors.

Funding This work is supported by the National Science Foundation of China [grant number 71571023], [grant number 71701027]; the Scientific and Technological Research Programme of Chongqing Municipal Education Commission, China [grant number KJ1600626].

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