A novel network optimization partner selection method based on collaborative and knowledge networks

Information Sciences 484 (2019) 269–285

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Information Sciences journal homepage: www.elsevier.com/locate/ins

A novel network optimization partner selection method based on collaborative and knowledge networks Jing Han a,b, Xinyu Teng a,∗, Xun Cai a a b

International Business School, Shaanxi Normal University, Xi‘an 710119, China School of Management, Xi’an Jiaotong University, Xi‘an 710049, China

a r t i c l e

i n f o

Article history: Received 17 October 2018 Revised 24 January 2019 Accepted 29 January 2019 Available online 30 January 2019 Keywords: Innovation Network deconstruction optimization Network redundancy Collaborative network Knowledge networks Network benefits maximization

a b s t r a c t Organizational innovation requires strong social collaboration and knowledge networks as well as focused partner selection strategies that complement employee strengths. Therefore, this paper proposes an effective, innovative partner selection method on the basis of collaboration network deconstruction optimization using collaboration and knowledge networks. To ensure collaborative network deconstruction optimization, the proposed method firstly improves the focal actor’s management efficiency by eliminating network redundancy and identifying the key primary contacts. Then, to fully consider the knowledge benefits to be gained from joint collaboration, the knowledge fusion process is modeled using knowledge combinations from the knowledge networks. Further, social benefits and knowledge benefits maximization are jointly considered in the selection of suitable partners. And at last, a case study is given that demonstrates the proposed method is highly effective in selecting suitable partners for the focal actor that significantly improves both the social and knowledge benefits. © 2019 Published by Elsevier Inc.

1. Introduction Innovation is vital to enhance the core competencies of individuals and organizations for personal learning and organizational progress [38]. Generally, innovative ideas arise from collective, social activities and scientific collaboration can result in extraordinary scientific innovations [44]. Therefore, finding suitable partners from diverse knowledge domains is vital for effective, successful organizational collaboration and innovation [46]. In the late 1980s, many psychologists and human resource management scholars began to focus on the effects of the social environment and social capital influence on individual innovation output [3,4,22,35]. It was found that the extent of the freedom and autonomy given to employees by, for example, drawing together individuals with diverse skills when forming work teams and positive work environments, were important management practices for employee innovation [4]. Further, developing social networks through social cooperation was found to provide employees with a sense of collectively owned social capital [34] in which they felt free to share information [18] and build specific expertise or skills [30]. Studies have also found that innovative collaborative networks can lead to an optimal allocation of resources and improve organizational performances [5]. There has been a lot of research focusing on the partner selection methods that managers can use to coordinate their collaborative networks to improve innovative performance, most of which have examined collaboration

∗

Corresponding author. E-mail addresses: [email protected] (J. Han), [email protected] (X. Teng), [email protected] (X. Cai).

https://doi.org/10.1016/j.ins.2019.01.072 0020-0255/© 2019 Published by Elsevier Inc.

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network from four main perspectives: occupying key collaborative network positions, knowledge relevance, collaborative diversity, and external available resources. 1) The key collaborative network positions are related to the network structures that enhance actors’ ability to gain access to and control information, with network evolution being dependent on internal structural factors [50]. Several network attributions, such as centrality [16], structural holes [7], and network efficiency [25] have been used to identify entity network structural states by measuring the actors’ network positions, influences, and ability to control information quantitatively. For example, Li et al. found that betweenness centrality played the most important role in taking advantage of non-redundant resources in a co-authorship network [27] and that researchers who collaborate with prolific scholars could develop such centralities. Guan et al. studied evidence from the wind power field and found that both centrality and structural holes fully mediated the relationships between collaborative features and scientific outputs [19]. 2) Domain-relevant knowledge refers to an individual’s knowledge of the facts, circumstances, and issues surrounding a given problem or area [4]. Knowledge relevance is a prerequisite for forming cooperative relations, and when knowledge sharing is embedded in collaborative networks, knowledge transfer takes place as part of the members’ interactions. Rothaermel and Boeker claimed that when organizations form alliances, the enterprise searching for partners always requires that the potential partners have some knowledge similarities and complementarities [39]. Dushnitsky et al. found that knowledge cooperation started with knowledge heterogeneity and especially complementary knowledge, as this could lead to more effective knowledge utilization and maximize knowledge creation [14]. And when finding experts for a given task, the expert team always collectively covers all the skills and knowledge the task requires [28,29]. 3) Collaborative diversity refers to the richness of the partners and fully rich partnerships can provide diversified knowledge exchanges, broaden the employee perspectives to solve problems and provide extra resource for reinforcing research quality [30,31]. From a network structure perspective, employees who collaborate with more different people may have higher centrality and richer structural holes, which can prevent network closure and provide them with greater access to external social resources. Guan et al. have found that collaborative diversity is an important collaborative feature for positive scientific output [19]. Although many scholars suggested that diversification may harm innovation [21], Sang et al. reconciled the above inconsistencies and suggested that collaborative diversity and greater innovation were also related to an individual’s ability to search for knowledge and the use of diversification strategies based on appropriate technological search [42]. 4) External cooperation is a more common strategy for new product development. Contacting with external professionals can broaden employee problem solving channels and assist in generating new ideas [36]. Extensive cooperation also can help scientific personnel accumulate social capital and occupy key positions in social networks [27]. Social networks have also been seen as important tools for understanding organizational behavior and for locating needed external resources. For example, Wi et al. [47] proposed a model to evaluate employee knowledge competence, in which the Know-Who refers to an employee’s ability to ask their acquaintances for help and the Know-Who constitutes an employee’s extra knowledge, which is as important as the Know-What and Know-How for employee knowledge. Coscia et al. [11] believed that knowledge flowed in a social environment and proposed an efficient algorithm to rank employee comprehensive skills based on Know-Who. Besides, on the research of expert finding systems, Bozzon et al. [6] have confirmed that social networks were both a source of expertise information and a route to reaching expert users, and socially shared content could improve the effectiveness of expert finding systems. These studies have demonstrated the importance of seeking and mobilizing external resources. The above studies all found that partner selection is an essential part of organizational knowledge management. Due to the advances in information technology, there are now many methods and applications available for professionals [11] or HR departments to find suitable partners. Previous studies have made significant contributions to partner selection and team formation, while these studies still have several limitations. (1) First, most of these approaches focused on how to find suitable partners, while the focal actor of a given collaboration network has the freedom to manage the collaborative network and collaborative network management should be autonomic and effective. However, less attention has been paid to suggest focal actor to manager social network effectively considering costs, time, and technical limitations. Although Burt [7] has proposed the idea of network optimization by social network deconstruction, there is still no detailed and practical method to improve the efficiency of collaborative network management. (2) Second, larger scale cooperation can broaden employees’ horizons to solve problems, improve actors’ network status and help employees to get social capital, but it also can lead to higher costs [20]. There are limited research focusing on methods that can guide managers to keep the balance among collaborative diversity, cooperation benefits and cost with limited time and restricted finances. (3) Third, the organization’s knowledge network is decoupled from its collaboration network and organizational innovation is doubly embedded in both knowledge and collaborative networks. However, previous research about partner selection are only considering single layer collaboration network and research has not addressed the different structures and different roles these networks play in partner selection for innovation. To go some way in filling these research gaps, this study proposes a novel partner selection method, in which a given egocentric collaboration network is firstly deconstructed and optimized by eliminating network redundancy with the aim of

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Fig. 1. Partner selection framework in this paper.

assisting the focal actor achieve network autonomy and develop a greater number of external resources under limited time and financing restrictions; then, after network deconstruction optimization, the maximum number of new partners that focal actor can connect with current network capacity can be determined; and at last, a knowledge fusion model considering task requirements is developed, and a partner selection model based on collaboration and knowledge networks is developed to realize both social benefit and knowledge benefit maximization. The stages for this work are shown in Fig. 1. The remainder of this paper is organized as follows. In Section 2, previous research on network optimization and collaborative and knowledge networks is discussed, after which in Section 3, the proposed collaborative and knowledge network model for choosing suitable partners from many project candidates is presented. In Section 4, a case study is given to show the practicalities of the proposed method, and in Section 5, the discussion, limitations, and conclusions are given. 2. Related work 2.1. Social network governance and deconstruction optimization Egocentric networks are developed using an egocentric approach that involves an interplay between individual social structures and social activity behavior [32]. “Egocentric” designs, which obtain information about only the portion of a network that is in the immediate locality of a given node, have often been used to measure social networks in survey-based studies. An egocentric network structure reveals the focal actors’ situations and environments, such as their information access points, the resources that can be directly mobilized, and the constraints. From a micro-dynamics perspective, network evolution occurs when actors purposively change their social structures and seek to overcome the network constraints [2,7], which also reveals the importance of organizational empowerment. As freedom and autonomy are key to positive work environments and significantly contribute to innovation [4], empowering employees is an active, participatory process by which individuals can gain greater permission to make choice and promote their creativity [49]. Network deconstruction optimization is an important part of network governance. As network operation is an essential part of organizational governance [2,7], network structural embeddedness can govern how the alliance partners behave or cooperate [40]. The main purpose of network deconstruction optimization is to gain greater information benefits while at the same time getting controlling benefits [7]. However, the methods that individuals employ to reach their partners and the form of their egocentric network can influence access to resources, which then can impact innovation. Because network information transmission and resource allocation are uneven generally, actors in key positions can get more network benefits [7]. The key to maximizing information benefits and controlling network benefits is to occupy a key position in the collaborative network and reduce network redundancy [7].

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Social capital is related to an individual’s ability to access network resources [1], which is usually measured by structural holes and network efficiency [7]. Structural holes indicate an absence of any connections between two actors, and generally the actor who is occupying the structural holes position is tied to disconnected clusters and acts as a broker or intermediary [7]. The network efficiency of an actor in an egocentric collaborative network indicates the average degree to which the direct connections are not connected to each other [7]. These two attributes are closely related, and they also can be used to measure an actor’s non-redundant relationships in their social network. An actor, who spans rich structural holes or has high network efficiency, often has more non-redundant relationships and has ability to arbitrage non-redundant information exchanges. Because the non-redundant relationships corresponding to the non-repetitive benefits can be accumulated, Burt [7] suggested that actors embedded in sparsely connected network have brokerage advantages, and Rowley et al. also suggested that strong connections are less advantageous when the actor is situated in a dense network of alliances [40]. Therefore, the pivotal deconstruction optimization tactic is to reduce network redundancy and construct efficient egocentric networks. Redundancy corresponds to network homogeneity and resources wasting, and there are two types of redundancy in social networks: cohesive redundancy and structural equivalence, with cohesive redundancy emphasizing the information homogeneity arising from cliques or strong relationships, and structural equivalence revealing the same pattern for the network positions [43]. While previous research has revealed the values associated with network governance and deconstruction optimization, but few specific methods have been developed to optimize and refactor an actor’s collaborative network structure to improve partner selection network performance. 2.2. Knowledge network and collaboration network Related organizational knowledge management enterprise theories, such as resource-based view, competence-based view and knowledge-based theory all emphasize that knowledge is the main source of sustainable organizational competitive advantage. In recent years, knowledge management has become more diverse [26] due to the development of information technologies that have made knowledge management and knowledge networks more visual. In a knowledge network, nodes represent knowledge elements and the connections between the knowledge elements represent the different knowledge combinations [9]. Knowledge management processes allow managers and researchers to mine employee knowledge and explore organizational knowledge stock. These types of bottom-up visualizations can assist managers gain a fuller understanding of what their employees know, how the knowledge is embodied in different actors, and how knowledge combinations occur between different domains [13]. Therefore, as observing knowledge networks over time can revealing the process of knowledge fusion, managers can take positive measures to encourage knowledge production. As mentioned, the patterns in collaboration networks reveal how social resources are being used and how network structure influence innovation opportunities. Innovation studies have found that in-house staff members tend to have isomorphic collaboration and knowledge networks. In other words, the collaboration connection patterns are similar to the knowledge element combination patterns [48]. However, this inaccurate perception has been corrected since Wang’s seminal work [45] on these two networks, with individual collaboration and knowledge networks having been integrated into a comprehensive research framework for the first time. And it has been found that the organizational collaboration and knowledge networks are decoupled and even the same network features may have different influences on innovation. For instance, the researcher whose knowledge elements have more structural holes in the firm’s knowledge network tends to explore fewer new knowledge elements, while the researcher who has rich structural holes in the collaborative network increases their exploratory innovation. The average centrality degree of a researcher’s knowledge elements has been found to have an inverted-U-shaped relationship with researchers’ exploratory innovation, and the collaborative network centrality degree has a negative effect. Guan et al. [20] analyzed nano-energy patent data and also found the similar conclusion that innovation is doubly embedded in both the knowledge network and the collaborative network. For instance in [20], the non-redundancy between the agent’s knowledge element connections in their knowledge network impeded exploitative innovation, but the non-redundancy between the connections in an organizational collaborative network favored exploitative innovation. These findings, therefore, confirmed that “decoupling of the two networks is the rule rather than the exception” [45] and should focal actors be embedded in the suitable collaborative knowledge networks, they could gain social capital and favorable knowledge combinations opportunities. 3. Problem description and solution framework Based on previous studies, this paper proposes a novel framework for partner selection, in which the focal actor of the egocentric network can achieve network governance and improve performance under limited time and cost constraints by deconstruction optimization. Therefore, to ensure the development of a positive environment to improve an actor’s innovation output, we propose a partner selection framework based on a collaborative network and a knowledge network to achieve network benefit maximization. For a given egocentric collaborative network GC = (VC , EC ), where |VC | = N and VC = {v f , v1 , v2 , v3 , ...vi , ...vN }. vf is the focal actor in the collaborative network. For vf , his egocentric collaborative network is made up of “primary contacts” and “secondary contacts” [18], with so-called “primary contacts” being the focal actor’s neighbors, and the “secondary contacts” being those actors who are two degrees away from the local actor (i.e. neighbors of the primary contacts). And this paper

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Fig. 2. Primary contacts and secondary contacts for node v1 .

Fig. 3. Strategic expansion of egocentric network.

defines PC(vf ) as the set of primary contacts of vf , SC(vf ) as the set of secondary contacts of primary contacts of vf , Cm as the community number m and KPC(Cm , vf ) as the key primary contact of focal actor vf in community Cm . The network constraint is represented by ci , and generally structure holes are calculated by Si = 2 − ci . As shown in Fig. 2, node v2 , node v3 and node v4 are the primary contacts of node v1 ; node v5 , node v6 , node v7 and node v8 are the secondary contacts of node v1 . The edge set is EC = {ω12 , ω13 , ω14 , ...ωi j , ...ωN,N−1 }, where ωij ≥ 0, which represents the relationship strength between vi and vj (Note that ωi j = 0 indicates that there is no edge between vi and vj ). Due to the collaborative relationships between the network actors, the people who work together have also formed their own knowledge networks. The knowledge elements are the nodes in the knowledge network, the total number of knowledge elements for which is n, which together form the knowledge network GK = (VK , EK ), in which |VK | = n and VK = {k1 , k2 , k3 , ...kα , ...kn }. The knowledge network edge set is EK = {KWk1 ,k2 , KWk1 ,k3 , KWk1 ,k4 , ...KWkα , kβ , ...KWkn ,kn−1 }, where KWkα ,kβ ≥ 0, which represents the edge weight between the knowledge elements kα and kβ , and in reality KWkα ,kβ shows the number of knowledge element combinations for kα and kβ .

3.1. Network deconstruction optimization – identify and remove network redundancy Burt’s social capital theory [7] states that in the first step of network optimization, it is necessary to deconstruct the social network. Actors need to adjust their egocentric network constantly to change the network embedded state and ensure that the social network is non-redundant and efficient. As mentioned, both cohesive redundancy and structural equivalence exist in social networks. However, as network cohesion emphasizes the information homogeneity resulting from the compact relationships or cliques, these can be analyzed as a special type of jointly occupied network position; and as structural equivalence underlines the same network position patterns actors are involved in, actors with similar patterns can be aggregated [8] because these actors may have the same information sources and they provide repetitive information. From a network function view, actors with structurally equivalence can be replaced by each other [7,8]. Fig. 3 shows an example of the effective expansion of node v1 ’s egocentric network. At the beginning of the network deconstruction, node v1 has 16 primary contacts (stage A); however, due to the structural redundancy between the nodes, there are only 4 non-repetitive contacts for node v1 . Then, the key primary contacts are selected. In this case, as v2 has complete structural equivalency with v3 , v4 and v5 (as well as with v6 , v10 and v14 ), v2 , v6 , v10 and v14 can be chosen as the key primary contacts and v1 can contact others through these key primary contacts. Therefore v1 can get the same information benefits but at only a quarter of the cost of before (stage B). Node v1 is then used to save the time and energy needed to establish new relationships with new primary nodes (such as v18 and v24 in stage C). In the context of this paper, to identify and remove cohesive redundancy and structural equivalence, the cohesion between subgroups must be determined and the substitution relationships between the primary contacts confirmed.

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3.1.1. Identify and remove network cohesion redundancy The different cohesive subgroups in a given social networks are the different people clusters intrinsically. Common ways to determine cohesive subgroups are community detection methods as a social network community refers to a group of people who have close contact and the same interests or behavioral preferences [24,33]. In this paper, the Louvain method is chosen to determine the cohesive subgroups of the focal actor’s egocentric network. Because hierarchical clustering is an ideal approach to partition network actors discretely into groups [24], and actually the Louvain algorithm is based on hierarchical clustering. This method is able to discover the hierarchical community structure, and can identify the furthest cohesion redundancy, which has better clustering results. It has been widely used as it can analyze large weighted networks as well as sparse networks [33]. The common evaluation standard for the quality of community detection is the maximization of a benefit function called network modularity Q, which is a given value between 0 and 1; when Q approaches to 1, the community connectivity of a given network is strong:

Q=

1  2W

  ss ωi j − i j W

i, j

  δ Ci , C j ,

(1)

 where W is the sum of the weights of all the edges in the network, ωij is the weight between vi and vj , si = j ωi j is the sum of weights between the edges that link node vi , and Ci and Cj are the communities (i.e. cohesive subgroups) to which vi and vj respectively belong to. If the two nodes belong to the same community, δ (Ci , Cj ) is equal to 1; otherwise δ (Ci , Cj ) is 0. The Louvain method rationale has two phases. In the first phase, each node is assigned to a community to maximize the network modularity Q, with the modularity gain Q being derived by moving a node vi into a community C, which is calculated as follows.



Q =

+sCi − 2W C

 ∧

C +si 2W



2

−

C

2W

−

 ∧ 2 C

2W

−

s 2 i 2W



,

(2)

 where  C is the sum of the edge weights inside C, C∧ is the sum of the edge weights incident to the nodes in C, sCi is the sum of the edge weights between vi and the nodes in C, and si is the sum of the weights of the edges incident to node vi . If vi moves into a different community, a different Q is generated, and the maximal Q selected. If the maximal Q is positive, the nodes vi should join are in the corresponding community C; otherwise, vi stays in the original community. The second phase nominates the previously found communities as new nodes to allow for the construction of a new network, in which the “edge weight” is the sum of edge weights between the new nodes (i.e. the edge weights between the communities detected in the first phase). Then, the first phase operations are repeated and the process iterates until significant network modularity improvements are obtained. At this point, modularity Q is measured using (1). Therefore, if there exists a hierarchical structure in the network, such structure can be identified by Louvain method. Especially, the proposed framework in this paper is suitable for deconstructing dense and rigid egocentric networks. After the communities detection, all primary contacts and secondary contacts can generally be divided into different communities (i.e. cohesive subgroups). As some primary contacts or secondary contacts may appear in same community, the number of communities is usually less than the total number of the primary contacts. As a result, a group management of all network actors can be implemented, which reduces the cohesive redundancy. This action is similar to organizational departmentalization, which is an effective strategy for improving management efficiency. Actors who belong to the same community jointly occupy the network position [8], and because the people in the same community are in close contact with each other, some primary contacts can be replaced by a key primary contact [7]. According to the definition of structural equivalence, complete structural equivalence is essentially nonexistent in reality [43], which means that the primary contacts belonging to the same community are approximately structurally equivalent. And the relations of approximately structurally equivalence among primary contacts mean that their network functions may have differences. Therefore, in the next step, it is essential to select the key primary contact from the primary contacts who belong to the same community. 3.1.2. Remove structural equivalence redundancy On the basis of [7], the key primary contacts not only should have a good ability to control information transmission and communicate with the other actors in the same community, but should also be trustworthy to maintain network stability. As an important role of the key primary contacts is information transmission, the key primary contacts should have good centrality and network connectivity. Generally, centrality is generally measured by degree centrality, closeness centrality, and betweenness centrality [43], with the closeness and betweenness measurements being related to the network connectivity as the closeness centrality and betweenness centrality of a given node are calculated based on the shortest network path. Furthermore, betweenness centrality is a valid metric to measure the trustworthiness and reputation of an actor [23]. The definition calculations of betweenness centrality BC(vi ) and closeness centrality CC(vi ) are as follows.

BC (vi ) =

i  t pq p=i=q

Tpq

(3)

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i is the number of shortest paths from v to v that pass where Tpq is the number of shortest paths from vp to vq , and t pq p q though vi .

N CC (vi ) = N j=1

di j

(4)

where N is the number of network nodes and dij is the shortest path length from node vi to node vj . The closeness centrality of an actor reflects how close an actor is to the other actors in the network, which represents the actor’s ability to influence other actors [41]; however, individual betweenness centrality refers to how much an actor can control or mediate the information spread [17], and the actor with high betweenness centrality is an important hinge and crossing of information flow in social network. As the focal actor achieves information benefit maximization, the key primary contact should be the actor with high betweenness centrality. And according to the definition calculation, focal actor manages his collaboration network though the key primary contacts with higher betweenness centrality can reduce the network loss of shortest paths as far as possible and then maintain a robust network. Therefore, betweenness centrality is more suitable than closeness centrality when evaluating key primary contacts. While in the special case, if actor vi and actor vj belong to a community which has r primary contacts, and BC (vi ) = BC (v j ) = max{BC (v1 ), BC (v2 ), ..., BC (vr )}, vi and vj may not become the key primary contacts simultaneously. So this paper combines betweenness centrality and closeness centrality to make sure the key primary contact in the community. And the key primary contact is determined when one of the following conditions is true: (1) ∀ Cm , ∃ v1 , v2 , ..., vr ∈ Cm , BC[KPC(Cm , vf )] ∈ max {BC(v1 ), BC(v2 ), ..., BC(vr )}; (2) If max{BC (v1 ), BC (v2 ), ..., BC (vr )} = {BC (vl ), BC (vo ), ...}, and |{BC(vl ), BC(vo ), ...}| ≥ 2, so CC[KPC(Cm , vf )] ∈ max {CC(vl ), CC(vo ), ...}. The conditions above indicate that the primary contact with the maximum betweenness centrality is suitable to be the key primary contact; and if there are at least 2 actors having the maximum betweenness centrality, the one of these actors with the highest closeness centrality is chosen as the key primary contact. That is, in the case that at least 2 primary contacts in a community have the same level of information control ability, the one who is more influential is suitable to become the key primary contact. It should be noticed that although the computations of betweenness centrality and closeness centrality is based on the global network, a primary contact in a certain community is always more tightly connected to the actors in the same community than outsiders. Therefore, a primary contact with high betweenness centrality or closeness centrality not only has ability to control global information, but also has the power to make good communication with other secondary contacts inside community. For example, if actors v1 , v2 , and v3 are all the primary contacts of focal actor vf and they all belong to the same community in which BC(v1 ) > BC(v2 ) > BC(v3 ).It indicates that v1 has the best ability to gather information and vf can chose node v1 as the key primary contact in this community. The size of node betweenness centrality determines the order in which the nodes are replaced. Here, as v1 is approximately structurally equivalent with v2 and v3 , while v1 is more competitive than v2 and v3 , v3 should be first replaced by v1 and then v2 . If BC (v1 ) = BC (v2 ) > BC (v3 ), while CC(v2 ) > CC(v1 ), it indicates that v2 is qualified to replace the other primary contacts as key primary contact in the community, and v3 should be first replaced by v2 and then v1 . The process of removing network redundancy is described above. First, the Louvain algorithm is deployed to determine the number of the communities (i.e. cohesive subgroups) and the smallest number of primary contacts. Then, each community has at least one key primary contact and the key primary contacts from all primary contacts in the same community are selected by comparing their respective betweenness centralities and closeness centralities. Finally, the focal actor is able to manage their original egocentric collaborative network through the least number of primary contacts. In practice, this process corresponds to organizational departmentalization and empowerment management, which allows the focal actor to maintain the original egocentric collaborative network at minimum cost and save time to develop new collaborative partners to enhance collaborative diversity [7]. 3.2. Knowledge fusion and knowledge benefits In a knowledge network, a node represents a knowledge element and the ties between the knowledge elements represent the different combinations of every two knowledge elements [9]. Within the knowledge network, the structural features of a knowledge element reflect its combinatorial opportunities in its egocentric knowledge domain and its combinatorial potential with other knowledge elements [20,45]. Wang et al. [45] found that there are three factors influencing the knowledge combination process: natural relatedness between knowledge elements; strong researcher beliefs of promising knowledge combinations; and the feasibility and the availability of resources. For a given organizational knowledge network, the degree centrality of the knowledge elements is a good indicator of these factors. First, the knowledge element degree centrality indicates its potential to be combined and recombined with other elements [45]. Second, the knowledge element degree centrality is the number of direct ties between the focal element and other knowledge elements [20], and as learning is generally associative and the search is always local [10], it is cognitively convenient for a researcher to seek inspiration from successful knowledge combinations [9,20,48]. Third, the pooling of knowledge is done elementwise [12], for a person’s

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knowledge network, the number of direct ties for a specific knowledge element indicates that they have a full understanding of this knowledge element. Therefore, degree centrality is helpful when constructing a bottom-up visualization for a person’s knowledge profiles as well as to explore the knowledge combinations between the different knowledge domains [13]. A knowledge element is a fundamental building block for innovation knowledge fusion and creation [15]. Previous research has measured joint innovation based on a knowledge space vector; however, when putting together the knowledge from two individuals, deeper issues of complementarities [13] as well as the knowledge fusion contexts need to be considered. So it is especially important that the relationships between the knowledge elements are identified as knowledge search channels, which guide further potential combinations [37]. The way that firms pool their knowledge resources and the methods used by firms to gain information about potential partners are the two core features for the innovation process [12]. Therefore, it is important to model the knowledge fusion process accurately and visually. Based on joint innovation models [12] and the advantages of knowledge element degree centrality when determining knowledge combinatorial potentials, the knowledge fusion process can be modeled as follows.

K Di j,kα =

n 

β =1,β =α



(1 − θkα ) min KWi,kα kβ , KW j,kα kβ +

n 

β =1,β =α



θkα max KWi,kα kβ , KW j,kα kβ ,

(5)

where n is the total knowledge elements that knowledge element kα could be combined with by vi and vj ; K Di,kα = n β =1,β =α KWi,kα kβ is the degree centrality of knowledge element kα ; KWi,kα kβ is the number of combinations between

knowledge elements kα and kβ (i.e. the edge weight between knowledge elements kα and kβ ); and K Di j,kα is vi ’s new element degree centrality for knowledge type kα after vi collaborates with vj , which indicates what actor vi and vj can learn from each other from the knowledge combinations related to knowledge type kα . K Di,kα is used as a variation of vi ’s element degree centrality of knowledge type kα to measure the knowledge gains when actor vi choose actor vj as the partner.

K Di,kα =



n 

β =1,α =β

KWi j,kα kβ − KWi,kα kβ



(6)

If actor vi collaborates with actor vj , the total knowledge gains of actor vi can be calculated by n  

α =1

n−1  n     K Di j,kα = KWi j,kα kβ − KWi,kα kβ

(7)

α =1 β =α +1

In this equation, θkα ∈ [0, 1], which scales the pooled knowledge between actor vi and vj between the minimum and maximum level and is related to the innovation task features. If the innovation process is made up of discrete tasks that can be done isolatedly, a partner with a high degree of professionalization is required. As the number of K Di j,kα should tend toward knowledge element degree centrality maximization, θkα should be close to one. On the contrary, if the innovation process is systematic and actor vi needs to work closely with others to achieve the goal, then an θkα close to zero which indicates that the actors with weaker kα and kβ knowledge combinations may become collaboration bottlenecks. Another interpretation of θkα is as a measure of the degree of actor vi ’s preference for a specific knowledge combination, or when θkα is used to express actor vi ’s knowledge requirement for a special knowledge combination between kα and kβ . Regardless of actors’ skill proficiency, an θkα close to one indicates that actors vi hopes the partners are familiar with the application of the specific knowledge combination, and an θkα close to zero indicates that actor vi thinks that the knowledge combination between kα and kβ is not necessary to complete the mission. Besides, if actors vi and vj have a high level of knowledge similarity, an θkα close to one indicates that actor vi wants actor vj to convey some experiences about the knowledge combinations related to kα . If actor vi and vj have a high level of knowledge heterogeneity, a θkα close to one signifies that actor vi needs his partner as a generalist in the area of knowledge combinations related to kα . Word segmentation techniques are often used when forming co-word knowledge network. However, for some hightech companies, patent data is often neglected to mining the details of organizational innovations. In related empirical research, the international patent classification codes (IPC) in patent documents are regarded as knowledge element proxies. And in fact, each international patent classification code is a standard coded knowledge element that has natural language features. Fig. 4 gives an example of knowledge fusion, for which the knowledge elements are represented by IPCs. For actor vi , the knowledge combination vector related to knowledge elements kα is represented as KWi,kα = (KWi,kα k1 , KWi,kα k2 , KWi,kα k3 , ..., KWi,kα kβ , ..., KWi,kα km ) (kα = kβ ), where KWi,kα kβ ∈ N. As is shown in Fig. 4, there are two knowledge actors, vi and vj ; and the complete knowledge element set is:



VK =



G06F − 003/0487, G06F − 003/0488, G06F − 003/048, G06F − 003/0484, H04L − 012/58, H04M − 0 01/0 0, G06F − 003/01, G06F − 003/0482, G06F − 009/44

For actor vi , the knowledge combination vector related to knowledge element “G06F − 003/0487” is K Di,G06F −003/0487 =

(3, 2, 2, 1, 1, 1, 1, 1), where the number 3 is the total number of knowledge combinations between “G06F − 003/0487” and

“G06F − 003/0488” from all patents filed by vi .

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277

Fig. 4. Knowledge fusion.

For actor vj , the knowledge combination vector related to knowledge element “G06F − 003/0487” is K D j,G06F −003/0487 =

(5, 3, 3, 2, 2, 1, 0, 0). When θkα = 0.9, the knowledge fusion between vi and vj is n 

K Di j,G06F −003/0487 =

β =1,β =α

+



0.1 min KWi,G06F −003/0487.kβ , KW j,G06F −003/0487.kβ



n 

β =1,β =α

0.9 max KWi,G06F −003/0487.kβ , KW j,G06F −003/0487.kβ

= 0.1(3, 2, 2, 1, 1, 1, 0, 0) + 0.9(5, 3, 3, 2, 2, 1, 1, 1) = (4.8, 2.9, 2.9, 1.9, 1.9, 1, 0.9, 0.9). The final knowledge fusion value between “G06F − 003/0487” and “G06F − 003/01” is 1 and the final knowledge fusion value between “G06F − 003/0487” and “G06F − 003/0482” is 0.9, which is equal to or less than the knowledge value before vi collaborates with vj . This is because vj is weaker than vi in the corresponding knowledge combinations, which impacts the knowledge benefits for vi . From an opportunity cost perspective, vi may gain greater knowledge benefits from a more professional partner. Therefore, if vi collaborated with vj , the finally total knowledge benefits related to knowledge element “G06F − 003/0487” would be

K Di,G06F −003/0487 =

m 

β =1,α =β

(KWi j,G06F −003/0487.kβ − KWi,G06F −003/0487.kβ )

= 4.8 − 3 + 2.9 − 2 + 2.9 − 2 + 1.9 − 1 + 1.9 − 1 + 1 − 1 + 0.9 − 1 + 0.9 − 1 = 5.2. 3.3. Suitable partner selection based on the collaborative network and the knowledge network To improve dense and rigid egocentric networks, this paper deconstructs and optimizes the egocentric network by reducing network redundancy, which allows the focal actor in the egocentric network to develop new partners and develop a more open and active work environment. In detail, the definition calculation of network constraint of node vi is

 2   ωi j + ω ji  , ci = pi j =   pi j + piq pq j j ωi j + ω ji j q,q=i,q= j

(8)

where vj and vq are all primary contacts of node vi . So it is clear that for node vi , the more severe his network redundancy, the higher the network constraint and the lower the structure hole level. Meanwhile from this definition we can see that network constraint is only related to the relations among focal actor’s primary contacts, but has nothing to do with the relations among secondary contacts. While, according to Burt [7], the efficiency and effectiveness of a network should remain balanced between network diversity and network size. Therefore, it is better to develop a new partner connecting more neighbors that the focal actor can add to the ambient secondary contacts and the “ports of access” to the external environment. Based on this, when a focal actor meets new partners connecting more neighbors and collaborates with them, his structural holes change and the information channels improve better. The direct knowledge benefits that prospective partners can bring should be maximized for successful collaboration, which can be achieved using mathematical programming with multiple objective functions. The functions are expressed in the following model:

max Z1 =

m  i=1

SC

  v f , vci  Xi

278

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Fig. 5. Egocentric collaborative network for v13 . Table 1 Basic topological properties for the given egocentric network. Number of network nodes Number of components Network diameter Network density Average path length Average degree

max Z2 =

r  

α =1 m 

s.t.

 Xi =

Xi

62 1 4 0.115 2.468 7.0 0 0

Average clustering coefficient Network degree centralization Network closeness Centralization Network betweenness Centralization Effective size Network efficiency

0.511 0.220 0.354 0.214 12.508 0.695

 K Di,kα  Xi ≤P

i=1

1, 0,

vci can be selected as f ocal actor s partner vci can t be selected as f ocal actor s partner

(9)

where m is the total number of candidates; P is the maximum new partners that the focal actor can collaborate with (i.e.  Pmax = PC (v f ) − m=1 KPC (Cm , v f )); r is the types of knowledge elements that the focal actor needs and prefers; and SC(vf , vic ) is the number of secondary contacts that candidate vic can connect to vf . While it is usually difficult to determine an optimal solution using multiple objective programming that satisfies all objectives, there is generally a pareto solution set that includes pareto solutions that can be provided to the decision maker, with all pareto solutions in the pareto solution set forming a pareto front.

4. Case study The proposed method was tested on a technology-intensive industry, in which firms are characterized by advances in science and technology and have large patent stocks. A collaborative employee network from a technical enterprise in China and their corresponding knowledge network were taken as examples to help an employee select suitable partners. Stable and close cooperative relationships between the network nodes were required to better the effect of network demonstration optimization and then give reasonable network management proposals to the focal actor. Therefore, actors who worked together at least three times from 2011 to 2017 were selected. The related patent data was extracted from the frequently used Derwent Innovation Index database (DII). Fig. 5 shows the complete collaborative network for the given focal actor v13 . The basic topological properties for the given egocentric network and its knowledge network are shown in Table 1 and 3. v13 was given an innovation task that involved at least 10 knowledge elements, for which v13 wanted to find 3 suitable partners from 8 candidates. The details of the social benefits and knowledge benefits under the different technical requirements are shown in Tables 4–7.

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279

Fig. 6. Different cohesive subgroups in v13 ’s egocentric collaborative network.

4.1. Basic topological properties for the given egocentric network Fig. 5 shows the egocentric collaborative network for v13 , in which the important primary and secondary contacts that work closely with v13 are displayed. As can be seen, actor v13 had 18 primary contacts and 43 secondary contacts. In v13 ’s egocentric network, the network diameter was 4, the network density was 0.115, and all network nodes formed 1 connection component, indicating that this egocentric network had good connectivity. The average degree was 7 and the network degree centralization was about 0.220, which indicated that there was a relatively uniform degree of centrality distribution in this egocentric network and that most network actors had approximately similar social network status. As the average path length was 2.468 and the network closeness centralization was 0.354, most actors were near other actors in the network. Further, as the network betweenness centralization was 0.214, the betweenness degree distribution was also relatively uniform and for most actors, there were no distinct differences between their abilities to control the network information and regulate the network relations. The average clustering coefficient was 0.511, which indicated that v13 ’s friends were closely connected to each other, and v13 ’s egocentric network tended to be more closed. The values for these basic topological properties all indicated that this network had closely connected homogenized members. The value of actor v13 ’s network constraint was 0.224 (the smaller the network constraint, the higher the level of structural holes), the effective size of the network was 12.508, and the network efficiency was about 69.5%, all of which indicated that actor v13 had sufficient social capital but that there was some network redundancy. In the following section, a further analysis is made to determine the redundant relationships in v13 ’s egocentric network. 4.2. Identify and remove network cohesion redundancy After the analysis using the Louvain algorithm, actor v13 ’s primary contacts (i.e. the neighbors) were divided in eight communities, one of which (i.e. community C8 ) was made up of secondary contacts. The modularity Q of the community detection for the Louvain algorithm was 0.512, indicating that actor v13 ’s egocentric network had a distinct communities structure and there was cohesion redundancy. v13 ’s primary contacts were v1 , v2 , v3 , v8 , v12 , v14 , v16 , v19 , v25 , v33 , v35 , v36 , v38 , v39 , v41 , v43 , v45 , and v51 . The community detection details are shown in Fig. 6 using different colors, with the nodes belonging to the same communities being in the same color. 4.3. Remove network structural equivalence redundancy The analysis showed that there were cohesion redundancies primarily in communities C1 , C2 , C3 and C4 . For instance, because v1 , v2 and v3 belonged to the same community and were closely connected, v13 can reach the same group of secondary contacts through v1 , v2 and v3 ; that is, these three contacts are structurally equivalent, which means that some can be replaced by others. As a result, v13 can choose one of these three as a key primary contact, thereby saving two thirds of the time and energy in community C1 to develop new partners. To determine the number of optimal primary contacts, the focal actor can contact more non-repetitive secondary contacts by minimizing the primary contacts. To assess the substitutional relationship between the primary contacts in the same community to determine the number of key primary contacts, the normalized value of betweenness centrality of each primary contact from each community was calculated as follows. (1) For the primary contacts from community C1 : BC (v1 ) = 0.019, BC (v2 ) = 0.071, and BC (v3 ) = 0.04; therefore, BC(v2 ) > BC(v3 ) > BC(v1 ), v2 is an appropriate key primary contact in C1 and v1 should be replaced first by v2 and then by v3 .

280

J. Han, X. Teng and X. Cai / Information Sciences 484 (2019) 269–285 Table 2 Details of the communities. Community

Primary contacts

Community

Primary contacts

C1 C2 C3 C4

v1 , v2 , v3 v8 , v16 , v33 , v41 v12 , v14 , v38 v35 , v39 , v43 , v45 , v51

C5 C6 C7 C8

v19 v25 v36 No primary contact belongs to this community.

Table 3 Basic topological properties of v13 ’s knowledge network. Number of network nodes Number of edges Network diameter Network density Average path length

187 1286 8 0.069 2.673

Average degree Average weighted degree Average clustering coefficient Number of communities Modularity

12.898 15.872 0.788 8 0.543

(2) For the primary contacts from community C2 : BC (v8 ) = 0.032, BC (v16 ) = 0.034, BC (v33 ) = 0.02, and BC (v41 ) = 0.049; therefore, BC(v41 ) > BC(v16 ) > BC(v8 ) > BC(v33 ), v41 is an appropriate key primary contact in C2 and v33 should be first replaced by v41 and then by v8 , and v16 . (3) For the primary contacts from community C3 : BC (v12 ) = 0.14, BC (v14 ) = 0.016, BC (v38 ) = 0.031; therefore BC(v12 ) > BC(v38 ) > BC(v14 ), therefore, v12 is an appropriate key primary contact in C3 and v14 should be replaced first by v12 and then by v38 . (4) For the primary contacts from community C4 : BC (v35 ) = 0.051, BC (v39 ) = 0.175, BC (v43 ) = 0.006, BC (v45 ) = 0.091, BC (v51 ) = 0.002; therefore, BC(v39 ) > BC(v45 ) > BC(v35 ) > BC(v43 ) > BC(v51 ), v39 is an appropriate key primary contact in community C4 and v51 should be first replaced by v39 and then by v43 , v35 , and v45 . As is shown in Table 2, v19 is an appropriate key primary contact in community C5 ; v25 is an appropriate key primary contact in community C6 ; and v36 is an appropriate key primary contact in community C7 . Although no primary contact is identified in community C8 , it can be seen that key primary contacts v12 , v25 and v39 all worked closely with the secondary contacts in community C8 . Therefore, v13 can maintain and manage the original network through at least 7 key primary contacts, and therefore saves at most 11/18 of the time and energy needed to develop up to 11 new friends (i.e. here Pmax = 11). 4.4. Basic topological properties of the given knowledge network As an inventor, v13 had applied for 308 patents up till May 2018 with the achievements being mainly focused on digital computers, telephone and data transmission systems, and computer peripherals. After text word segmentation processing, v13 was identified as an image processing expert. In this section, the patents v13 applied for are analyzed to extract the international patent classification codes (IPC) as the knowledge element proxies. Fig. 7 shows the knowledge network for v13 from which the personal knowledge reserve can be assessed in detail. In Fig. 7, the knowledge nodes with same color represent the knowledge elements that are closely related to each other, with the size of the knowledge nodes and labels indicating the importance degree. For instance, the knowledge elements H 04M − 001/725, H 04L − 029/08, G06F − 003/0484 and G06F − 017/30 all have high centrality degrees, which indicates that these knowledge elements have stronger combinatorial potential than the other knowledge elements and are therefore more important in v13 ’s knowledge portfolio. After the isolated knowledge nodes in v13 ’s knowledge network in Fig. 7 were removed, there were 187 knowledge elements that made up v13 ’s knowledge network. Therefore, some knowledge elements could be used alone, while others needed to be used with other knowledge elements for knowledge combinations. As this knowledge network has 1286 edges, v13 has created 1286 different knowledge combinations. The network diameter was 8 and the average path length was 2.673, which indicated that there was good connectivity in v13 ’s knowledge network and it was good for a local knowledge search. The average knowledge degree was 12.898 and the average weighted knowledge degree was 15.872, which indicated that each knowledge element had been combined many times by v13 and there was high combination potential in v13 ’s knowledge elements. As the network density was only 0.069 and the average Clustering Coefficient was as high as 0.788, the knowledge network tended to be more dense and closed generally. The knowledge network modularity was 0.543 and could be detected in 8 communities, indicating that v13 was possibly involved in different skill areas.

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281

Fig. 7. Knowledge network of v13 .

Table 4 Social benefits of each candidate. Candidates

Secondary contacts

Candidates

Secondary contacts

vc1 vc2 vc3 vc4

121 9 145 33

vc5 vc6 vc7 vc8

229 228 282 64

Table 5 Knowledge benefits of each candidate (θk1 = θk2 = ... = θk10 = 0.9). Candidates

Knowledge gains

Candidates

Knowledge gains

vc1 vc2 vc3 vc4

52.5 56.2 101.5 −17

vc5 vc6 vc7 vc8

9.3 9.7 75.6 366.3

4.5. Select suitable partners based on the collaborative and knowledge networks To select a suitable partner based on collaborative network benefit maximization and knowledge network benefit maximization under v13 ’s technical requirements, the focal actor v13 sets requirements for each knowledge item were θk1 = θk2 = ... = θk10 = 0.9. Table 4 shows the number of secondary contacts that each candidate could connect with and Table 5 shows the knowledge benefits received from each candidate under the technical requirements θk1 = θk2 = ... = θk10 = 0.9. Fig. 8 shows the feasible solutions and the pareto front for the multiple objective programming. In Fig. 8 above, it can be seen that the pareto front for the model is non-convex, and it is impossible to achieve the social benefits maximization and the knowledge benefits maximization at the same time in this case. θk1 = θk2 = ... = θk10 = 0.9 indicates that the innovation task requires more specialized partners and v13 has a high technical specialization demand. Therefore, there are 4 pareto solutions: (vc3 , vc5 , vc7 ), (vc3 , vc7 , vc8 ), (vc5 , vc6 , vc7 ) and (vc5 , vc7 , vc8 ), and the respective results for which are (656, 186.4), (491, 543.4), (739, 94.6) and (575, 451.2). If focal actor v13 chooses vc5 , vc6 and vc7 as the new partners, a maximum number of new secondary contacts can be connected; however there would be fewer knowledge benefits. In other words, while collaborating with vc5 , vc6 and vc7 allows v13 to meet reputable and sociable partners that

282

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Fig. 8. Feasible solutions and the Pareto front.

Fig. 9. Optimized collaborative network.

can provide more “ports of access”, they may not provide the skills or knowledge v13 needs. Although (vc3 , vc5 , vc7 ) can provide significant secondary contacts, the prospective knowledge outputs are non-ideal. In contrast, the pareto solutions for (vc3 , vc7 , vc8 ) and (vc5 , vc7 , vc8 ) are more acceptable, which not only guarantees that v13 can connect to more secondary contacts, but also ensures good collaborative outputs.

4.6. Deconstruction optimization of v13 ’s egocentric collaborative network After the analysis of the pareto solutions, v13 chooses vc3 , vc7 and vc8 as the new partners for local optimization. After calculating the betweenness centrality of each primary contact in part 4.2, it was identified that v1 , v14 , v33 and v51 should be replaced by their corresponding key primary contacts firstly. However, v13 only needed 3 new partners. As mentioned, betweenness centrality is measured based on the global network, which meant that the three actors from v1 , v14 , v33 and v51 with a smaller betweenness centrality value can be replaced by their corresponding key primary contacts. If v13 empowered v2 , v12 and v39 to respectively manage the information from v1 , v14 and v51 , then v13 could save time and energy when building new relationships with vc3 , vc7 and vc8 . Fig. 9 shows the network local optimization implementation process, in which the black nodes v63 , v64 , and v65 respectively represent candidates vc3 , vc7 and vc8 , and the size of the black nodes indicates the number of secondary contacts they are connected to. After optimization, the effective collaboration network size increases from 12.508 to 13.272 and network efficiency increases significantly from 0.695 to 0.737, indicating that some network redundancy was removed. As the collaborative network constraints decreases from 0.224 to 0.193, v13 structural holes are markedly improved. v13 also gains considerable knowledge benefits, the value of which is 543.4. Therefore, using the proposed method, v13 gains additional information benefits from the outside environment, and is able to select more suitable partners.

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283

Table 6 Knowledge benefits from each candid. Candidates

Knowledge gains

Candidates

Knowledge gains

vc1 vc2 vc3 vc4

−161 −145.4 −112 −206

vc5 vc6 vc7 vc8

−184.6 −188.4 −158.2 −9.6

Table 7 Knowledge benefits from each candidate (θk1 = 0.9, θk2 = 0.3, θk3 = 0.4, θk4 = 0.5, θk5 = 0.6, θk6 = 0.7, θk7 = 0.8, θk8 = 0.9, θk9 = 0.4, θk10 = 0.9). Candidates

Knowledge gains

Candidates

Knowledge gains

vc1 vc2 vc3 vc4

−60.9 −41.3 −6.4 −114.8

vc5 vc6 vc7 vc8

−93.7 −93.3 −59.7 201.8

5. Discussion and conclusion 5.1. Analysis under different θkα 5.1.1. Selecting suitable partners for a more systemic innovation task If the innovation task were more systemic, members needed to work closely together and everyone should be involved in all aspects of the task. In this analysis, the θk1 = θk2 = ... = θk10 = 0.2 are set. Table 6 shows the knowledge benefits to be gained from each candidate under the technical requirements θk1 = θk2 = ... = θk10 = 0.2. In this condition, no matter who v13 works with, the knowledge benefits from the partner are all negative, which demonstrates that a weaker partner can significantly damage the joint innovation output and that the two sides in the cooperation would need to make greater efforts to overcome the difficulties caused by inadequate knowledge. Of all the candidates, vc8 would be easier to cooperate with and collaborating with vc4 would not cost-effective. The multiple objective function calculations show that there are 5 pareto solutions: (vc2 , vc3 , vc8 ), (vc3 , vc5 , vc7 ), (vc3 , vc7 , vc8 ), (vc5 , vc6 , vc7 ) and (vc5 , vc7 , vc8 ); the respective result values for which are (218, −267 ), (656, −454.8), (491, −279.8), (739, −531.2) and (575, −352.4). Compared to the results for the high technical specialization demand (i.e. θk1 = θk2 = ... = θk10 = 0.9), (vc2 , vc3 , vc8 ) is a particular solution in this case. However, if v13 chose vc2 , vc3 and vc8 as the new partners, there were fewer secondary contacts but the lowest cost to build the knowledge collaboration. On the contrary, if v13 chose vc5 , vc6 and vc7 as the new partners, there would be rich social benefits with up to 739 secondary contacts; however, the cooperative costs would be very high. Therefore, in this condition, the solutions (vc2 , vc3 , vc8 ) and (vc3 , vc7 , vc8 ) are acceptable. 5.2. Selecting suitable partners for a more complicated innovation task In this analysis, the innovation task is more complicated and requires both job division and cooperation. Therefore, different technical requirements are set for the knowledge elements to conduct analysis. Table 7 shows the knowledge benefits from each candidate under a complicated technical requirements scenario. In this condition, there are 5 pareto solutions, which are the same as θk1 = θk2 = ... = θk10 = 0.2: (vc2 , vc3 , vc8 ), (vc3 , vc5 , vc7 ), (vc3 , vc7 , vc8 ), (vc5 , vc6 , vc7 ) and (vc5 , vc7 , vc8 ); the result values for which are (218, 154.1), (656, −159.8), (491, 135.7), (739, −246.7) and (575, 48.4). Compared with the other results under different knowledge requirements, the results under the complex technical requirement condition are more distinctive. Although by collaborating with vc5 , vc6 and vc7 , v13 would significantly increase the number of social relations, the collaboration would be more difficult; therefore, (vc2 , vc3 , vc8 ) and (vc3 , vc7 , vc8 ) are acceptable solutions. 5.3. Global optimization of v13 ’s egocentric collaborative network In the case study above, v13 collaborated with only 3 new partners and did not take full advantage of all key primary contacts to manage the collaborative network. In the following analysis, all key primary contacts replaced other primary contacts from the same community to become the “manager” of their community. Fig. 10 shows the global optimization process for v13 ’s egocentric collaborative network (The blue boxes in Fig. 10 are the 7 key primary contacts and the green nodes v63 , v64 , and v65 are candidates of vc3 , vc7 and vc8 respectively.). In the first step, v13 can sever connections with 11 primary contacts and keep connections with at most 7 key primary contacts, and then builds new connections with vc3 , vc7 and vc8 . After global optimization, it can be seen that the collaborative network efficiency significantly increases from 0.695 to 1, completed removing any network redundancy. In the first global optimization step, v13 ’s collaborative network constraint

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Fig. 10. Global optimization for v13 ’s collaborative network.

increase from 0.224 to 0.341; however when v13 continues to collaborate with 3 new partners, v13 ’s collaborative network constraint decrease from 0.341 to 0.308. As mentioned, v13 can meet 11 new partners at most. Therefore, by continually improving the egocentric collaboration network, v13 can reduce the network constraint, and gain greater social benefits using less time and energy. We find though simulation experiment that the v13 ’s network constraint would finally drop to 0.241 and have rich social channels to get information if he collaborated with 11 new partners once on average. Furthermore, if v13 collaborated with 11 new partners twice on average, his network constraint would drop to 0.183. 5.4. Conclusion and limitations This paper proposed an effective and novel partner selection method based on collaborative and knowledge networks that considered network deconstruction optimization. With the focus on collaborative network management, this method was shown to improve a focal actor’s management efficiency by removing network redundancy. First, natural network subgroup cohesion was determined using the Louvain method, after which the betweenness centrality and closeness centrality of the primary contacts in each community were determined to identify the key primary contact in each community. Then, the ordinary primary contacts inside the communities were replaced with the key primary contacts, and the focal actor can empower the key primary contacts to manage the whole collaborative network. Next, considering the knowledge benefits from joint collaboration, knowledge combinations from the knowledge networks were used to model the process of knowledge fusion. And finally, this paper considers social benefit and knowledge benefit maximization simultaneously to select suitable partners by multiple objective programming. The contributions of this paper are as follows. First, this paper proposes an effective method for network deconstruction optimization on the research basis of [7]. Second, the method proposed in this paper can assist focal actor to achieve collaboration management under limited time and restricted finances, which expends his network diversity and broadens channels to get information benefits. Third, in view of deeper issue of knowledge fusion, the combinational relations between knowledge elements are considered to model the process of knowledge cooperation. Fourth, considering the rule that knowledge network is decoupled from its corresponding collaboration network, this research of partner selection is on the basis of two layer network, which fully considers the multiple reasons for the success of the cooperation. In this paper, different results have been found for different technical requirements θkα . We find that when the different technical requirements were analyzed, different solutions are generated to accommodate the various requirements. However, regardless of the technical requirements, it is found that high skill level candidates were always selected (such as vc8 in this case), which conforms with reality as highly skilled employees are generally able to work effectively alone or collaborate with others. However, this study has some limitations. Although social benefits and knowledge benefits are important for partner selection, other aspects such as personal quality and loyalty need to be accounted for. Further, as the model only examined the direct links between the knowledge elements in the knowledge network for the knowledge fusion process, the application of knowledge networks in organizational knowledge management needs to be further examined. Acknowledgments This research was supported by the National Natural Science Foundation of China (No. 71403158), the Humanities and Social Sciences of Ministry of Education Foundation (No. 18XJA840 0 02), and the China Postdoctoral Science Foundation (No. 2016M590960). The authors would like to thank the anonymous referees as well as the editors. References [1] [2] [3] [4]

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