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Supply chain has been described as a complex network of interrelated firms transforming materials into finished goods and services. Complexity in the supply network has been known to reduce the supply chain efficiency and effectiveness. However, given the present and embedded impact of social network in the transfer of resources, recognizing alternate influence of social networks to the supply chain is relevance to management of supply chain. In this article, we present a tentative framework to study the impact of supply chain complexity on the supply chain innovation from the perspective of social network theory.
Keywords: Complexity, Social Network Theory
This article applies social network theory in linking supply chain complexity to the innovation performance of the supply chain. The last two decades have seen an unwavering confluence of the conventionally rooted field of logistics, purchasing, sourcing and operation management into a distinguished area widely known as the supply chain management (SCM) . According to the proponents of the SCM, these conventional areas can no longer run as loosely linked pocket of excellence [2-4]. In addition to that, businesses must also expand, establish and regulate the material and information flows as well as the relationship that tie these fields together, and connect these fields with the external entities such as the suppliers and the customers . Concurrently, SCM perspectives obligate firms to expand the scope and network of their business activities that need be managed . The nature of these activities have taken the turn to be more complex and challenging as businesses have become a global network, making widely and geographically dispersed partners and customers difficult to control and managed , and more customers demanding customized produce, creating an increasingly shortening product life cycles . The management of the supply chain, hence, is certainly a challenging task, and many would acknowledge that a supply chain is a complex network of interrelated entities.
In this article, we employ some of the concepts of the social network theory to clarify and provide a pictorial rendition of the aspects of the supply chain network that make them complex and the suitability of SNA to the supply chain research. It begins with an outline of social network theory and the uses to which the theory has been applied to explain organizational phenomena. Then we provide the relevant literature foundation in the areas of supply chain complexity which is posited as structural and relational complexity, grounded in the social network theory. We then peruse the topical work, carried out to date, linking the social network theory to supply chain and apply the salient concepts of social network theory to the supply chain complexity. Base on that, we provide initial propositions that through the lens of social network theory. In summary, this paper provides theoretical and managerial implications related to supply chain complexity with the objective of guiding future studies and supply chain investment and strategic activities.
2.0 Social Network Theory
Social network theory focuses on pattern of relationships and interactions between the actors of the network and examines the availability of resources and the exchange of resources between these actors [7-9]. In the context of social network theory, the resource exchange can be in the form of tangible materials such as raw materials , goods , and money . Resource can also be intangible such as information , and consultation . Each relationship in a social network refers to the type of resource exchange. These exchanges occur between actors of the network which can be an individual, a clique, or an organizations link in a complex supply chain network [5, 13-14].
Network structures are an extension of these dyadic exchanges or ties between two actors . Network models explicate structures in the network in terms of the relational pattern between actors. Combination of network relational ties can form the bridge through which non-adjacent actors or organizations can communicate . The quantitative analysis of networks in the form of socio-graphs or socio-matrices has form the basis of Social Network Analysis (SNA). The SNA methodology has been documented extensively in several literature such as Knoke and Kuklinski , Wasserman and Faust , and Scott . Seminal work in applying the concepts of social network to the supply chain management matters were undertaken by Lazzarini, Chaddad and Cook  and Borgatti and Li .
Concepts of social network theory have been applied extensively in the innovation literature and gained extensive application in the last couple of decade . In his seminal paper Granovetter  stated that differing relational characteristics with regard to the strength of relationships enabled innovation to flow through the social network. The Strength of Weak Ties paper by Granovetter , paved the way to many more research applying SNA to innovation studies. Ibarra  study the effect of network centrality on the innovation performance and concluded that network centrality is important in administrative innovation. Abrahamson and Rosenkopf  argue that the number of links in a network, weak or small, can have a very large effect on adoption of innovation among actors of the network. Ahuja  research into the chemical industry patents indicated that network direct ties and indirect ties both positively contribute to firm innovation. Tsai's  study of 24 business unit in petrochemical and 36 business unit in food company showed that interaction between network position and absorptive capacity significantly impact the business unit performance and innovation. Obstfeld's  result of multi-method study of social network and innovation in an automobile engineering departments show that network density and diversity contribute positively to innovation performance of the unit. Fritsch and Kauffeld-Monz  indicated that strong ties are more beneficial for the exchange of knowledge and information than weak ties essential for innovation development.
In contrast to the use of social network theory in the innovation and organization literature, the usage of social network constructs to the supply chain management hasn't been well developed . For example, although the early articulation of supply chain as supply network by Harland et al.  call upon the concept of social network in supply chain, their usage of the term social network did not enunciate the terminology commonly associated with social network theory. Choi and Hong  used SNA to depicts the actual flow of material and information in an automobile supply chain, however, the network depiction did not discuss the relationship content, the essence of social network theory . Carter, Ellram and Tate  gave example of the application of social network in the context of logistics research. Recently, scholars have highlighted the salience of SNA to study the complex supply network. For example Borgatti and Li  apply network concepts to both "hard" and "soft" types of ties, e.g. materials and friendship respectively. Lazzarini et al.  introduced the concept of net chain analysis. Net chain analysis is a set of network consists of horizontal ties between supply chain actors which are arranged base on vertical ties between the actors in different layers of the supply chain. In their article Lazzarini et al.  acknowledge the quantitative use of social network theory in the depiction of supply chain structure and stated that:
"..network analysis stress the importance of interdependencies between firms and how inter-organizational relationship can be a source of competitive advantage" (p.1)
3.0 Why the study of supply chain complexity needs SNA and the Theoretical Foundation
Existing models and approaches to understand and model the complex supply chain have been reviewed in the literature . In an empirical case study base on the air line industry, Brookes and Lewis (2006) concluded that the approaches were somewhat insufficient to describe some phenomena in the supply chain. They claimed that the existing approaches are not capable of exploring and determining the appearance of similar organizations at every tier of the supply network. For example, in an automobile supply chain, some small group of suppliers of materials could be supplying to other tiers of other automobile manufacturers supply chain. This phenomena although seems irrelevant due to contractual agreements, could be explored for different purposes. In addition, Brookes and Lewis (2006) claimed that the existing approaches to understand the complex supply chain network are not able to model and determine the suppliers in the network whom also supply to and communicate with the network competitors. The featuring of these suppliers in the competitive supply chain must be identified so that its potential economical effects and risk can be abstained.
Moreover, with the move towards greening the supply chain , the complexity of the supply chain has increased. The green supply network demands the need to capture the network bi-directional and complex flow within the green supply chain. The effects of this bi-directional flow of the network need to be captured and understand in order to capture the true nature of network structure and communication flow (Brookes and Lewis 2006). Furthermore, the common generation of supply chain network diagrams are not able to describe the actual complexity of the supply network. The following illustration highlights the issue. Figure 1 display a linear perspective of Honda Accord supply chain. The data was obtained by Choi and Hong  through case study over a period of five years. Base on Figure 1, the diagram only provide the visualization of the formal supply chain interaction activities. The complexity of the supply chain only reflects the linear perspective of this supply chain. Many research on the supply chain complexity have adopted the linear perspective in explaining the negative impact of supply chain complexity [2, 29-31].
Figure 1: A sample supply chain structure of Honda Supply Chain (Model Accord)
Source: Choi and Hong 
Figure 1, however, is merely a representation of the formal interactions of the networks' actors. The supply network also consists of informal interactions that take place amongst the firms inside the supply chain. These interactions can be in the form of a communication network (informal) or as exchange network (formal). For example, Figure 2 represents more complex supply network links of the same data by Lin et al. (2011). This supply chain network is the pictorial rendition of Honda supply network investigated using the social network analysis.
Figure 2: Honda's Supply Network visualization using social network approach
Source: Lin et al. (2011)
The two diagrams reflect two different visualizations of a focal firm supply network. Hence, understanding supply chain complexity requires a much detailed visualization of the network exchange and communication network in order for the firms to benefit from the relationships and tie that exist within this inter-relationship. According to the network theory, the complexity of the supply chain, resulting form the multiple firms and multiple formal and informal relationships could also positively influence the performance or innovation of firms [12, 32-35].
The lens of social capital theory also provides more supportive arguments for a network approach to supply chain complexity. The premise of social capital theory is the notion of embeddedness . Granovetter  argue that during interaction and communication activities actors in the network behave in an imperfect economic rationality because actors are embedded in network with other actors. These actors are capable of providing more resources than would otherwise be possible. Granovetter  added that two form of embeddedness are most salient, the structural embeddedness i.e. the actors structural form of constructed world, and the relational embeddedness, the embeddedness with relate to direct and indirect relationship between actors within a related network. Example of structural embeddedness of firms in a supply network would be the relative positions of firms, the firms distance from others and connections, and the relational embeddedness example would be the relationship strength, quality and duration .
The structural and relational embeddedness concept of Granovetter , are relevant for analysis of supply chain complexity. Firms operating in a global and complex supply chain are evidently connected with each other working to meet the demand of the end users. Despite the network structural and relational complexity firms has actually different level of relationship closeness such as process integration and business relationship, between them. Social capital theory suggest that each of this dimensions influence actors' performance . Similar findings of have also been stated in other studies such as .
In advancing the concept of social network to the supply chain complexity, this paper argues that the salient network theory concepts of actors and ties and embeddedness of firms within the complex supply chain network may result positively to the innovation performance of the firms. In the next section, we discuss the relevant social network theory concepts and relate them to the supply chain complexity.