This study has two main classifications of network data variables. First are the independent variables, i.e. the firms‟ embeddedness variable. The second is the relational capital performance variables which form the outcome variables of this study.
In this section, the researcher first discusses the definition of six measures of network structure measures of embeddedness. These include: reciprocity, k-core, centralization, density, geodesic distance and clustering coefficient. These structural measures illustrate the overall pattern of network embeddedness of the firms in the network of different types of linkages of relationship, namely: contracts, referrals, and information-sharing. The researcher then presents the definition of firm measures of network embeddedness, which include: clique overlapped, degree centrality, multiplexity and betweeness centrality.
4.7.1NETWORKSTRUCTURALMEASUREOFEMBEDDEDNESS
Network Structural Measures: Network reciprocity
The network reciprocity index measures the rate of reciprocation of relationships. Whether that who was the centre of communication also receive communications from the organization concern is determined by the nature of the reciprocal nature of the ties (Sommerfeld et al., 2007).
Network Structural Measures: Network K-Core
Network k-core index measures the strength of connectedness of firms in the network. A k- core is a subset of all the nodes in a network such that each node is linked to at least k nodes in the same subset. A k-core is a highly-interlinked collection of nodes within a larger network.
Comparisons of k-cores of a network having different levels of k also provide some insight into the strength of the connectedness of the actors in the network (Mueller, Buergelt and Seidel-Lass, 2007).
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Network Structural Measures: Network Centralization
The network centralization index refers to the extent to which the relations or connectivity between the actors or firms in the network centre around an actor or a few actors or firms (Freeman, 1979). According to Freeman (1979), network, centralization is, specifically: the ratio of the difference between the centrality index of the most central actor in the network and other actor centrality index in the network, as well as the highest total differences of actor centrality index score possible in the network.
CENTRALIZATION =
Where Ca (ni) is an actor centrality index. Ca (n*) is the largest centrality index of all the g actors (Freeman, 1979). A centralization index value of one indicates greater network centralization, and zero indicates no central actor in the network structure.
Network Structural Measures: Network Density
Network density is the degree or strength of interrelatedness among actors in a network. Network density is calculated by dividing the number of actual ties between the network actors by the total of possible ties in the network (Wasserman and Faust, 1994)
DENSITY =
Where L is the total number of connections represented by the lines in the network. The total number of actors is represented by g. A network index of density is often recorded in a percentage format. Thus, the nearer the density index is to 1; the closer is the strength and connectivity between the network actors. A network with a density index of zero indicates a completely disconnected network structure. A high density score indicates that the networks are much interconnected.
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Network Structural Measures: Network Geodesic distance
The cohesiveness of the different networks of contractual ties, information-sharing ties and referral ties respectively is first examined by calculating the distance between firms of the networks and the number of ties between the firms. The geodesic distance is the shortest path between the firms and measures the extent of connection in the network (Knoke and Kuklinski, 1982). Understanding the geodesic distance firms in the network allows the researcher to determine the level of connectivity among firms in the supply ties. Consequently, it gives general descriptions of embeddedness levels of firms in each of the network ties.
Network Structural Measures: Clustering Coefficient Index score
The clustering coefficient is the extent to which any two organisations in the network are connected to the same organisations and hence are also directly connected to each other. In other words, the clustering coefficient score indicates the degree to which inter-clique interactions may exist in the particular buyer supplier network. A higher cluster coefficient score may indicate more collaborative activities between different sets of cliques. Hence interactions in this network are expected to be higher.
In the following sections, the researcher discusses the organizational measures of the network embeddedness in relation to this study.
4.7.2ORGANIZATIONALMEASURESOFTHENETWORKEMBEDDEDNESS
Organisational Measures of the Network Embeddedness: Degree centrality
Degree centrality measures the number of other actors in the network to which the focal organization or ego is tied. The index is defined as,
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For C(ni), C refers to the degree of the node i. The total number of actors in the network is identified by n. However, because degree centrality of an actor is not inclusive of the actor itself, the total number of actors in the network is always minus the actor where n = n-1 (Wasserman and Faust, 1994).
Organizational Measures of the Network Embeddedness: Betweeness
Centrality
Betweeness centrality index refers to the extent to which an actor is located in a bridging position between actors of a network. For example, let us suppose actor B is located in a betweeness centrality position between actor A and C in a triad network (Freeman, 1979). Because of the bridging position of the actor, betweeness centrality is also an indication of an actor‟s brokerage power in the network. Betweeness centrality index is defined as,
BETWEENESS CENTRALITY =
Where gjk and gjk(ni) are the minimum ties needed for linking actor, i and actor j in the network of
g nodes. Index score of zero shows that an actor is not occupying any bridging position in the
network of g actors, while an index score of one indicates that the actor is in a bridging position among all the network actors (Wasserman and Faust, 1994). Ibarra (1993) stated that, actors that occupy this brokerage position often possessed the advantage as the broker for the flow of information among the network actors. Hence, taking away a node betweeness centrality index may result in the network becoming disconnected through the indirect connections.
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Organizational Measures of the Network Embeddedness: Multiplexity
This network concept refers to the extent to which two or more network actors are connected to each other through more than one type of relation (Knoke and Kuklinski, 1982; Scott, 1988). For example, actors A and B may be connected to each other through a contract tie. The two actors may also be connected to each other through an information-sharing tie.
It is assumed that the more types of relations that actor A has with actor B, the stronger the relations between the two actors would become. In this study, the researcher assesses the multiplexity of ties between the network actors in four types of network relations, namely: the contract tie, information-sharing tie, referral made tie and referral received tie. It is argued that when the firm has all these connections or a multiplexity of ties with other firms in the network, relations between the firms will become stronger.
Organisational Measures of the Network Embeddedness: Clique and Clique
Overlap
In network analysis, a clique refers to a group of three or more actors in a larger network structure which are connected to each other through direct or indirect ties (Wasserman and Faust, 1994).
Clique overlap is the degree to which an actor in clique structure is also in interaction or communication with other actors from other cliques of the network (Knoke and Kuklinski, 1982). In this study, an actor clique overlapped is measured by the number of times that an actor of a clique appears in other cliques of actors. Wasserman and Faust (1994) stated that network often consisted of clique overlaps. Clique overlap can add additional value to the study of the clique itself. Adopting the proposition of Wasserman and Faust (1994), this study investigates the clique overlap position of firms rather than the cliques only.
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4.7.3RELATIONALCAPITALVARIABLES
The following sections describe the outcome variables (relational capital performance) for this study.
Trust
Trust is the extent to which a firm can be depended upon to honour its obligations. In the context of this research, trust is considered when a firm believes that another individual will take actions that are mutually beneficial and not solely to one‟s own advantage (Burt, 2001). Thus, it implies the quality of relationship among actors or firms in a network structure.
For this research, the actor‟s ratings of relationship quality with other firms are rated from one to four. With one indicating a poor relationship and four indicate an excellent relationship. These are identified by respondent firms in the questionnaire matrix. Overall, trust is the ratio of the sum of a firm relationship quality score to the number of firms that give the quality rating of the
particular firm (Provan and Milward, 2000).
Influence
In this study, influence refers to the extent to which a particular firm in the APMMHQ-1 centralized upstream supply network is taken into consideration when other firms are making important decisions (Brass, 1984; Marsden and Friedkin, 1993). In the survey instrument, the researcher used a name generator question to elucidate the influence network. Respondents were asked to name up to five other firms whose opinions would be considered when the respondents are about to make some decisions related to the supply of spares and parts in the APMMHQ-1 upstream supply network for the product RHIB (Stone, 2001). A firm level of influence is the number of times that a firm‟s name appears in the snowball questions that reported the firm as being influential in the network structure. The answers were also used to develop the influence network structure of the APMMHQ-1 supply system.
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Reputation
Reputation refers to the perception of good performance that a firm may have upon other firms in the network (Kilduff and Krackhardt, 1994). In the survey instrument, the researcher asks the respondent to name up to five other firms in the APMMHQ-1 centralized upstream supply network that they admired. This was primarily in relation to the performance of an excellent job in terms of providing the materials and services to the APMMHQ-1 upstream supply network for RHIB. Reputation score is the number of times that the firm is named by others in the APMMHQ-1 centralized upstream supply network for completing a good job.