Indicators of Social Network Analysis

Density

The density of a network is an examination of how many correlations there are between actors compared to the maximum possible number of connections that exist between actors.

It takes on a value between 0 and 1. When density is close to 1, the network is considered dense; otherwise it is sparse.

In the social network literatures there are a lot of debates about the impact of network structures and their features, that is, sparse (dense) networks and strong (weak) ties, on firm performance. Dense networks may provide communication pathways by which information and resources can be channeled effectively. Other research has shown that too much density can restrict access to outside resources or sources of information and retard adoption of best practices (Valente, Chou, and Pentz, 2007). And, in some cases, larger and more communicative coalition networks might not lead to effective collaborations (Jasuja et al., 2005). About string and weak ties, according to one view, strong ties in a highly interconnected alliances network negatively impact firm performance (Rowley et al., 2000) and weak ties positively impact firm technological performance (Kogut, 2000; Ruef, 2002).

And according to an alternative viewpoint, however, strong network ties provide better impact on firm performance than weak ties (Krackhardt, 1992; Uzzi, 1997; Kale et al., 2000;

Wong and Ellis, 2002).

Centrality

Centrality indicates the degree to which a firm has succeeded in developing a dominant position in the overall network of inter-firm partnerships. The centralization, or the centrality, of the entire network measures the distribution of centrality among firms in a

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network. It measures the extent to which a focal firm is more central than all other firms in the network.

Social network scholars distinguish between three measures of centrality: degree, closeness and betweenness (Wasserman & Faust, 1994). Degree centrality simply reflects the total number of collaborative ties (scores) that a firm formed in a period. A firm with more ties is considered to be closer to the center of the network and have more opportunities to play an essential role in the network. In contrast, a firm with a low degree of centrality is considered to be isolated from other firms, and consequently expected to play a marginal role in the network. While the degree centrality takes into account only the number of direct ties that a node has, the closeness centrality also considers indirect ties (which are not directly connected to that node). In formal terms, closeness measures the centrality of a point by summing the geodesic distances from that point to all other points in the network.

If a firm has high closeness centrality in a network, this means that it is close to most of the other firms, and hence is able to avoid the control of others (Freeman, 1979). To explain betweenness centrality, the author have already known degree and closeness centrality are based on the reach-ability of an actor in the network, however, betweenness centrality may be to what extent an actor dominates the flow of information because of his position within a network. A node with few ties may play an important intermediary role and so be very central to the network. It measures the number of geodesics (a geodesic is the shortest path between any particular pair of nodes in a network), and consequently the extent to which a firm, landing on the shortest path between two other companies, has a potential for control.

So Betweenness centrality finds the node in a position where it is acting as a” bridge “from one node/group of nodes to another.

However, since this study did not include all companies in automobile industry, instead of partial, the author have to use another measures. Both closeness centrality and betweenness centrality take into account the links among all nodes in the network for their

calculation. So, out- and in-degree centrality is more appropriate for the study.

Out-degree is the number of other organizations each organization nominates and in-degree is the number of choices received by each organization. Out-and in-degree may be normalized by dividing the number of ties by N-1, the maximum possible number of nominations within each network. Out- and in-degree are local centrality measures calculated by examining each node’s immediate neighborhood. Out-and in-degree centrality are less sensitive to missing data (Borgatti, Carley & Krackhardt,2006; Costenbader &

Valente, 2003) and may be more appropriate when less than complete data are available.

Structural holes

In several important works, Ronald Burt coined and popularized the term "structural holes" to refer to some very important aspects of positional advantage/disadvantage of individuals that result from how they are embedded in neighborhoods. Burt's formalization of these ideas, and his development of a number of measures has facilitated a great deal of further thinking about how and why the ways that an actor is connected affect their constraints and opportunities, and their behavior. The basic idea is simple. Imagine a network of three actors (A, B, and C), in which each is connected to each of the others as in Figure 2.1.

Figure 2-1 Three actors network with no structural holes

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Let's focus on actor A (of course, in this case, the situations of B and C are identical in this particular network). Suppose that actor A wanted to influence or exchange with another actor. Assume that both B and C may have some interest in interacting or exchanging, as well. Actor A will not be in a strong bargaining position in this network, because both of A's potential exchange partners (B and C) have alternatives to treating with A; they could isolate A, and exchange with one another.

Now imagine that the author open a "structural hole" between actors B and C, as in Figure 2-2. That is, a relation or tie is "absent" such that B and C cannot exchange (perhaps they are not aware of one another, or there are very high transaction costs involved in forming a tie).

Figure 2-2 Three actors network with a structural hole

In this situation, actor A has an advantaged position as a direct result of the "structural hole" between actors B and C. Actor A has two alternative exchange partners; actors B and C have only one choice, if they choose to (or must) enter into an exchange.

Effective size of the network (EffSize)

It is the number of alters that ego has, minus the average number of ties that each alter has to other alters, essentially, the number of alters minus the average degree of alters within

the ego network, not counting ties to ego (Burt, 1992).

Suppose that A has ties to three other actors. Suppose that none of these three has ties to any of the others. The effective size of ego's network is three, as in Figure 2-3. Alternatively, suppose that A has ties to three others, and that all of the others are tied to one another. A's network size is three, but the ties are "redundant" because A can reach all three neighbors by reaching any one of them. The average degree of the others in this case is 2 (each alter is tied to two other alters), as in Figure 2-4. So, the effective size of the network is its actual size of 3, reduced by its redundancy of 2, to yield an efficient size of 1.

All in all, the greater effective size one actor has, the smaller reduplicated network it owns. That is to say, the actor located on structural hole with higher possibility.

Figure 2-3 High effective size for A

Figure 2-4 Low effective size for A

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Constraint index

It is a summary measure that the extents to which ego’s connections are to others who are connected to one another. Essentially, it is a measure of the extent to which ego is invested in people who are invested in other of ego's alters (Burt, 1992). For example, if A's potential trading partners all have one another as potential trading partners, A is highly constrained. If A's partners do not have other alternatives in the neighborhood, they cannot constrain A's behavior. The logic is pretty simple, but the measure itself is not. The idea of constraint is an important one because it points out that actors who have many ties to others may actually lose freedom of action rather than gain it -- depending on the relationships among actors.

All in all, the smaller constraint scores one actor has, higher possibility the actor located on has. That means actor who is not limited by partners, can utilize the position advantage and control power.

Figure 2-5 The situation that partners constraint A