Defining triadic structures

CHAPTER 5: CONCEPTUALIZING TRIADIC

5.1.1 Social Network Analysis definition of triadic structures

The methodology applied for the analysis of triads¹ in SNA is the triad census which is a set of counts of the different kinds of triadic constellations in an observed network. In social network analysis, a set of three actors is called a triple. A set of three actors and their relationships is called a triad. A triad offers six possible ties as each actor can relate to two other actors, either unilaterally or bilaterally. Each of these six ties may either be present or absent, resulting in 2⁶=64 possible states of a triad. The 64 possible states of triads can be reduced to 16 isomorphic types when the labelling of the actors is left out.

This typology of triads is referred to as the MAN labelling (not to be confused with the MAN approach): The number of Mutual, Asymmetric and Null dyads in the triad (Wasserman, Faust 1994). Business relationships are expected to be characterized by mutual exchange, therefore studies of business triads are mainly concerned with two specific types; the closed triad with three mutual ties (MAN: 300= 3 mutual, 0 asymmetric, 0 null dyads) and the open triad with two mutual ties (MAN: 201= 2 mutual, 0 asymmetric, 1 null dyad). This type of open and the closed triads in a MAN categorization are illustrated in figure 5.1 below.

MAN:300 MAN:201

Figure 5.1: The MAN categorization of closed and open triads

1 As SNA applies the idiom triad in their definition of triadic relationships this is replicated in this section to reflect the terminology applied in this scientific domain

Based on the MAN typology, the triad census can distinguish between and illustrate varieties of triadic patterns. Little attention has been paid to the triad census as an instrument for the analysis of inter-firm networks. But advanced graph analysis of business triads indicates that such analysis can contribute to the understanding of the differing motives behind tie formation in closed business triads (Madhavan, Gnyawali & Jinyu He 2004); see section 4.3.2. Owing to this, the triad census may also have the potential to distinguish between and to analyze the possible differing motives behind open triads.

However, graph analysis is founded on the analysis of an expanded set of actors and relationship. Therefore, it is not a relevant method for this study which focuses on qualitative data from a small number of cases.

5.1.2 The Market-as-Networks definition of triadic structures

As pointed out in section 2.2, the predominant approach to triadic relationships in studies which apply the MAN perspective is to regard triadic constellations as a micronetwork; a set of three actors and their relationships. At the same time focus is on dyads as the network unit from which networks emerge. This has resulted in a discussion of the definition of the basic network unit. Is the triadic constellation, the micro-network, the basic unit of network analysis, which offers insights which cannot be achieved in the study of dyads (Choi, Wu 2009a, Choi, Wu 2009b, Ritter 2000, Smith, Laage-Hellman 1992)? Or are triadic relationships exclusively of interest for strategic, managerial analysis, but of no theoretical significance in the theorizing of networks (Dubois 2009)?

The discussion is interesting, because the MAN approach introduces a third element of potential significance for the study of triadic structures: Interconnections. Interconnections refer to contingencies between relationships. How they affect each other. The

conceptualization of interconnections as a matter of contingencies is founded on Cook and Emerson’s (1978) definition of networks as connected relationships:

“An exchange network is a set of two or more connected exchange relations.

Two exchange relations are connected to the degree that exchange in one relation is contingent upon exchange (or non-exchange) in the other relation”

(p. 725)

In the MAN approach studies of interconnection focus on the “specific connections between a company’s relationships...when a given relationship affects or is affected by what is going on in certain other relationships” (Håkansson, Snehota 1995a p. 17). Such studies are concerned with the analysis of the ways in which relationships influence each other, and relate to the surrounding network. Consequently, a framework for the analysis

of triadic structures not only relates to positions and ties as the basic network phenomena.

It must also include interconnection as a distinct network phenomenon.

One of the issues related to the introduction of interconnections is the duality of interaction and interconnections. Conceptual papers on business triads point to this duality; whether interconnection is a result of interaction or vice-versa, but they are rare (Ritter 2000, Smith, Laage-Hellman 1992). Studies which apply a triadic MAN perspective are primarily case-studies which collect qualitative data (Andersson, Mattsson 2004, Cunningham, Pyatt 1989, Dubois, Fredriksson 2008, Havila 1996, Holma 2009, Hu, Tsai 2007, Jaaskelainen, Kuivalainen & Saarenketo 2000, Komulainen et al. 2005, Narayandas 2002, Odorici, Corrado 2004, Pardo, Salle 1994, Ronström 2005, Trimarchi 2002, Wu, Choi 2005, Wuyts et al. 2004). They yield rich, localized, and specific empirical data which illustrate that the understanding of the interplay of actors and relationships is enriched, when the unit of analysis is expanded from the dyad to the triad. But they do not offer conceptualizations of the interplay of interaction and interconnection.

Summing up, the SNA definition of triads enables the collection and analysis of

quantitative data about networks and triads, based on a categorization of ties as mutual, asymmetric or null. The method results the mapping and analysis of structures of actors and relationships, but it cannot include qualitative aspects, such as the contents of ties in terms of activities. However, advanced graph analysis has been applied in a study of motives behind tie formation. The MAN approach inspires the collection and analysis of qualitative data. When combined with a triadic perspective it results in enrichment of the analysis and increased understanding of the interplay of actors and relationships.

Moreover, the MAN approach introduces interconnection as a third element in triadic structures, but offers few conceptualizations of triadic relationships as structures including three elements; interaction, interconnection and position. The conceptualization of triadic relationships as structures which include all three elements is the purpose of the following section.