Network models

Cross and Parker’s data on energising is network data. Could clues on how to model it lie in the flourishing world of social network analysis (SNA)? (Holland & Leinhardt, 1979; Wasserman & Faust, 1994; Scott, 2000; Carrington et al, 2005) Additions are needed to the graph theoretic constructs of the traditional SNA, including culture and dynamics.

Interest in social network dynamics - primarily changes to a network such as node and link addition and removal - has been aided by developments outside sociology, especially those made by physicists. Simple, abstract computer models have connected the statistical mechanics of graphs (Albert & Barabasi, 2001) to small world effects known from real social networks (Watts & Strogatz, 1998; Watts, 1999; Milgram, 1967; Granovetter, 1973), and scale-free degree distributions identified in various natural and artificial networks (Barabasi & Albert, 1999; Strogatz, 2001). Attempts are being made to inform various disciplines using these studies (Barabasi, 2002; Watts, 2003; Newman, 2003), not least social sciences (Watts, 2004; Kossinets & Watts, 2006).

These attempts at “sociophysics” (Stauffer, 2003) are not without their faults, however. For example, Barabasi & Albert’s model (1999) that grows networks with scale-free architecture generated much excitement through its use of a “rich-get- richer” approach to adding links to nodes based on their current number of links. Analogies were drawn with the growth of the world-wide web and wealth distribution

(Barabasi, 2002). But Pujol et al (2005) point out this model lacks any basis in sociological theory, and so we should hesitate before drawing any conclusions about social phenomena. Various alternative algorithms have been identified for producing scale-free architecture, and they argue for one in which individual agents (represented by nodes) do not require knowledge of the degree distribution of the entire network - so-called “global knowledge”. In their “Lo-Model”, agents obtain knowledge of others’ properties through direct interaction (“local knowledge”) which they then store in agent memories of limited - or bounded - size. Choosing interaction partners via this “bounded rationality” they still manage to produce networks with interesting global architecture, including scale-free degree distributions for some interaction parameter values. Their interactions are given grounding in a micro-sociological theory by basing them on a prisoner’s dilemma type game and social exchange theory. It would be interesting to test if rival theories of interaction (such as Collin’s interaction rituals) can produce the same range of network architectures.

Along with dynamics, the other feature to be added to network studies is that of culture. Johnson-Cramer et al (2007) collected data on social networks - including energising relations - and on cultural values held by individuals in organisations. Their maps of the social networks use different node shapes to indicate different responses to questions on particular values and illustrate an association between clusters in the networks and common cultural values. Cultural values here would include attitudes towards participation, empowerment, teamwork, flexibility at work and innovation - the kinds of values a manager might want to encourage in their organisation, or might believe they have been encouraging. The success of attempts at cultural change could be assessed, and potential cultural divides identified. Adding

energising relations to the analysis suggested “people were energised in interactions that confirmed their views and were more likely to seek out those with similar views over time”. (Johnson-Cramer et al, 2007, p.102) But this interpretation must come supported by interview data as well. The networks are one-off samples - “snapshots” of the organisations. Ascribing causal relations between energising, interactions and culture cannot be done on the basis of just one snapshot.

This calls for a dynamic social network analysis, a subject that was identified as the cutting edge of network studies in (Breiger et al, 2003, especially Carley’s closing address). Monge and Contractor (2003) also call for it as part of their multi-theoretic, multi-level modelling approach (MTML; see also Contractor et al, 2006). They describe a simulation package, Blanche, intended to model network evolution involving mechanisms found in multiple (and rival) theories of communication networks (theories of collective action, homophily, contagion, and exchange, among others), and to model it using the attributes of nodes, links, cliques and whole networks of different modes. As noted already, Collins’s theory of interaction rituals does not feature in their book, so it is no surprise that Blanche does not represent a good starting point for modelling network evolution due to emotional energy. But if one already has network data from multiple time points (such as pre-merger, post- merger, or at six month intervals), then the SNA tools of p* or Exponential Random Graph Models (ERGM) could be applicable (Robins et al, 2005). The powerful analysis package, SIENA (Huisman & van Duijn, 2003), allows one to fit binary data on edges and node attributes taken at multiple time points, using maximum-likelihood estimation via Markov Chain Monte Carlo simulation (Snijders, 2001; 2002). This offers a statistical route to models separating influence effects (where node attributes

change due to network links) from selection (where links change due to node attributes) (Steglich et al, 2004; Snijders et al, 2005). It is to be hoped that in the future authors in possession of data on energising relations - either from real organisations (for example, Baker et al, 2003; Cross & Parker, 2004b; Reinke, 2005) or the product of artificial ones in computer simulations (Baker & Quinn, 2007) - will try to analyse them using ERGM.

Where such network data are missing information on particular links, it may be useful to estimate the likelihoods of the link’s presence and absence using other data, including node attribute data, and the Bayesian approach described by Rhodes & Keefe (2007). Their paper also proposes using the approach to dynamically model networks “as it is feasible to calculate how a network will reconfigure following an intervention”. We are sceptical that Bayesian techniques that work well enough on “protein-protein interactions in genomic data” will extend to social networks. An intervention in a social network - for example, the removal of an energiser from an organisation, perhaps in an unprecedented or dramatic manner - is an event that generates discussion and reaction - even among those not directly linked to the removed person - and thereby alters the cultural resources of the network as a whole in complex ways. The applicability to social network data of this approach therefore needs investigating in future work.

In conclusion, then, there have been in recent years studies introducing culture and dynamics to network analysis and models. In the case of abstract models of network evolution, we have highlighted the absence of a sociological grounding that could include concepts of energy. In the case of empirical studies, the powerful dynamic

statistical tools now available have yet to be applied to energy networks. Thus we proceed with no quantitative analysis of the relations between energy, culture and networks of social interactions.