Model of an imbalanced social network

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Fig. 2. An imbalanced network with four three- and two-cluster partitions.

Fig. 2 presents a simple network that is not exactly balanced together with four partitions of this network into two and three clusters. These partitions, each with a single inconsistency with perfect balance, were located by using the Doreian and Mrvar (1996) method. Consider the two cluster partitions. For the partition {{1, 2, 4, 5, 6, 7}, {3}} in the bottom-left panel in Fig. 2, the tie from actor 1 to actor 2 is inconsistent with balance because it is a negative tie within a plus-set. For the partition {{1, 4, 5, 6, 7}, {2, 3}} in the bottom-right panel of Fig. 2, the tie from actor 2 to actor 4 is identified as inconsistent with balance because it is a positive tie between plus-sets. We note that the tie identified in this fashion depends on which (optimal) partition is considered. When we turn our attention to three cluster partitions there are another two partitions with the same number of inconsistencies with balance. For {{1, 5, 7}, {2, 4, 6}, {3}} partition in the top-left panel of Fig. 2, yet another tie is identified as being inconsistent with balance. It is the positive tie from actor 1 to actor 4 that goes between plus-sets. For the partition {{1, 4, 5, 6, 7}, {2}, {3}} in the top-right panel of Fig. 2, the positive tie from actor 2 to actor 4 is identified again as inconsistent with balance.

To focus our discussion, consider actor 1 and the bottom-left partition of Fig. 2 as actor 1's perception of the structure. Actor 1 has one option for generating a balanced structure in its image of the network: change the negative tie to actor 2 into a positive tie. If actor 1's perception is the lower-right partition in Fig. 2, the actor has one option: change the positive tie to actor 4 into a negative tie. Actor 1 cannot do anything about the positive tie from actor 2 to actor 4, except recognize it (or not). If actor 2 perceives either the top- or bottom-right partition of Fig. 2 as the group structure, that actor's option is to change its positive tie to actor 4 to a negative tie in an effort to reach balance. Each of these changes, even though they are instances of the same generative process, they lead to distinct collective outcomes when expressed in terms of partitioned structures.

Structural (or social) balance is regarded as a fundamental social process. It has been used to explain how the feelings, attitudes and beliefs, which the social actors have towards each other, promotes the formation of stable (but not necessarily conflict free) social groups. While balance theory has a rich and long history, it has lost favor in recent times. The empirical work has taken one of two forms. Most empirical work on social balance has focused on dyads and triples, and findings have been inconsistent. The remaining studies focus on the structure of the group as a whole. Results here have been inconsistent also. One major problem is that the first line of work is based only on the source ideas of Heider while the second has been based only on the ideas of Cartwright and Harary. Some of the inconsistencies may be due to this empirical split where the two streams of ideas do not inform each other. We propose a new theoretical model for social balance in the form of an agent-based simulation model. The results we present account for several of the inconsistencies found in the literature. The model simulates distinct but interdependent social actors making positive and negative selections of each other in efforts to reach balanced cognitive states. The design variables for the simulations are group size, degree of contentiousness of a group and the mode of communicating choices regarding the existence and sign of social ties. The group level balance mechanism used by the dynamic model is based on the idea of partition balance, as proposed by Doreian and Mrvar [Soc. Netw. 18 (1996) 149]. Actor selections, over time, generate networks that partition group members into stable, balanced subsets at equilibrium or near equilibrium. The design variables have complicated impacts on the number of actor choices made to reach balance, the level of group imbalance, the number of actors with balanced images and the number of plus-sets formed.

Norman P. Hummon and Patrick Doreian, "Some dynamics of social balance processes: bringing Heider back into balance theory," Social Networks, Volume 25, Issue 1, Pages 17-49 (January 2003)

Full paper (PDF)

This diagram presents a complex social network in a fairly simplistic viewpoint. It allows one to analyze and discover where imbalance or tension is present in a social network amongst the actors in the network. Further, one can break the social network into sub-networks, or smaller sets of actors, that can be analyzed in the same manner as the larger social network. (CR)
Document contributed by Colin Rego, Northeastern University, 2/2004.

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