Heider vs Simmel: Emergent Features in Dynamic Structures

Heider’s balance theory has been a cornerstone of structural explanations and explorations of network dynamics. Most frequently, Heider’s theory is interpreted as inducing reciprocated and transitive ties among nodes in a graph. Empirical work consistently shows that these structural features (reciprocity and transitivity) occur in naturally emergent networks more often than we would expect under standard random graph assumptions, a result that is often used to claim that Heider’s model is a valid representation of the real world. The problem is, any simulation of a generative model based on Heider’s principles almost invariably leads to a degenerate result of complete graphs or components. Fifty years prior to Heider, Simmel proposed a triadic model of social analysis, one that has distinct parallels with Heider but has a structural/sociological rather than psychological base. Simmel’s model, while it also explains the relatively frequent existence of reciprocated and transitive ties, is based on a simpler premise. We provide both empirical evidence for Simmel’s alternate view of the social world and compare the dynamics of Heiderian and Simmelian structures in a generative model of tie formation. We find that when the triadic Heiderian statistics are modeled that they are not taken into account by the Simmelian terms. But the reverse is also not true. So both effects appear to exist simultaneously. 1 Heider’s Balance Theory One of the central questions in the field of network analysis is: How do networks form? A cornerstone to our understanding of this process from a structural point of view has been Heider’s (1946) theory of balance[1]. According to this theory, a person is motivated to establish and maintain balance in their relationships. What constitutes balance has been the subject of some debate (e.g., [2, 3]), but the core principle has survived and underlies many of our attempts to model this process of network formation (see, for example, [4]). ? The research of Handcock was supported by Grant DA012831 from NIDA and Grant HD041877 from NICHD.