Structural balance theory postulates that positive and negative network ties will be intertwined into triadic structures through specific triadic processes. The theory was developed for undirected networks where a relationship could be either positive or negative but not both. In many empirical studies, directed ties are important and ties can be simultaneously positive and negative (for instance, a relationship of trust can still be difficult). In these circumstances, it is an open question how positive and negative ties intertwine, and structural balance theory does not provide clear guidance.
In this paper, triadic structures between positive and negative ties are investigated empirically using trust and work-difficulty networks. Using Exponential Random Graph Models (ERGMs) for univariate and multivariate networks (Pattison & Wasserman, 1997; Robins, Snijders, Wang, Handcock, & Pattison, 2007; Snijders, Pattison, Robins, & Hancock, 2006) we study trust and work-difficulty networks individually and then model the networks together. When modelling the networks individually, we found strong endogenous triangulation effects in both networks. However, parameter estimates in these separate network models were not greatly changed when the two types of tie were modeled together, implying that the endogenous triangulation remains and is not explained by balance-type triadic effects. The joint model suggests that positive and negative ties are associated at the dyadic level, and also in multivariate activity and popularity effects, but all multivariate triangulation configurations can be reproduced without resort to a balance-type parameter. In other words, in this example, any balance-like triangulation of positive and negative ties can be plausibly explained by endogenous triangulation within the two types of tie, and simpler processes of association between the types. So while balance-type configurations may be present in the data, a balance-type process is not a necessary explanation.