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Structural balance in social network theory starts from signed networks withactive relationships (friendly or hostile) to establish a hierarchy betweenfour different types of triadic relationships. The lack of an active link alsoprovides information about the network. To exploit the information that remainsuncovered by structural balance, we introduce the inactive relationship thataccounts for both neutral and nonexistent ties between two agents. Thisaddition results in ten types of triads, with the advantage that the networkanalysis can be done with complete networks. To each type of triadicrelationship, we assign an energy that is a measure for its average occupationprobability. Finite temperatures account for a persistent form of disorder inthe formation of the triadic relationships. We propose a Hamiltonian with threeinteraction terms and a chemical potential (capturing the cost of edgeactivation) as an underlying model for the triadic energy levels. Our model issuitable for empirical analysis of political networks and allows to uncovergenerative mechanisms. It is tested on an extended data set for the standingsbetween two classes of alliances in a massively multi-player on-line game(MMOG) and on real-world data for the relationships between countries duringthe Cold War era. We find emergent properties in the triadic relationshipsbetween the nodes in a political network. For example, we observe a persistenthierarchy between the ten triadic energy levels across time and networks. Inaddition, the analysis reveals consistency in the extracted model parametersand a universal data collapse of a derived combination of global properties ofthe networks. We illustrate that the model has predictive power for thetransition probabilities between the different triadic states.

Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks