Structural balance in social network theory starts from signed networks with
active relationships (friendly or hostile) to establish a hierarchy between
four different types of triadic relationships. The lack of an active link also
provides information about the network. To exploit the information that remains
uncovered by structural balance, we introduce the inactive relationship that
accounts for both neutral and nonexistent ties between two agents. This
addition results in ten types of triads, with the advantage that the network
analysis can be done with complete networks. To each type of triadic
relationship, we assign an energy that is a measure for its average occupation
probability. Finite temperatures account for a persistent form of disorder in
the formation of the triadic relationships. We propose a Hamiltonian with three
interaction terms and a chemical potential (capturing the cost of edge
activation) as an underlying model for the triadic energy levels. Our model is
suitable for empirical analysis of political networks and allows to uncover
generative mechanisms. It is tested on an extended data set for the standings
between two classes of alliances in a massively multi-player on-line game
(MMOG) and on real-world data for the relationships between countries during
the Cold War era. We find emergent properties in the triadic relationships
between the nodes in a political network. For example, we observe a persistent
hierarchy between the ten triadic energy levels across time and networks. In
addition, the analysis reveals consistency in the extracted model parameters
and a universal data collapse of a derived combination of global properties of
the networks. We illustrate that the model has predictive power for the
transition probabilities between the different triadic states.Comment: 21 pages, 10 figure