Emergent Features of Triadic Relations in Political Networks

Jan Ryckebusch¹, Andres M. Belaza¹, Kevin Hoefman¹, Koen Schoors¹

We propose a model with five energy levels that encodes the dynamics of triadic relationships in a political network. The model builds on insights gleaned from structural balance theory to which we add elements from Boltzmann-Gibbs statistical physics and go beyond the restrictions of signed networks. We start from the idea that two agents that maintain ties in a political network can be either enemies, or friends, or neutrals to each other. The generic Hamiltonian associated with the five energy levels contains three parameters. One is connected with a three-body interaction inspired on social balance theory. The other two parameters take into account the costs of symmetry breaking and of changing a link. We stress the role of the degeneracy of the different energy levels and how it affects the degree of frustration in the political network. The validity of our model is tested on an extended data set for the time series of triadic relationships for the standings between alliances in a massive multiplayer online role-playing game. We also analyze real-world data for the different factions that play a role in the current war in Syria. We find emerging properties in the triadic relationships between the nodes in a political network, for example reflecting itself in a persistent hierarchy between the different energy levels.