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2017 ; 12
(8
): e0183696
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Statistical physics of balance theory
#MMPMID28846726
Belaza AM
; Hoefman K
; Ryckebusch J
; Bramson A
; van den Heuvel M
; Schoors K
PLoS One
2017[]; 12
(8
): e0183696
PMID28846726
show ga
Triadic relationships are accepted to play a key role in the dynamics of social
and political networks. Building on insights gleaned from balance theory in
social network studies and from Boltzmann-Gibbs statistical physics, we propose a
model to quantitatively capture the dynamics of the four types of triadic
relationships in a network. Central to our model are the triads' incidence rates
and the idea that those can be modeled by assigning a specific triadic energy to
each type of triadic relation. We emphasize the role of the degeneracy of the
different triads and how it impacts the degree of frustration in the political
network. In order to account for a persistent form of disorder in the formation
of the triadic relationships, we introduce the systemic variable temperature. In
order to learn about the dynamics and motives, we propose a generic Hamiltonian
with three terms to model the triadic energies. One term is connected with a
three-body interaction that captures balance theory. The other terms take into
account the impact of heterogeneity and of negative edges in the triads. The
validity of our model is tested on four datasets including the time series of
triadic relationships for the standings between two classes of alliances in a
massively multiplayer online game (MMOG). We also analyze real-world data for the
relationships between the "agents" involved in the Syrian civil war, and in the
relations between countries during the Cold War era. We find emerging properties
in the triadic relationships in a political network, for example reflecting
itself in a persistent hierarchy between the four triadic energies, and in the
consistency of the extracted parameters from comparing the model Hamiltonian to
the data.
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