Volume 118, Number 5, June 2017
|Number of page(s)||5|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||18 August 2017|
A small chance of paradise —Equivalence of balanced states
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science al. Mickiewicza 30, 30-059 Kraków, Poland
Received: 11 April 2017
Accepted: 24 July 2017
A social network is modeled by a complete graph of N nodes, with interpersonal relations represented by links. In the framework of the Heider balance theory, we prove numerically that the probability of each balanced state is the same. This means in particular, that the probability of the paradise state, where all relations are positive, is . The proof is performed within two models. In the first, relations are changing continuously in time, and the proof is performed only for N = 3 with the methods of nonlinear dynamics. The second model is the Constrained Triad Dynamics, as introduced by Antal, Krapivsky and Redner in 2005. In the latter case, the proof makes use of the symmetries of the network of system states and it is completed for .
PACS: 89.65.-s – Social and economic systems / 89.75.-k – Complex systems / 02.10.Ox – Combinatorics; graph theory
© EPLA, 2017
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.