Mean-field solution for critical behavior of signed networks in competitive balance theory

R. Masoumi, F. Oloomi, A. Kargaran, A. Hosseiny, and G. R. Jafari
Phys. Rev. E 103, 052301 – Published 4 May 2021

Abstract

The competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks. In this model, two different paradigms or interests compete with each other to dominate the network's relations and impose their own values. In this paper, using the mean-field method, we examine the thermal behavior of the competitive balance model. Our results show that under a certain temperature, the symmetry between two competing interests will spontaneously break which leads to a discrete phase transition. So, starting with a heterogeneous signed network, if agents aim to decrease tension stemming from competitive balance theory, evolution ultimately chooses only one of the existing interests and stability arises where one paradigm dominates the system. The critical temperature depends linearly on the number of nodes, which is a linear dependence in the thermal balance theory as well. Finally, the results obtained through the mean-field method are verified by a series of simulations.

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  • Received 29 July 2020
  • Revised 3 February 2021
  • Accepted 30 March 2021

DOI:https://doi.org/10.1103/PhysRevE.103.052301

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsNetworks

Authors & Affiliations

R. Masoumi, F. Oloomi, A. Kargaran, A. Hosseiny*, and G. R. Jafari

  • Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran

  • *al_hosseiny@sbu.ac.ir
  • g_jafari@sbu.ac.ir

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Issue

Vol. 103, Iss. 5 — May 2021

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