Towards the Heider balance with a cellular automaton

TL;DR

This paper introduces a deterministic cellular automaton model on a triangular lattice to simulate the evolution of social networks towards structural balance, analyzing triad configurations and their dynamics.

Contribution

It presents a novel cellular automaton approach to model the dynamics of Heider balance in social networks, including analysis of triad configurations and blinking unbalanced triads.

Findings

Time evolution increases local correlations of balanced triads

Unbalanced triads can exhibit blinking behavior with a period of two steps

The model provides insights into the dynamics of social balance formation

Abstract

The state of structural balance (termed also `Heider balance') of a social network is often discussed in social psychology and sociophysics. In this state, actors at network nodes classify other individuals as enemies or friends. Hence, the network contains two kinds of links: positive and negative. Here a new cellular automaton is designed and investigated, which mimics the time evolution towards the structural balance. The automaton is deterministic and synchronous. The medium is the triangular lattice with some fraction $f$ of links removed. We analyse the number of unbalanced triads (parameterized as `energy'), the frequencies of balanced triads and correlations between them. The time evolution enhances the local correlations of balanced triads. Local configurations of unbalanced triads are found which are blinking with period of two time steps.