Heider and coevolutionary balance: From discrete to continuous phase transition

TL;DR

This paper investigates how social balance in complex networks transitions under varying social disorder, revealing that Heider balance exhibits a discrete phase transition while coevolutionary balance shows a continuous one, with critical temperature scaling linearly with network size.

Contribution

It introduces a model comparing Heider and coevolutionary balance, demonstrating their different phase transition behaviors through analytical and numerical methods.

Findings

Heider balance has a discrete phase transition.

Coevolutionary balance exhibits a continuous phase transition.

Critical temperature scales with the square root of network size.

Abstract

Structural balance in social complex networks has been modeled with two types of triplet interactions. First, the interaction that only considers dynamic role for links or relationships (Heider balance), and second, the interaction that considers both individual opinions (nodes) and relationships in network dynamics (coevolutionary balance). The question is, as the temperature varies, which is a measure of social disorder, how structural balance can be created or destroyed by each of these triplet interactions? We use statistical mechanics methods and observe through analytical calculation and numerical simulation that unlike the Heider balance triplet interaction which has a discrete phase transition, the coevolutionary balance has a continuous phase transition. The critical temperature of the presented model change with the root square of network size which is a linear dependence in thermal Heider balance.