Entropic determination of the phase transition in a coevolving opinion-formation model

TL;DR

This paper investigates a co-evolving opinion formation model on complex networks, using entropy to identify phase transitions between consensus and opinion coexistence, revealing scale-free group size distributions at criticality.

Contribution

It introduces an entropy-based method to detect phase transitions in a co-evolving opinion network model, linking network plasticity to opinion dynamics.

Findings

Entropy effectively locates the phase transition point.

At the transition, group size distribution is scale-free.

Minimum sample size for accurate detection is identified.

Abstract

We study an opinion formation model by the means of a co-evolving complex network where the vertices represent the individuals, characterised by their evolving opinions, and the edges represent the interactions among them. The network adapts to the spreading of opinions in two ways: not only connected agents interact and eventually change their thinking but an agent may also rewire one of its links to a neighborhood holding the same opinion as his. The dynamics depends on an external parameter {\Phi}, which controls the plasticity of the network. We show how the information entropy associated to the distribution of group sizes, allows to locate the phase transition between full consensus and a society where different opinions coexist. We also determine the minimum size of the most informative sampling. At the transition the distribution of the sizes of groups holding the same opinion is scale free.