Emergent structures in coupled opinion and network dynamics

TL;DR

This paper models how opinions and social network structures co-evolve, revealing positive feedback loops that lead to community formation, supported by analytical and numerical analyses of different interaction functions.

Contribution

It introduces a coupled differential equation model for opinion and network dynamics, analyzing the effects of different interaction functions on community emergence.

Findings

Opinion clustering correlates with community structure formation.

Positive feedback enhances community emergence.

Transient dynamics are captured by a short-time approximation.

Abstract

This paper investigates a model of opinion formation on an adaptive social network, consisting of a system of coupled ordinary differential equations for individuals' opinions and corresponding network edge weights. A key driver of the system's behaviour is the form of the interaction function, which determines the strength of interactions based on the distance between individuals' opinions and appears in both opinion and network dynamics. Two cases are examined: in the first the interaction function is always positive and in the second case the interaction function is of bounded-confidence type. In both cases there is positive feedback between opinion clustering and the emergence of community structure in the social network. This is confirmed through analytical results on long-term behaviour, extending existing results for a fixed network, as well as through numerical simulations. Transient network dynamics are also examined through a short-time approximation that captures the `typical' early network dynamics. Each approach improves some aspect of our understanding of the interplay between opinion and network evolution.