Continuous opinion model in small world directed networks

TL;DR

This paper investigates how continuous opinion dynamics evolve in small world directed networks, revealing complex behaviors in the number of final opinions depending on network structure and tolerance levels.

Contribution

It extends the Deffuant et al. opinion model to directed networks and analyzes the impact of network directionality and disorder on opinion convergence.

Findings

Directed networks show a richer structure in the number of final opinions.

Higher tolerance levels lead to more diverse final opinions in directed networks.

Network directionality influences opinion convergence differently than in undirected networks.

Abstract

In the compromise model of continuous opinions proposed by Deffuant et al, the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance $\epsilon$. In directed networks, if agent i is a neighbor of agent j, j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions $<F>$ and their distribution as a function of $\epsilon$ and of the network structural disorder. In directed networks $<F>$ exhibits a rich structure, being larger than in undirected networks for higher values of $\epsilon$, and smaller for lower values of $\epsilon$.