Designing Laplacian flows for opinion clustering in structurally balanced and unbalanced networks

TL;DR

This paper introduces a Laplacian-based model for opinion dynamics in signed and unsigned networks, analyzing conditions for its application and validating results through numerical simulations.

Contribution

It proposes a novel Laplacian-based opinion model applicable to both balanced and unbalanced networks, with analysis and validation of its effectiveness.

Findings

Conditions for applying the Laplacian-based model are established.

Numerical results validate the theoretical analysis.

The model effectively captures opinion evolution in various network structures.

Abstract

In this work, we consider a group of n agents whose interactions can be represented using unsigned or signed structurally balanced graphs or a special case of structurally unbalanced graphs. A Laplacian-based model is proposed to govern the evolution of opinions. The objective of the paper is to analyze the proposed opinion model on the opinion evolution of the agents. Further, we also determine the conditions required to apply the proposed Laplacian-based opinion model. Finally, some numerical results are shown to validate these results.