Eigenmode of Decision-By-Majority Process on Complex Networks

TL;DR

This paper investigates opinion formation dynamics in complex networks using eigenmode analysis, revealing that the initial state's largest eigenvector magnitude significantly influences the final consensus outcome.

Contribution

It introduces an eigenmode analysis approach to decision-by-majority dynamics on complex networks, linking initial eigenvector magnitudes to final states.

Findings

Largest eigenvector magnitude at initial state predicts final opinion consensus

Eigenmode analysis effectively characterizes opinion dynamics

Network structure influences eigenmodes and dynamics

Abstract

The nature of dynamics of opinion formation modeled as a decision-by-majority process in complex networks is investigated using eigenmode analysis. Hamiltonian of the system is defined, and estimated by eigenvectors of the adjacency matrix constructed from several network models. The eigenmodes of initial and final state of the dynamics are analyzed by numerical studies. We show that the magnitude of the largest eigenvector at the initial states are key determinant for the resulting dynamics.