Eigenmode of Decision-By-Majority Process on Complex Networks

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.