EIGENMODE OF THE DECISION-BY-MAJORITY PROCESS IN COMPLEX NETWORKS
The nature of the dynamics of opinion formation or zero-temperature Ising models modeled as a decision-by-majority process in complex networks is investigated using eigenmode analysis. The Hamiltonian of the system is defined and estimated by eigenvectors of the adjacency matrix constructed from several network models. The rule of the process is assumed to be equivalent to the minimization of the Hamiltonian. The initial and final states of the dynamics are decomposed on the basis of the eigenvectors. The process and the eigenmodes are analyzed by numerical studies. We show that the magnitude of the coefficient for the largest eigenvector at the initial states is the key determinant for the resulting dynamics. We thus prove that the final state of the dynamics can be estimated by the eigenmodes of the initial state.
In order to set up a list of libraries that you have access to,
you must first login
or sign up.
Then set up a personal list of libraries from your profile page by
clicking on your user name at the top right of any screen.