EIGENMODE OF THE DECISION-BY-MAJORITY PROCESS IN COMPLEX NETWORKS

Makoto Uchida () and Susumu Shirayama ()
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Makoto Uchida: School of Engineering, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8568, Japan
Susumu Shirayama: Research into Artifacts, Center for Engineering (RACE), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8568, Japan

Advances in Complex Systems (ACS), 2008, vol. 11, issue 04, pages 565-579

Abstract: 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.

Keywords: Complex networks; opinion formation; Ising model; Glauber dynamics; eigenmode analysis; spectral method (search for similar items in EconPapers)
Date: 2008

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