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Eigenmode Of The Decision-By-Majority Process In Complex Networks

Author

Listed:
  • 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)

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.

Suggested Citation

  • Makoto Uchida & Susumu Shirayama, 2008. "Eigenmode Of The Decision-By-Majority Process In Complex Networks," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 565-579.
    • Handle: RePEc:wsi:acsxxx:v:11:y:2008:i:04:n:s0219525908001775
    DOI: 10.1142/S0219525908001775
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