Networks maximizing the consensus time of voter models

Yuni Iwamasa and Naoki Masuda
Phys. Rev. E 90, 012816 – Published 30 July 2014

Abstract

We explore the networks that yield the largest mean consensus time of voter models under different update rules. By analytical and numerical means, we show that the so-called lollipop graph, barbell graph, and double-star graph maximize the mean consensus time under the update rules called the link dynamics, voter model, and invasion process, respectively. For each update rule, the largest mean consensus time scales as O(N3), where N is the number of nodes in the network.

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  • Received 25 April 2014

DOI:https://doi.org/10.1103/PhysRevE.90.012816

©2014 American Physical Society

Authors & Affiliations

Yuni Iwamasa1 and Naoki Masuda2,3,4,*

  • 1Faculty of Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
  • 2Department of Mathematical Informatics, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
  • 3Department of Engineering Mathematics, University of Bristol, Merchant Venturers Building, Woodland Road, Clifton, Bristol BS8 1UB, United Kingdom
  • 4CREST, JST, 4-1-8, Honcho, Kawaguchi, Saitama 332-0012, Japan

  • *naoki.masuda@brsitol.ac.uk

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Vol. 90, Iss. 1 — July 2014

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