title: Networks maximizing the consensus time of voter models.
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(N^{3}), where N is the number of nodes in the network.
authors.affiliation: Faculty of Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
authors.forename: Yuni
authors.initials: Y
authors.lastname: Iwamasa
authors.affiliation: Department of Mathematical Informatics, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan and Department of Engineering Mathematics, University of Bristol, Merchant Venturers Building, Woodland Road, Clifton, Bristol BS8 1UB, United Kingdom and CREST, JST, 4-1-8, Honcho, Kawaguchi, Saitama 332-0012, Japan.
authors.forename: Naoki
authors.initials: N
authors.lastname: Masuda
mesh_terms: D003196:Computer Graphics; D032921:Consensus; D008962:Models, Theoretical; D013997:Time Factors