title: Multilayer weighted social network model.
abstract: Recent empirical studies using large-scale data sets have validated the Granovetter hypothesis on the structure of the society in that there are strongly wired communities connected by weak ties. However, as interaction between individuals takes place in diverse contexts, these communities turn out to be overlapping. This implies that the society has a multilayered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when merging such WSN models, a sufficient amount of interlayer correlation is needed to maintain the relationship between topology and link weights, while these correlations destroy the enhancement in the community overlap due to multiple layers. To resolve this, we devise a geographic multilayer WSN model, where the indirect interlayer correlations due to the geographic constraints of individuals enhance the overlaps between the communities and, at the same time, the Granovetterian structure is preserved.
authors.affiliation: RIKEN Advanced Institute for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo, 650-0047, Japan and CREST, Japan Science and Technology Agency 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan.
authors.forename: Yohsuke
authors.initials: Y
authors.lastname: Murase
authors.affiliation: Department of Theoretical Physics, Budapest University of Technology and Economics, HU-1111 Budapest, Hungary.
authors.forename: János
authors.initials: J
authors.lastname: Török
authors.affiliation: Department of Biomedical Engineering and Computational Science, Aalto University School of Science, P.O. Box 12200, FI-Espoo, Finland and BK21plus Physics Division and Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea.
authors.forename: Hang-Hyun
authors.initials: HH
authors.lastname: Jo
authors.affiliation: Department of Biomedical Engineering and Computational Science, Aalto University School of Science, P.O. Box 12200, FI-Espoo, Finland.
authors.forename: Kimmo
authors.initials: K
authors.lastname: Kaski
authors.affiliation: Department of Theoretical Physics, Budapest University of Technology and Economics, HU-1111 Budapest, Hungary and Department of Biomedical Engineering and Computational Science, Aalto University School of Science, P.O. Box 12200, FI-Espoo, Finland and Center for Network Science, Central European University, Nádor u. 9, HU-1051 Budapest, Hungary.
authors.forename: János
authors.initials: J
authors.lastname: Kertész