  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.
