  Researchers have extensively studied the social mechanisms that drive the
formation of networks observed among preschool children. However, less
attention has been given to global network structures in terms of blockmodels.
A blockmodel is a network where the nodes are groups of equivalent units
(according to links to others) from a studied network. Cugmas et al. (2019)
showed that mutuality, popularity, assortativity, and different types of
transitivity mechanisms can lead the global network structure to the proposed
asymmetric core-cohesive blockmodel. Yet, they did not provide any evidence
that such a global network structure actually appears in any empirical data. In
this paper, the symmetric version of the core-cohesive blockmodel type is
proposed. This blockmodel type consists of three or more groups of units. The
units from each group are internally well linked to each other while those from
different groups are not linked to each other. This is true for all groups,
except one in which the units have mutual links to all other units in the
network. In this study, it is shown that the proposed blockmodel type appears
in empirical interactional networks collected among preschool children. Monte
Carlo simulations confirm that the most often studied social network mechanisms
can lead the global network structure to the proposed symmetric blockmodel
type. The units' attributes are not considered in this study.
