# Symmetric core-cohesive blockmodel in preschool children's interaction networks

## TL;DR

This study introduces a symmetric core-cohesive blockmodel for preschool children's interaction networks, demonstrating its empirical occurrence and how social mechanisms can produce such structures.

## Contribution

It proposes and empirically validates a symmetric core-cohesive blockmodel in preschool networks, extending previous asymmetric models and analyzing the influence of social mechanisms.

## Key findings

- The symmetric core-cohesive blockmodel appears in empirical preschool interaction networks.
- Monte Carlo simulations show social mechanisms can produce this network structure.
- The model does not consider units' attributes.

## Abstract

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.