# The Heider balance and the looking-glass self

## TL;DR

This paper extends the Heider balance theory to directed networks by incorporating self-evaluation based on the 'looking-glass self' concept, analyzing stable relation configurations with asymmetric relations and self-acceptance indices.

## Contribution

It introduces a new self-acceptance index and generalizes the Heider balance dynamics to include self-evaluation in directed networks.

## Key findings

- Stable configurations with negative self-evaluation are identified.
- The structure of relation sets remains consistent within each stable configuration.
- The model accounts for asymmetric relations and self-perception in social networks.

## Abstract

We consider the dynamics of interpersonal relations which leads to balanced states in a fully connected network. Here this approach is applied to directed networks with asymmetric relations, and it is generalized to include self-evaluation of actors, according to the 'looking-glass self' theory. A new index of self-acceptance is proposed: the relation of an actor to him/herself is positive, if the majority of his/her positive relations to others are reciprocated. Sets of stable configurations of relations are obtained under the dynamics, where the self-evaluation of some actors is negative. Within each set all configurations have the same structure.