Stereotype graph: A mathematical framework of category stereotypes via graph theory

TL;DR

This paper introduces a mathematical graph theory framework to model and analyze human category stereotypes, defining criteria for stereotype stability and introducing the chromatic stability index (CSI) to quantify it.

Contribution

It provides a novel graph-theoretic approach to formalize and measure the stability of stereotypes in human cognition, filling a gap in mathematical modeling.

Findings

Defined criteria for stereotype stability using graph theory.

Introduced the chromatic stability index (CSI) to quantify stereotype stability.

Explained why stereotypes tend to persist in human cognition.

Abstract

In social psychology and cognitive science, there has been much interest in studying category stereotypes. However, we still lack a consensual mathematical definition or framework, which is necessary for us to hold a deeper understanding of stereotypes in human cognition. In this paper, we use graph theory to portray category stereotypes in human cognition, based on pairs of labels having special relations. By using methods and conclusions in graph theory (including algebraic graph theory and vertex coloring) as well as strict ratiocination, we give criteria for judging the stability of a given stereotype, some of which are computationally practicable. We also define the chromatic stability index (CSI) to measure the stability of a stereotype in human cognition, as well as to provide its precise range. From the perspective of stereotype graphs and CSI, we may explain why stereotypes can easily stay in human cognition.