Análise utilizando teoria de redes complexas aplicada aos microdados do ENEM

Abstract

The Minimum Spanning Tree (MST) tool, in Portuguese Minimum Spanning Tree, has been used to find clusters of similarities in stock exchanges, deputy votes, etc. all variables. The brightness distance d(i, j) is defined by d(i, j) = p 2(1−ρ(i, j)), where ρ(i, j) is the Pearson radiance coefficient. Similarity clusters are extracted by MST obtained with Prim’s algorithm. In ENEM, a group of over 100,000 students in Ceará answered the same 180 questions. An initial cleaning, in relation to missing data, restricted this number to approximately 80,000, from which we sampled 25,000 students stratified proportionally by municipality. The microdata were obtained from the Kaggle platform for the years 2018 and 2019 and for the years 2020 to 2023 they were obtained from the INEP page. We placed the templates for the 4 types of face-to-face tests into a discretized standard template that we used to obtain the student-by-student brightness matrix. Our objective is to extract student clusters from response vectors only, with which we analyze the role of socioeconomic variables to understand the nature of correlations. The positive correlations came from the best grades, as expected. We also analyzed the role of income, parental education, municipality and school.