Matemática e relações humanas: utilização de matrizes para compreender interações em redes sociais

Abstract

Human relationships, regardless of their format and their levels of organisation and institutionalisation, are generally regarded as a domain far removed from Mathematics and from analytical techniques that involve some degree of quantification. This perceived separation between the two disciplines inspired us to investigate how Mathematics might be brought closer to the Humanities. In this study, by employing adjacency matrices (Discrete Mathematics), we set out to explore the potential of this tool for describing and analysing interactions between individuals that routinely occur within social networks. Consequently, our aim was to examine how the concept of matrices can be applied to the study of both online and offline social networks. Faced with the logistical and ethical challenges of conducting research with human subjects, we opted to construct a artificial social network based on the Erdős–Rényi model using RStudio. This approach allowed us to establish relationships among individuals in social networks and, through the use of centrality metrics to characterise the network’s structure alongside its graphical representation, to analyse the interactions between its members. As a result, we concluded that the subject of social networks—whether experienced offline or as online social media—being so topical, can be employed to engage students in understanding matrices and, in conjunction with Computer Science, can provide a pathway to grasp this mathematical concept and its applications across diverse contexts. We also demonstrated how interactions between individuals in a social network, which may appear random and chaotic, can at least partly be understood through mathematics. Moreover, we hope that this work will serve as a resource for those who, like us, wish to understand how to bridge two seemingly disparate branches of knowledge: the Humanities and the Exact Sciences