Gutiérrez García-Pardo, InmaculadaGómez González, DanielCastro Cantalejo, JavierGuevara Gil, Juan AntonioEspínola Vílchez, María RosarioNescolarde Selva, Josue Antonio2024-02-072024-02-072021-02-23Gutiérrez, I.; Guevara, J.A.; Gómez, D.; Castro, J.; Espínola, R. Community Detection Problem Based on Polarization Measures: An Application to Twitter: The COVID-19 Case in Spain. Mathematics 2021, 9, 443, doi:10.3390/math9040443.10.3390/math9040443https://hdl.handle.net/20.500.14352/100076In this paper, we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the risk of polarization. Particularly, we are interested in dealing with the problem of taking into account the polarization of nodes in the community detection problem. Adding this type of information to the community detection problem makes it more realistic, as a community is more likely to be defined if the corresponding elements are willing to maintain a peaceful dialogue. The polarization capacity is modeled by a fuzzy measure based on the JDJpol measure of polarization related to two poles. We also present an efficient algorithm for finding groups whose elements are no polarized. Hereafter, we work in a real case. It is a network obtained from Twitter, concerning the political position against the Spanish government taken by several influential users. We analyze how the partitions obtained change when some additional information related to how polarized that society is, is added to the problem.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal article2227-7390https//doi.org/10.3390/math9040443https://www.mdpi.com/2227-7390/9/4/443open access004.6519.22-7NetworksCommunity detectionExtended fuzzy graphsPolarizationFuzzy setsOrdinal variationRedesEstadística aplicada1209.03 Análisis de Datos1209 Estadística