Community detection problem based on polarization measures:an application to Twitter: the COVID-19 case in Spain
Inmaculada Gutiérrez, Juan Antonio Guevara, Daniel Gómez, Javier Castro, Rosa Espínola
TL;DR
This paper tackles enhancing community detection by incorporating polarization information on online social networks using polarization extended fuzzy graphs. It defines polarization-based fuzzy measures $\mu_{P^-}$ and non-polarization $\mu_{P^+}$, proves $2$-additivity, and derives a weighted graph $F$ from Shapley values to combine with the topology in a Polarization Louvain algorithm with $M=\gamma A+(1-\gamma)F$. The authors apply the method to a Twitter network around Spain's COVID-19 response, showing partitions adapt to polarization information and yield lower $JDJ_{pol}$ within communities than classical Louvain. The work demonstrates that integrating attitudinal information via fuzzy measures yields more realistic, cohesive communities and provides a scalable framework for networks with multi-criteria information.
Abstract
In 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.