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.

翻译：本文探讨了社会网络分析领域的一个核心议题：融合附加信息的社群检测问题。该附加信息通过表示极化风险的模糊测度进行建模。我们特别关注如何在社群检测中考虑节点的极化程度。将此类信息纳入社群检测问题使其更贴近现实，因为只有当社群成员愿意进行和平对话时，该社群才更可能被有效定义。极化能力采用基于JDJpol双极极化测度的模糊函数进行建模。我们同时提出了一种高效算法，用于识别非极化节点群组。最后，我们基于从推特平台获取的真实网络数据展开研究——该网络涉及多位具有影响力的用户针对西班牙政府所持的政治立场。通过分析，我们揭示了当社会极化程度相关信息被纳入问题框架后，网络划分结果产生的具体变化。