Overlapping Community Detection to Generate a Maximum Proximity-Driven Feedback Method for Group Consensus Under Social Network

With the rise of social network group decision-making (SN-GDM), research on trust relationships has aided in achieving group consensus. However, as network structures grow more complex, there is a growing focus on studying overlapping communities. Most existing methods do not take into account the overlap between communities, thereby not fully revealing the interactive consensus within groups where many users are involved. Additionally, the role of overlapping nodes, which belong to multiple communities, in information exchange and promoting cooperation deserves further investigation. To address these issues, this research provides a maximum proximity-based feedback mechanism, utilizing overlapping structures, which offers effective and acceptable recommendations to guide subgroup interactions. First, higher order structural importance-based method (HoSIM) is used to detect overlapping communities, followed by the concept of proximity degree (PD) for the first time to identify high-quality overlapping nodes within them. Second, a feedback mechanism driven by overlapping communities based on proximity is proposed. By using PDs as weights, it participates in the formation of recommendations and the determination of interaction willingness, thereby improving the group consensus to the desired level. Finally, through numerical experiments and comparative analysis, the superiority of this study is demonstrated not only in consensus rounds but also in adjusting costs.