This paper studies community detection for a nonlinear opinion dynamics model from its equilibria. It is assumed that the underlying network is generated from a stochastic block model with two communities, where agents are assigned with community labels and edges are added independently based on these labels. Agents update their opinions following a nonlinear rule that incorporates saturation effects on interactions. It is shown that clustering based on a single equilibrium can detect most community labels (i.e., achieving almost exact recovery), if the two communities differ in size and link probabilities. When the two communities are identical in size and link probabilities, and the inter-community connections are denser than intra-community ones, the algorithm can achieve almost exact recovery under negative influence weights but fails under positive influence weights. Utilizing fixed point equations and spectral methods, we also propose a detection algorithm based on multiple equilibria, which can detect communities with positive influence weights. Numerical experiments demonstrate the performance of the proposed algorithms.
Model Predictive Control for Coupled Adoption-Opinion Dynamics
Institute of Electronics, Computer and Telecommunication Engineering, National Research Council of Italy（意大利国家研究委员会电子、计算机和通信工程研究所）；Politecnico di Torino（都灵理工大学）；Department of Computer Science, Institute of Science Tokyo（东京科学大学计算机科学系）；Department of Information Physics and Computing, The University of Tokyo（东京大学信息物理与计算学系）
Behavior of Nonlinear Opinion Dynamics over Large Networks
Faculty of Computer Science, RWTH Aachen University（亚琛工业大学计算机学院）；Sibley School of Mechanical and Aerospace Engineering, Cornell University（康奈尔大学西尔比机械与航空航天工程学院）；Division of Decision and Control Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology（皇家理工学院电气与计算机学院决策与控制系）；Digital Futures（数字未来）
