论文标题
广义随机块模型中的相变
Phase Transition in the Generalized Stochastic Block Model
论文作者
论文摘要
我们研究了从广义随机块模型（GSBM）检测社区结构的问题。基于对经验光谱分布的Stieljtes变换的分析，我们证明了GSBM最大特征值的BBP型转变。对于诸如隐藏的社区模型和不平衡的随机模型之类的特定模型，我们为两个最大的特征值提供精确的公式，从而在BBP型过渡中建立了差距。
We study the problem of detecting the community structure from the generalized stochastic block model (GSBM). Based on the analysis of the Stieljtes transform of the empirical spectral distribution, we prove a BBP-type transition for the largest eigenvalue of the GSBM. For specific models such as a hidden community model and an unbalanced stochastic model, we provide precise formulas for the two largest eigenvalues, establishing the gap in the BBP-type transition.
