AI 中文总结
研究随机块模型及其变体生成网络的组件结构和渗流特性，采用基于概率生成函数的精确方法，推导相关表达式并建立模型生成函数映射。
AI 中文摘要
随机块模型是网络中广泛研究的社区结构模型。本文利用基于概率生成函数的精确方法，研究了该模型及其变体生成网络的组件结构和渗流特性。具体推导了原始随机块模型及其度校正版本中巨组件大小、小子组件分布、渗流簇大小以及节点和边渗流的渗流阈值位置的表达式。还建立了微正则和正则块模型生成函数之间的映射。
英文摘要
The stochastic block model is a widely studied model of community structure in networks. Here we study the component structure and percolation properties of networks generated from this model and its variants, using exact methods based on probability generating functions. In particular, we derive expressions for the size of the giant component and the distribution of small components in such networks and for the size of the percolating cluster and position of the percolation threshold for both node and edge percolation, for the original stochastic block model and for its degree-corrected versions. In passing, we also develop a mapping between generating functions for microcanonical and canonical block models that allows us to generalize results for the former to the latter with minimal effort.
Comments14 pages, 5 figures
