There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choices, the block models do not have a nested structure. In addition, there is a substantial jump in the number of parameters from the DCBM to the PABM. The objective of this paper is formulation of a hierarchy of block model which does not rely on arbitrary identifiability conditions. We propose a Nested Block Model (NBM) that treats the SBM, the DCBM and the PABM as its particular cases with specific parameter values, and, in addition, allows a multitude of versions that are more complicated than DCBM but have fewer unknown parameters than the PABM. The latter allows one to carry out clustering and estimation without preliminary testing, to see which block model is really true.

翻译：存在各种类型的网络块模型,如斯托切斯特区块模型(SBM)、度校正区块模型(DCBM)和广度调整区块模型(PABM),这导致各种选择,但区块模型没有嵌套结构。此外,从DCBM到PABM的参数数量大幅上升。本文件的目的是制定不依赖任意识别条件的区块模型的等级结构。我们建议采用内斯特德区块模型(NBM),将SBM、DCBM和PABM作为具体参数值的具体案例处理,此外,允许多种比DCBM更复杂但比PABM的未知参数更少的版本。后者允许不经初步测试就进行集群和估算,看哪个区块模型是真实的。