In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum probability of connections between any pair of nodes. As a result, sparsity describes only the behavior of network as a whole, without distinguishing between the block-dependent sparsity patterns. To the best of our knowledge, the recently introduced Popularity Adjusted Block Model (PABM) is the only block model that allows to introduce a {\it structural sparsity} where some probabilities of connections are identically equal to zero while the rest of them remain above a certain threshold. The latter presents a more nuanced view of the network.

翻译：在本文中,我们研究了一个带块结构的稀疏的随机网络。流行的斯托切斯特区块模型(SBM)和度校正区块模型(DDCBM)通过对任何对结点之间最大连接概率设定一个上限,从而解决了宽度问题。因此,宽度只描述整个网络的行为,而没有区分区块依赖的聚度模式。据我们所知,最近引入的广度调整区块模型(PABM)是唯一允许引入 ~it 结构宽度的区块模型(PABM), 其某些连接概率等于零,而其余的连接则仍然高于某一阈值。后者更细化地展示了网络的视角。