In this work, we describe a method that determines an exact map from a finite set of subgraph densities to the parameters of a stochastic block model (SBM) matching these densities. Given a number $K$ of blocks, the subgraph densities of a finite number of stars and bistars uniquely determines a single element of the class of all degree-separated stochastic block models with $K$ blocks. Our method makes it possible to translate estimates of these subgraph densities into model parameters, and hence to use subgraph densities directly for inference. The computational overhead is negligible; computing the translation map is polynomial in $K$, but independent of the graph size once the subgraph densities are given.

翻译：本文描述了一种方法，该方法能够精确地将有限个子图密度集合映射到匹配这些密度的随机块模型参数。给定块数 $K$，有限数量的星形和二星形子图密度唯一确定了所有具有 $K$ 块的度分离随机块模型类别中的单一元素。我们的方法使得将这些子图密度的估计值转化为模型参数成为可能，从而可以直接利用子图密度进行推断。计算开销可忽略不计；映射的计算复杂度关于 $K$ 呈多项式关系，且一旦给定子图密度，其与图规模无关。