论文标题
常规随机块模型中社区的独特性
Uniqueness of communities in regular stochastic block models
论文作者
论文摘要
本文研究了包括\ emph {几个}社区的常规随机块模型：$ k $非重叠的社区中的每个社区，价格为$ k \ geqslant 3 $，具有$ n $的顶点，每个顶点都有$ d $ $ d $。群集内度（即\ \群集属于群集内的顶点的邻居数）和集群间度（即\ \群集内部与其自身群集中不同的邻居邻居的数量）的值可以在群体上变化。我们讨论了两个主要结果：第一个比较了我们的模型引起的概率度量与$ kn $顶点的$ d $期权图的均匀度量，第二个确定在相当弱的假设下，群集在相当弱的假设下肯定是$ n \ rightarrow \ rightarrow \ rightarrow \ rightarrow \ rightarrow \ infty \ infty $。
This paper studies the regular stochastic block model comprising \emph{several} communities: each of the $k$ non-overlapping communities, for $k \geqslant 3$, possesses $n$ vertices, each of which has total degree $d$. The values of the intra-cluster degrees (i.e.\ the number of neighbours of a vertex inside the cluster it belongs to) and the inter-cluster degrees (i.e.\ the number of neighbours of a vertex inside a cluster different from its own) are allowed to vary across clusters. We discuss two main results: the first compares the probability measure induced by our model with the uniform measure on the space of $d$-regular graphs on $kn$ vertices, and the second establishes that the clusters, under rather weak assumptions, are unique asymptotically almost surely as $n \rightarrow \infty$.
