The stochastic block model (SBM) is widely employed as a canonical model for network community detection. Recovering community labels under SBM is not a trivial task, since its theoretical optimization problem is NP‐hard. To solve this problem, numerous statistical methods have been developed in the literature, most of which are, however, not applicable to large‐scale networks. To overcome this limitation, in this paper, we propose a split likelihood (SL) framework, under which we provide a fast converging algorithm, named the SL algorithm, with significant advantages in terms of both community detection accuracy and computational efficiency. Moreover, to deal with networks with hub nodes or those with substantial degrees of variation within communities, we develop a variant of the SL algorithm, named the conditional SL (CSL) algorithm. We present the computational and statistical properties of the proposed algorithm. Then, we demonstrate the superiority of the proposed methods through a large amount of numerical experiments as well as two empirical analyses on real‐world networks.

中文翻译：

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基于高效分割似然法的大型网络社区检测方法

随机块模型（SBM）被广泛用作网络社区检测的规范模型。在SBM下恢复社区标签并不是一件容易的事，因为它的理论优化问题是NP-hard。为了解决这个问题，文献中已经开发了许多统计方法，但是其中大多数不适用于大规模网络。为了克服这一限制，在本文中，我们提出了一种分裂似然（SL）框架，在该框架下，我们提供了一种称为SL算法的快速收敛算法，在社区检测准确性和计算效率方面均具有显着优势。此外，为了处理具有中心节点或社区内变化程度较大的网络，我们开发了SL算法的一种变体，称为条件SL（CSL）算法。我们介绍了该算法的计算和统计特性。然后，我们通过大量的数值实验以及在现实世界网络上的两次经验分析，证明了所提出方法的优越性。