Stochastic block model (SBM) has been extensively studied for undirected network data with community structure, yet its extension to directed network, stochastic co-block model (ScBM), has only been proposed recently. The key difference of the ScBM model is to introduce out- and in-communities to capture different sending and receiving patterns among nodes. In this paper, we further extend the ScBM model so that each node may belong to multiple out- or in-communities. Particularly, we formulate the ScBM model as a generative model, where the unknown community assignment is modeled based on the exclusive or overlapped community. We also establish the corresponding identifiability of the generative ScBM model, and estimate its parameters via an efficient variational EM algorithm. The advantage of the generative ScBM model is demonstrated in a variety of simulated networks and a real political blog network.

随机块模型（SBM）已被广泛研究用于具有社区结构的无向网络数据，但它对有向网络的扩展，随机共块模型（ScBM）直到最近才被提出。ScBM 模型的主要区别在于引入社区外和社区内以捕获节点之间不同的发送和接收模式。在本文中，我们进一步扩展了 ScBM 模型，使每个节点可以属于多个外部或内部社区。特别是，我们将 ScBM 模型制定为生成模型，其中未知社区分配是基于排他或重叠社区建模的。我们还建立了生成 ScBM 模型的相应可识别性，并通过有效的变分 EM 算法估计其参数。