Complex networks enable to represent and characterize the interactions between entities in various complex systems which widely exist in the real world and usually generate vast amounts of data about all the elements, their behaviors and interactions over time. The studies concentrating on new network analysis approaches and methodologies are vital because of the diversity and ubiquity of complex networks. The stochastic block model (SBM), based on Bayesian theory, is a statistical network model. SBMs are essential tools for analyzing complex networks since SBMs have the advantages of interpretability, expressiveness, flexibility and generalization. Thus, designing diverse SBMs and their learning algorithms for various networks has become an intensively researched topic in network analysis and data mining. In this article, we review, in a comprehensive and in-depth manner, SBMs for different types of networks (i.e., model extensions), existing methods (including parameter estimation and model selection) for learning optimal SBMs for given networks and SBMs combined with deep learning. Finally, we provide an outlook on the future research directions of SBMs.

Stochastic blockmodel (SBM) is a widely used statistical network representation model, with good interpretability, expressiveness, generalization, and flexibility, which has become prevalent and important in the field of network science over the last years. However, learning an optimal SBM for a given network is an NP-hard problem. This results in significant limitations when it comes to applications of SBMs in large-scale networks, because of the significant computational overhead of existing SBM models, as well as their learning methods. Reducing the cost of SBM learning and making it scalable for handling large-scale networks, while maintaining the good theoretical properties of SBM, remains an unresolved problem. In this work, we address this challenging task from a novel perspective of model redefinition. We propose a novel redefined SBM with Poisson distribution and its block-wise learning algorithm that can efficiently analyse large-scale networks. Extensive validation conducted on both artificial and real-world data shows that our proposed method significantly outperforms the state-of-the-art methods in terms of a reasonable trade-off between accuracy and scalability. 1

Signed networks with positive and negative links attract considerable interest in their studying since they contain more information than unsigned networks. Community detection and sign (or attitude) prediction are still primary challenges, as the fundamental problems of signed network analysis. For this, a generative Bayesian approach is presented wherein 1) a signed stochastic blockmodel is proposed to characterize the community structure in the context of signed networks, by explicit formulating the distributions of the density and frustration of signed links from a stochastic perspective, and 2) a model learning algorithm is advanced by theoretical deriving a variational Bayes EM for the parameter estimation and variation-based approximate evidence for the model selection. The comparison of the above approach with the state-of-the-art methods on synthetic and real-world networks, shows its advantage in the community detection and sign prediction for the exploratory networks.