A Review of Stochastic Block Models and Extensions for Graph Clustering

Abstract

There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the type of the graph, the clustering approach, the inference approach, and whether the number of groups is selected or estimated. We also review models that combine block modelling with topic modelling and/or longitudinal modelling, regarding how these models deal with multiple types of data. How different approaches cope with various issues will be summarised and compared, to facilitate the demand of practitioners for a concise overview of the current status of these areas of literature.

93 pages, 3 figures, 4 tables

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• A Parrondo paradox in susceptible-infectious-susceptible dynamics over periodic temporal networks
• Discovering Block Structure in Networks
• Soft happy colourings and community structure of networks
• Dynamic Mixed Membership Stochastic Block Model for Weighted Labeled Networks
• Far-reaching consequences of trait preferences for animal social network structure and function
• Voter-like dynamics with conflicting preferences on modular networks
• Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models
• Factor-Driven Network Informed Restricted Vector Autoregression
• Symmetrical SyncMap for Imbalanced General Chunking Problems
• A Bayesian Nonparametric Stochastic Block Model for Directed Acyclic Graphs
• bioSBM: a random graph model to integrate epigenomic data in chromatin structure prediction
• Beyond One Solution: The Case for a Comprehensive Exploration of Solution Space in Community Detection
• SVD-based Causal Emergence for Gaussian Iterative Systems