Nonparametric weighted stochastic block models

Abstract

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the model, which are instead inferred from data. We give a comprehensive treatment of different kinds of edge weights (i.e. continuous or discrete, signed or unsigned, bounded or unbounded), as well as arbitrary weight transformations, and describe an unsupervised model selection approach to choose the best network description. We illustrate the application of our method to a variety of empirical weighted networks, such as global migrations, voting patterns in congress, and neural connections in the human brain.

19 pages, 11 figures. Code is freely available as part of graph-tool at https://graph-tool.skewed.de . See also the HOWTO at https://graph-tool.skewed.de/static/doc/demos/inference/inference.html

References in corpus (27)

• Community structure in social and biological networks
• Community detection in graphs
• Mixing patterns in networks
• Resolution limit in community detection
• Stochastic blockmodels and community structure in networks
• Community detection in networks: A user guide
• Modularity from Fluctuations in Random Graphs and Complex Networks
• Missing and spurious interactions and the reconstruction of complex networks
• Robust Detection of Dynamic Community Structure in Networks
• An efficient and principled method for detecting communities in networks
• Hierarchical Block Structures and High-resolution Model Selection in Large Networks
• Parsimonious module inference in large networks
• Efficient Monte Carlo and greedy heuristic for the inference of stochastic block models
• Learning Latent Block Structure in Weighted Networks
• Nonparametric Bayesian inference of the microcanonical stochastic block model
• Inferring the mesoscale structure of layered, edge-valued and time-varying networks
• Community detection for correlation matrices
• Modeling sequences and temporal networks with dynamic community structures
• Estimating the number of communities in a network
• Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity
• Clustering Network Layers With the Strata Multilayer Stochastic Block Model
• When are networks truly modular?
• Model selection and hypothesis testing for large-scale network models with overlapping groups
• Communities and bottlenecks: Trees and treelike networks have high modularity
• Community Detection in the Labelled Stochastic Block Model
• Accurate and scalable social recommendation using mixed-membership stochastic block models
• Active Learning for Hidden Attributes in Networks

Cited by in corpus (29)

• Social physics
• A Review of Stochastic Block Models and Extensions for Graph Clustering
• Bayesian stochastic blockmodeling
• Reconstructing networks with unknown and heterogeneous errors
• Merge-split Markov chain Monte Carlo for community detection
• A Framework for the Construction of Generative Models for Mesoscale Structure in Multilayer Networks
• Demarcating Geographic Regions using Community Detection in Commuting Networks with Significant Self-Loops
• Introduction to correlation networks: Interdisciplinary approaches beyond thresholding
• Brain tumour genetic network signatures of survival
• Layer reconstruction and missing link prediction of multilayer network with a Maximum A Posteriori estimation
• The Russian invasion of Ukraine selectively depolarized the Finnish NATO discussion
• Community detection for weighted bipartite networks
• Computational limits to the legibility of the imaged human brain
• Signed graphs in data sciences via communicability geometry
• Estimating the number of communities in weighted networks
• Generalised thresholding of hidden variable network models with scale-free property
• Community detection in bipartite signed networks is highly dependent on parameter choice
• Connectivity and Community Structure of Online and Register-based Social Networks
• A Social Network Analysis of Articles on Social Network Analysis
• The two sides of the Environmental Kuznets Curve: a socio-semantic analysis
• Evolution of global development cooperation: An analysis of aid flows with hierarchical stochastic block models
• Understanding How Network Geometry Influences Diffusion Processes in Complex Networks: A Focus on Cryptocurrency Blockchains and Critical Infrastructure Networks
• Feature Learning and Network Structure from Noisy Node Activity Data
• Community Detection in Weighted Multilayer Networks with Ambient Noise
• Loan maturity aggregation in interbank lending networks obscures mesoscale structure and economic functions
• Nondiagonal Mixture of Dirichlet Network Distributions for Analyzing a Stock Ownership Network
• Overlapping community detection in weighted networks
• Detectability threshold in weighted modular networks
• Learning dynamic representations of the functional connectome in neurobiological networks