Stochastic blockmodels and community structure in networks

Abstract

Stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks. Most blockmodels, however, ignore variation in vertex degree, making them unsuitable for applications to real-world networks, which typically display broad degree distributions that can significantly distort the results. Here we demonstrate how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks. We also propose a heuristic algorithm for community detection using this objective function or its non-degree-corrected counterpart and show that the degree-corrected version dramatically outperforms the uncorrected one in both real-world and synthetic networks.

11 pages, 3 figures

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• Community detection in graphs
• Assortative mixing in networks
• Cooperative Game Theory Approaches for Network Partitioning
• Mixing patterns in networks
• Benchmark graphs for testing community detection algorithms
• Comparing community structure identification
• Hierarchical structure and the prediction of missing links in networks
• An information-theoretic framework for resolving community structure in complex networks
• Missing and spurious interactions and the reconstruction of complex networks
• Mixture models and exploratory analysis in networks
• A Bayesian Approach to Network Modularity
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• Error-Correcting Decoders for Communities in Networks
• Block-corrected Modularity for Community Detection
• Model-based edge clustering for weighted networks with a noise component
• A Unified Framework for Community Detection and Model Selection in Blockmodels
• Hypothesis testing for community structure in temporal networks using e-values
• Essential metrics for Life on graphs
• Complex non-backtracking matrix for directed graphs
• Stochastic Blockmodels with Edge Information
• Drug-disease networks and drug repurposing
• Impact of behavioral heterogeneity on epidemic outcome and its mapping into effective network topologies
• Extending the Davis-Kahan theorem for comparing eigenvectors of two symmetric matrices II: Computation and Applications
• Community detection over a heterogeneous population of non-aligned networks
• Spectral Complexity of Directed Graphs and Application to Structural Decomposition
• Hidden space reconstruction inspires link prediction in complex networks
• A Semidefinite Program for Structured Blockmodels
• Community Detection by $L_0$-penalized Graph Laplacian
• Your Tribe Decides Your Vibe: Analyzing Local Popularity in the US Patent Citation Network
• Efficient ${\mathbb{Z}}_2$ synchronization on ${\mathbb{Z}}^d$ under symmetry-preserving side information
• Identification of hybrid node and link communities in complex networks
• Streaming Belief Propagation for Community Detection
• Hierarchical Hyperlink Prediction for the WWW
• Persistent homology method to detect block structures in weighted networks
• Approximate Conditional Sampling for Pattern Detection in Weighted Networks
• Overlapping and nonoverlapping models
• Nondiagonal Mixture of Dirichlet Network Distributions for Analyzing a Stock Ownership Network
• Latent Channel Networks
• Effects of Contact Network Models on Stochastic Epidemic Simulations
• Consistency of regularized spectral clustering in degree-corrected mixed membership model
• Estimating Mixed-Memberships Using the Symmetric Laplacian Inverse Matrix
• Scalable Modeling of Conversational-role based Self-presentation Characteristics in Large Online Forums
• Mixed-SCORE+ for mixed membership community detection
• Individual-centered partial information in social networks
• On The Network You Keep: Analyzing Persons of Interest using Cliqster
• An improved spectral clustering method for mixed membership community detection
• Trading off Accuracy for Speedup: Multiplier Bootstraps for Subgraph Counts
• Consistent Spectral Clustering of Network Block Models under Local Differential Privacy
• Leaders, Followers, and Community Detection
• Reducing Seed Bias in Respondent-Driven Sampling by Estimating Block Transition Probabilities
• On Equivalence of Likelihood Maximization of Stochastic Block Model and Constrained Nonnegative Matrix Factorization
• Logistic Regression Augmented Community Detection for Network Data with Application in Identifying Autism-Related Gene Pathways
• Group Network Hawkes Process
• Clustering on the Edge: Learning Structure in Graphs
• Distribution free optimality intervals for clustering
• Detecting Communities in Heterogeneous Multi-Relational Networks:A Message Passing based Approach
• A large deviation approach to super-critical bootstrap percolation on the random graph $G_{n,p}$
• Barlow Graph Auto-Encoder for Unsupervised Network Embedding
• Attributed Graph Modeling with Vertex Replacement Grammars
• MRAttractor: Detecting Communities from Large-Scale Graphs
• Unifying Local and Global Change Detection in Dynamic Networks
• Penalized Component Hub Models
• Outliers Detection in Networks with Missing Links
• Bayesian Modeling of Random Walker for Community Detection in Networks
• Tractably Modelling Dependence in Networks Beyond Exchangeability
• Disentangling the structure of ecological bipartite networks from observation processes
• Overlapping Communities Detection via Measure Space Embedding
• Overlapping community detection in weighted networks
• Spiked Laplacian Graphs: Bayesian Community Detection in Heterogeneous Networks
• Two-sample Testing on Latent Distance Graphs With Unknown Link Functions
• Consistent model selection for the Degree Corrected Stochastic Blockmodel
• Clustering Network Tree Data From Respondent-driven sampling with application to opioid users in New York City
• Scalable Deep Generative Relational Models with High-Order Node Dependence
• Tourism destinations as digital business ecosystems
• Variational Inference for Stochastic Block Models from Sampled Data
• Multi-view Banded Spectral Clustering with Application to ICD9 Clustering
• A Dynamic Additive and Multiplicative Effects Model with Application to the United Nations Voting Behaviors
• Co-factor analysis of citation networks
• Semi-supervised learning in unbalanced and heterogeneous networks
• The efficiency of community detection by most similar node pairs
• Discriminative community detection for multiplex networks