# Statistical clustering of temporal networks through a dynamic stochastic block model

arXiv: https://arxiv.org/abs/1506.07464 · HTML: https://mlsanity.com/paper/1506.07464/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2015.

## Built on by (most cited first, 30 of 30)

- [Deep Temporal Graph Clustering](https://mlsanity.com/paper/2305.10738/) (2023)
- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Using Motif Transitions for Temporal Graph Generation](https://mlsanity.com/paper/2306.11190/) (2023)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [Fundamental limits for learning hidden Markov model parameters](https://mlsanity.com/paper/2106.12936/) (2021)
- [Discourse Analysis of Covid-19 in Persian Twitter Social Networks Using Graph Mining and Natural Language Processing](https://mlsanity.com/paper/2109.00298/) (2021)
- [Structured Optimal Variational Inference for Dynamic Latent Space Models](https://mlsanity.com/paper/2209.15117/) (2022)
- [Restricted Tweedie Stochastic Block Models](https://mlsanity.com/paper/2310.10952/) (2023)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Concentration inequalities for correlated network-valued processes with applications to community estimation and changepoint analysis](https://mlsanity.com/paper/2208.01365/) (2022)
- [Deep Temporal Graph Clustering: A Comprehensive Benchmark and Datasets](https://mlsanity.com/paper/2601.12903/) (2026)
- [Poisson-Gamma Modeling of Inter-Relational Dependencies in Dynamic Knowledge Graphs](https://mlsanity.com/paper/2607.02872/) (2026)
- [Community Detection in Weighted Multilayer Networks with Ambient Noise](https://mlsanity.com/paper/2103.00486/) (2021)
- [Recurrent segmentation meets block models in temporal networks](https://mlsanity.com/paper/2205.09862/) (2022)
- [Efficient Estimation for Longitudinal Networks via Adaptive Merging](https://mlsanity.com/paper/2211.07866/) (2022)
- [Dynamic Vertex Replacement Grammars](https://mlsanity.com/paper/2303.11553/) (2023)
- [Dynamic Mixed Membership Stochastic Block Model for Weighted Labeled Networks](https://mlsanity.com/paper/2304.05894/) (2023)
- [Modeling Random Networks with Heterogeneous Reciprocity](https://mlsanity.com/paper/2308.10113/) (2023)
- [Functional-Edged Network Modeling](https://mlsanity.com/paper/2404.00218/) (2024)
- [A Spectral Framework for Tracking Communities in Evolving Networks](https://mlsanity.com/paper/2412.07378/) (2024)
- [Tensor State Space-based Dynamic Multilayer Network Modeling](https://mlsanity.com/paper/2506.02413/) (2025)
- [Model-free algorithms for fast node clustering in SBM type graphs and application to social role inference in animals](https://mlsanity.com/paper/2509.15989/) (2025)
- [Discovering Communities in Continuous-Time Temporal Networks by Optimizing L-Modularity](https://mlsanity.com/paper/2510.00741/) (2025)
- [Variational Estimators for Node Popularity Models](https://mlsanity.com/paper/2511.17783/) (2025)
- [Common Structure Discovery in Collections of Bipartite Networks: Application to Pollination Systems](https://mlsanity.com/paper/2512.01716/) (2025)
- [Nonparametric estimation of time-varying network connections by multi-stage smoothing](https://mlsanity.com/paper/2605.06862/) (2026)
- [Conditional Entropy of Heat Diffusion on Temporal Networks](https://mlsanity.com/paper/2605.21514/) (2026)
- [Fuzzy network jump models for soft dynamic clustering of graph-structured data](https://mlsanity.com/paper/2608.05786/) (2026)

## Abstract (arXiv)

Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for its static part with independent Markov chains for the evolution of the nodes groups through time. We model binary data as well as weighted dynamic random graphs (with discrete or continuous edges values). Our approach, motivated by the importance of controlling for label switching issues across the different time steps, focuses on detecting groups characterized by a stable within group connectivity behavior. We study identifiability of the model parameters, propose an inference procedure based on a variational expectation maximization algorithm as well as a model selection criterion to select for the number of groups. We carefully discuss our initialization strategy which plays an important role in the method and compare our procedure with existing ones on synthetic datasets. We also illustrate our approach on dynamic contact networks, one of encounters among high school students and two others on animal interactions. An implementation of the method is available as a R package called dynsbm.