# Learning Latent Block Structure in Weighted Networks

arXiv: https://arxiv.org/abs/1404.0431 · HTML: https://mlsanity.com/paper/1404.0431/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2014.

## Built on by (most cited first, 23 of 23)

- [Community detection for weighted bipartite networks](https://mlsanity.com/paper/2109.10319/) (2021)
- [Bipartite mixed membership distribution-free model. A novel model for community detection in overlapping bipartite weighted networks](https://mlsanity.com/paper/2211.00912/) (2022)
- [Graph Community Detection from Coarse Measurements: Recovery Conditions for the Coarsened Weighted Stochastic Block Model](https://mlsanity.com/paper/2102.13135/) (2021)
- [Mixed membership distribution-free model](https://mlsanity.com/paper/2112.04389/) (2021)
- [A pseudo-likelihood approach to community detection in weighted networks](https://mlsanity.com/paper/2303.05909/) (2023)
- [Restricted Tweedie Stochastic Block Models](https://mlsanity.com/paper/2310.10952/) (2023)
- [Benchmarking graph construction by large language models for coherence-driven inference](https://mlsanity.com/paper/2502.13953/) (2025)
- [A graph representation based on fluid diffusion model for data analysis: theoretical aspects and enhanced community detection](https://mlsanity.com/paper/2112.04388/) (2021)
- [A Dirichlet stochastic block model for composition-weighted networks](https://mlsanity.com/paper/2408.00651/) (2024)
- [PieClam: A Universal Graph Autoencoder Based on Overlapping Inclusive and Exclusive Communities](https://mlsanity.com/paper/2409.11618/) (2024)
- [DODO: Causal Structure Learning with Budgeted Interventions](https://mlsanity.com/paper/2510.08207/) (2025)
- [Identification of brain states, transitions, and communities using functional MRI](https://mlsanity.com/paper/2101.10617/) (2021)
- [Community Detection in Weighted Multilayer Networks with Ambient Noise](https://mlsanity.com/paper/2103.00486/) (2021)
- [Graph Neural Networks for Inconsistent Cluster Detection in Incremental Entity Resolution](https://mlsanity.com/paper/2105.05957/) (2021)
- [Block Dense Weighted Networks with Augmented Degree Correction](https://mlsanity.com/paper/2105.12290/) (2021)
- [Controllability of Coarsely Measured Networked Linear Dynamical Systems (Extended Version)](https://mlsanity.com/paper/2206.10569/) (2022)
- [Learning dynamic representations of the functional connectome in neurobiological networks](https://mlsanity.com/paper/2402.14102/) (2024)
- [VEC-SBM: Optimal Community Detection with Vectorial Edges Covariates](https://mlsanity.com/paper/2402.18805/) (2024)
- [Community Detection for Contextual-LSBM: Theoretical Limitations of Misclassification Rate and Efficient Algorithms](https://mlsanity.com/paper/2501.11139/) (2025)
- [Graph Neural Networks Based Analog Circuit Link Prediction](https://mlsanity.com/paper/2504.10240/) (2025)
- [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025)
- [Fuzzy network jump models for soft dynamic clustering of graph-structured data](https://mlsanity.com/paper/2608.05786/) (2026)
- [Analyzing the Dynamics of WSBM-based Echo State Networks using InputDSA](https://mlsanity.com/paper/2610.15380/) (2026)

## Abstract (arXiv)

Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network's large-scale structure, which can facilitate its scientific interpretation and the prediction of unknown or future interactions. Popular approaches, including the stochastic block model, assume edges are unweighted, which limits their utility by throwing away potentially useful information. We introduce the `weighted stochastic block model' (WSBM), which generalizes the stochastic block model to networks with edge weights drawn from any exponential family distribution. This model learns from both the presence and weight of edges, allowing it to discover structure that would otherwise be hidden when weights are discarded or thresholded. We describe a Bayesian variational algorithm for efficiently approximating this model's posterior distribution over latent block structures. We then evaluate the WSBM's performance on both edge-existence and edge-weight prediction tasks for a set of real-world weighted networks. In all cases, the WSBM performs as well or better than the best alternatives on these tasks.