# Adapting the Stochastic Block Model to Edge-Weighted Networks

arXiv: https://arxiv.org/abs/1305.5782 · HTML: https://mlsanity.com/paper/1305.5782/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2013.

## Built on by (most cited first, 7 of 7)

- [On the Fundamental Limits of Matrix Completion: Leveraging Hierarchical Similarity Graphs](https://mlsanity.com/paper/2109.05408/) (2021)
- [Restricted Tweedie Stochastic Block Models](https://mlsanity.com/paper/2310.10952/) (2023)
- [A Dirichlet stochastic block model for composition-weighted networks](https://mlsanity.com/paper/2408.00651/) (2024)
- [Block Dense Weighted Networks with Augmented Degree Correction](https://mlsanity.com/paper/2105.12290/) (2021)
- [Anchor Prediction: A Topic Modeling Approach](https://mlsanity.com/paper/2205.14631/) (2022)
- [Multiplex Dirichlet stochastic block model for clustering multidimensional compositional networks](https://mlsanity.com/paper/2412.11971/) (2024)
- [Analyzing the Dynamics of WSBM-based Echo State Networks using InputDSA](https://mlsanity.com/paper/2610.15380/) (2026)

## Abstract (arXiv)

We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation, which we solve using a Bayesian approach. We introduce a variational algorithm that efficiently approximates the model's posterior distribution for dense graphs. In specific numerical experiments on edge-weighted networks, this weighted stochastic block model outperforms the common approach of first applying a single threshold to all weights and then applying the classic stochastic block model, which can obscure latent block structure in networks. This model will enable the recovery of latent structure in a broader range of network data than was previously possible.