# Rate-Distortion Function of the Stochastic Block Model

arXiv: https://arxiv.org/abs/2309.14464 · HTML: https://mlsanity.com/paper/2309.14464/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2023.

## Built on by (most cited first, 1 of 1)

- [Explicit Bounds on the Entropy of Piecewise H"older Graphon Models](https://mlsanity.com/paper/2608.26501/) (2026)

## Abstract (arXiv)

The stochastic block model (SBM) is extensively used to model networks in which users belong to certain communities. In recent years, the study of information-theoretic compression of such networks has gained attention, with works primarily focusing on lossless compression. In this work, we address the lossy compression of SBM graphs by characterizing the rate-distortion function under a Hamming distortion constraint. Specifically, we derive the conditional rate-distortion function of the SBM with community membership as side information. We approach this problem as the classical Wyner-Ziv lossy problem by minimising mutual information of the graph and its reconstruction conditioned on community labels. Lastly, we also derive the rate-distortion function of the ErdHos-R'enyi (ER) random graph model.